Design Optimisation and Analysis of Heat Sinks

for Electronic Cooling

Amer Jameel Shareef Al-damook

Submitted in accordance with the requirements for the degree of Doctor of

Philosophy

The University of Leeds

School of Mechanical Engineering

Institute of ThermoFluids (iTF)

April, 2016

The candidate confirms that the work submitted is his own, except where work
formed jointly-authored publication has been included.

The contribution of the candidate and other authors to this work has been explicitly
indicated overleaf. The candidate confirms that appropriate credit has been given
within the thesis where reference has been made to the work of others.

This copy has been supplied on the understanding that it is copyrighted material and
that no quotation from the thesis may be published without proper
acknowledgement.
 -i-

Work Formed from Jointly Authored Publications

1- Chapters 2, 3, 4, 5, and section 7.2 of this thesis are journal paper jointly
authored by: Amer Al-damook, Kapur N., Summers J.L., Thompson H.M.,
An experimental and computational investigation of thermal airflows through
perforated pin heat sinks, Applied Thermal Engineering Journal, 2015. 89:
p.365-376.
2- Chapters 4, 6, and 7 of this thesis are journal paper jointly authored by: Amer
Al-damook, Kapur N., Summers J.L., Thompson H.M., Computational
design and optimisation of pin fin heat sinks with rectangular perforations,
Applied Thermal Engineering Journal, 2016, has been accepted.
3- Chapter 4 and sections 5.7 and 5.8 of this thesis are journal paper jointly
authored by: Amer Al-damook, Kapur N., Summers J.L., Thompson H.M.,
Effect different perforations shapes on the thermal-hydraulic performances of
perforated pinned heat sinks. Journal of Multidisciplinary Engineering
Science and Technology, 2016. 3(4): p. 4475–4480.
The following papers are in preparation:
1- Amer Al-damook, Kapur N., Summers J.L., Thompson H.M., Effect of the
variable air properties on the thermal airflow pinned heat sinks. In
preparation to be submitted for publication in International Communication
in Heat and Mass Transfer Journal.

The candidate has conducted the majority of the work that appears in the published
papers, such as developing the model, presenting and analysing the results. The co-
authors provided valuable review and guidance to the candidate.
 - ii -

Acknowledgements

I would like to express my extreme gratefulness to my supervisors, Prof.

Harvey Thompson, Prof. Nikil Kapur, and Dr. Jonathan Summers for their advice,
supportive guidance, encouragement, and assistance throughout the entire research.

Furthermore, I would like to thank the Higher Committee for Education

Development in Iraq (HCED) for financial support of this work, as well as Iraqi
Ministry of Higher Education and Scientific Research (MOHE), and Mechanical
Engineering Department University of Anbar, Iraq.

Above all else, I thank my family, my parents especially for my late father, my
sister, and my brother so much for their support and prayers. They gave me a lot, but
most especially, they gave me the strength to go on. Thank you very much.
 - iii -

Abstract

Since industrial devices create power dissipation in the form of heat created as
a by-product, which can have a negative effect on their performance, certain
temperature limit constraints are required for almost all these applications to work
within suitable conditions. That is, these engineering devices might fail in some way
if these limitations are surpassed by overheating. In all the related industries,
inexorable increases in power densities are driving innovation in heat exchange
techniques. Furthermore, electronic devices are becoming smaller at the same time
as their thermal power generation increases. Thus, heat sinks can be applied for
cooling critical components in many important applications ranging from aero-
engines and nuclear reactors to computers, data centre server racks and other
microelectronic devices.
The most common cooling technique for heat dissipation for thermal control of
electronics is air cooling. Reduced cost, simplicity of design, the easy availability of
air, and increased reliability are the main benefits of this cooling method. Heat sinks
with a fan/blower are commonly used for air-cooled devices as a forced convection
heat transfer. An amount of heat is dissipated from the heat source to environmental
air utilising a heat sink as a heat exchanger, which is a vital practice employed in air-
cooling systems. This transfer mechanism is easy, simple and leads to reduced cost
and increased reliability, and pinned heat sinks are more beneficial than plate fin heat
sinks.
The main interest of this study is to investigate the benefits of using perforated,
slotted, and notched pinned heat sinks with different configurations to reduce CPU
temperature and fan power consumption to overcome the pressure drop and
maximise a heat transfer rate through the heat sink. An experimental heat sink with
multiple perforations is designed and fabricated, and parameter studies of the effect
of this perforated pin fin design on heat transfer and pressure drops across the heat
sinks are undertaken, to compare it to solid pinned heat sinks without perforations.
Experimental data is found to agree well with predictions from a CFD model for the
conjugate heat transfer and turbulent airflow model into the cooling air stream. The
validated CFD model is used to carry out a parametric study of the influence of the
number and positioning of circular perforations, and slotted/notched pinned heat
sinks. Then, the multi-objective optimum pinned heat sink designs are tested to
obtain CPU temperature and fan power consumption as lowest as possible through
the heat sink. In addition, the limitations in application of pinned heat sinks based on
the pin density and applied heat flux are reported for active air-cooling electronic
systems.
An overview of the findings indicates that the CPU temperature, the fan power
consumption, and the heat transfer rate in terms of Nusselt number are enhanced
with the number of pin perforations and slotted/notched pinned heat sinks, while the
locations of the pin perforations are much less influential. These benefits arise due to
not only the increased surface area but also to the heat transfer enhancement near the
perforations through the formation of localised air jets. Finally, the perforated heat
sinks will be lighter in weight compared with solid pinned heat sinks.
 - iv -

Table of Contents

Work Formed from Jointly Authored Publications ............................................... i

Acknowledgements .................................................................................................... ii
Abstract ..................................................................................................................... iii
Table of Contents ..................................................................................................... iv
List of Tables ............................................................................................................ ix
List of Figures ........................................................................................................... xi
Nomenclature.......................................................................................................... xix
Chapter One: Introduction ...................................................................................... 1
1.1 Motivation ................................................................................................. 1
1.2 Introduction to Heat Sink Technology ...................................................... 3
1.3 Importance of Electronics Cooling ........................................................... 3
1.4 Liquid and Air Cooling of Data Centres ................................................... 4
1.5 Solid Plate Fin Heat Sinks (SPFHSs) ....................................................... 7
1.5.1 Experimental Studies ....................................................................... 7
1.5.2 Numerical Studies .......................................................................... 10
1.6 Solid Pinned Heat Sinks (SPHSs) ........................................................... 11
1.6.1 Experimental Studies ..................................................................... 12
1.6.2 Numerical Studies .......................................................................... 17
1.7 Plate-Pin Fin Heat Sinks (PPFHSs) or Compact Heat Sinks (CHSs) ..... 21
1.8 Perforated Fin Heat Sinks (PFHSs) ........................................................ 24
1.9 Perforated Plate Fin Heat Sinks .............................................................. 25
1.9.1 Plate Fins with Lateral Perforations ............................................... 25
1.9.2 Plate Fins with Longitudinal (Frontal) Perforations ...................... 27
1.9.3 Effect of Differently Shaped Perforations...................................... 28
1.9.4 Perforated Ribs and Blocks as Fins ................................................ 30
1.10 Perforated Folded Fin Heat Sinks (PFFHSs) .......................................... 31
1.11 Perforated Pinned Heat Sinks (PPHSs) ................................................... 32
1.11.1 Single Perforated Pinned HSs ............................................... 32
1.11.2 Multiple Perforated Pinned HSs............................................ 34
1.12 The Aims and Objectives of the Current Study ...................................... 36
 -v-

Chapter Two: The Fundamental of Convection Heat Transfer ......................... 40

2.1 Introduction ............................................................................................. 40
2.2 Physical mechanism of convection heat transfer .................................... 40
2.3 The basic concept of fluid flow types ..................................................... 41
2.3.1 Viscous and Inviscid Flow ............................................................. 41
2.3.2 Internal and External Flow ............................................................. 41
2.3.3 Compressible and Incompressible Flow ........................................ 41
2.3.4 Laminar and Turbulent Flow ......................................................... 42
2.3.5 Natural and Forced Flow ................................................................ 42
2.3.6 Steady and Unsteady Fluid Flow ................................................... 42
2.4 The concept of boundary layers .............................................................. 42
2.4.1 Velocity Boundary Layer (δu) ........................................................ 42
2.4.2 Thermal Boundary Layer (δth) ....................................................... 43
2.4.3 Boundary Layer Separation............................................................ 44
2.5 Hydraulic and Heat Transfer Characteristics .......................................... 46
2.5.1 Reynolds Number (Re)................................................................... 46
2.5.2 Pressure Drop (ΔP) ........................................................................ 46
2.5.3 Fan Power (Pfan) and Profit Power Factor (J) ................................ 46
2.5.4 Pressure Drag Coefficient (Pd) ....................................................... 47
2.5.5 Nusselt Number (Nu) ..................................................................... 47
2.5.6 Thermal Resistance (Rth) ................................................................ 48
2.5.7 Porosity (Ø) .................................................................................... 48
Chapter Three: Experimental Methods ................................................................ 49
3.1 Introduction ............................................................................................. 49
3.2 Experimental Objectives ......................................................................... 49
3.3 Heat Sink and Test Section Descriptions ................................................ 50
3.3.1 Heat Sink Fabrication ..................................................................... 52
3.4 Rig Description ....................................................................................... 56
3.4.1 Airflow Channel ............................................................................. 56
3.4.2 Heating and Control Sections ......................................................... 60
3.4.3 Measurement Devices .................................................................... 61
3.5 Experimental Measurements ................................................................... 61
3.5.1 Hot Wire Anemometer ................................................................... 61
3.5.2 Thermocouples ............................................................................... 61
3.1.1 Digital Manometer ......................................................................... 62
 - vi -

3.6 Experimental Procedure and Measurements ........................................... 62

3.6.1 Experimental Procedure ................................................................. 63
3.7 Experimental Data Analysis and Calculations ........................................ 65
3.8 Hydraulic Characteristics Analysis ......................................................... 65
3.9 Heat Transfer Analyses ........................................................................... 65
3.1.2 Heat Transfer Rate ......................................................................... 65
3.10 Summary ................................................................................................. 68
Chapter Four: Experimental Results .................................................................... 69
4.1 Introduction ............................................................................................. 69
4.2 Hydraulic Characteristics ........................................................................ 69
4.3 Heat Transfer Characteristics .................................................................. 72
4.3.1 Average Nusselt Number ............................................................... 72
4.3.2 Thermal Management of PHSs ...................................................... 73
4.4 Conclusion .............................................................................................. 75
Chapter Five: Numerical Methods ........................................................................ 76
5.1 Introduction ............................................................................................. 76
5.2 Numerical Modelling Overview ............................................................. 76
5.3 Numerical Simulation ............................................................................. 76
5.4 Pre-processing (Mesh Generation) .......................................................... 77
5.5 Numerical Solution (Processing) ............................................................ 80
5.5.1 Turbulent Airflow Model ............................................................... 80
5.5.2 Conjugate Heat Transfer Model ..................................................... 82
5.5.3 Solver Settings ............................................................................... 83
5.6 Boundary Conditions .............................................................................. 84
5.6.1 On the Pins ..................................................................................... 84
5.6.2 At the Bottom Wall of the Heat Sink ............................................. 84
5.6.3 At the Inlet Side ............................................................................. 84
5.6.4 At the Outlet Side ........................................................................... 85
5.6.5 Right and Left Sides ....................................................................... 85
5.6.6 The Other Surface Walls ................................................................ 85
5.7 Numerical Data Analysis (Post Processing) ........................................... 86
5.8 Methods of Validation............................................................................. 87
5.8.1 Domain Verification....................................................................... 87
5.8.2 Grid Independent Tests (GIT) (Mesh Verification) ....................... 90
5.8.3 Validation with Previous Studies ................................................... 92
 - vii -

5.9 CFD Validation with Present Experimental Results ............................... 95

5.9.1 Validation of Hydraulic Characteristics ......................................... 96
5.9.2 Validation of Heat Transfer Characteristics ................................... 98
Chapter Six: Pinned Heat Sinks with Circular Perforation ............................. 103
6.1 Introduction ........................................................................................... 103
6.2 Description of PHS Models .................................................................. 103
6.3 Perforated Pins ...................................................................................... 105
6.4 Hydraulic Characteristics ...................................................................... 109
6.4.1 Airflow Behaviour ....................................................................... 109
6.4.2 Pressure Drop, Fan Power, Profit Power Factor, and Pressure
Drag Coefficient ........................................................................... 111
6.4.3 Effect on Power Consumption ..................................................... 115
6.5 Heat Transfer Characteristics ................................................................ 115
6.5.1 Average Nusselt Number ............................................................. 115
6.5.2 Thermal Management of PHSs .................................................... 117
6.6 Effect of Perforation Position................................................................ 119
6.7 Effect of Pin Fins Arrangement ............................................................ 125
6.8 Effect of Square and Elliptic Perforation Shapes .................................. 127
6.9 Optimum Design of the Perforated Pinned Heat Sink (1P) .................. 132
6.10 Conclusions ........................................................................................... 135
Chapter Seven: The Benefits of Slotted and Notched PHSs ............................. 137
7.1 Introduction ........................................................................................... 137
7.2 Description of PHS Models .................................................................. 137
7.3 Open Slotted and Notched Area ............................................................ 140
7.4 Hydraulic Characteristics ...................................................................... 141
7.4.1 Airflow Behaviour ....................................................................... 141
7.4.2 Pressure Drop, Fan Power, Profit Power Factor, and Pressure
Drag Coefficient ........................................................................... 143
7.4.3 Effect on Power Consumption ..................................................... 146
7.5 Heat Transfer Characteristics ................................................................ 147
7.5.1 Average Nusselt Number ............................................................. 147
7.5.2 Thermal Management of PHSs .................................................... 150
7.6 Optimum Design of the Notched Pinned Heat Sink ............................. 152
7.7 Comparison between Circular Perforated Pins, Rectangular Slotted,
and Notched PHSs ................................................................................ 158
7.8 Weight Reduction of Heat Sinks ........................................................... 159
 - viii -

7.9 Conclusions ........................................................................................... 162

Chapter Eight: Effect of Pin Density and Applied Heat Flux ........................... 164
8.1 Introduction ........................................................................................... 164
8.2 Effect of Pin Density Distribution......................................................... 164
8.3 Effect of Applied Heat Flux .................................................................. 175
8.4 Conclusion ............................................................................................ 180
9 Chapter Nine: Conclusions and Recommendations ................................. 181
9.1 Main Conclusions ................................................................................. 181
9.1.1 Perforated PHSs ........................................................................... 181
9.1.2 Slotted and Notched PHSs ........................................................... 183
9.1.3 Pin Density and Applied Heat Flux ............................................. 184
9.2 Recommendations for Future Works .................................................... 186
References .............................................................................................................. 187
Appendix A: Drawing of Experimental Rig Design ........................................... 194
Appendix B: Experimental Uncertainty Analysis .............................................. 201
 - ix -

List of Tables

Table 1.1: The comparison between the plate fin heat sinks and pinned
heat sinks......................................................................................................... 20

Table 1.2: The practical examples of the heat sinks dimensions (Yang and
Peng, 2009) ...................................................................................................... 22

Table 1.3: Different pin diameter combinations for four types of PPFHS
(Yuan et al., 2012) .......................................................................................... 23

Table 4.1: The experimental enhancement of Nusselt number (Nu), fan

power (Pfan), and CPU temperature (Tcase) of the 3P heat sink
compared to the solid pinned heat sink........................................................ 75

Table 5.1: The variation of air properties with increasing air temperature,
Cengel (2006) .................................................................................................. 84

Table 5.2: The boundary conditions of the conjugate heat transfer model ....... 86

Table 5.3: The entrance and exit regions length of pin fins heat sinks .............. 88

Table 5.4: Mesh validation of Solid and Perforated pinned heat sink
designs ............................................................................................................. 91

Table 5.5: The experimental and numerical enhancement of Nusselt

number (Nu), fan power (Pfan), and CPU temperature (Tcase) of 3P
heat sink design compared to solid pins (0P) ............................................ 102

Table 5.6: The errors percentage between the experimental and numerical
data at constant and variable air properties ............................................. 102

Table 6.1: The enhancement of Nusselt number (Nu), and fan power (Pfan)
of each 3P and 5P design compared with solid (0P) pins HSs ................. 136

Table 6.2: The reduction of CPU temperature (Tcase), and the increasing
fan power (Pfan) of staggered array compared with in-line array for
solid (0P) and perforated (3P) pins HSs ..................................................... 136

Table 6.3: Enhancement of Nusselt number (Nu), fan power (Pfan), and
CPU temperature (Tcase) of different perforations shapes........................ 136

Table 7.1: Compare between Tcase and Pfan of predicted MLS and
simulated CFD .............................................................................................. 157

Table 7.2: Comparison of Nusselt number, fan power (Pfan), and CPU
Temperature (Tcase) between perforated, slotted, and notched PHSs ..... 159
 -x-

Table 7.3: Enhancement of Nusselt number (Nu), fan power (Pfan), and
CPU temperature (Tcase) of slotted and notched pinned heat sinks ......... 163

Table B.0.1: Uncertainties of Experimental Parameters Studies ..................... 204

 - xi -

List of Figures

Figure 1.1: Data centre infrastructure (Tripplite, 2012), server (DeepInIt,

2013), and pinned heat sink (Alutronic, 2015) .............................................. 2

Figure 1.2: Different types of fins: (A) solid plate fins, (B) solid pins, (C)
compact plate-pins, (D) perforated plate, (E) perforated pins, and (F)
perforated folded fin heat sinks ...................................................................... 6

Figure 1.3: Contour map of the thermal ratio for optimised plate, pin, and
cross-cut FHSs (Kim & Kim, 2009) ................................................................ 8

Figure 1.4: Test section and direction of short rectangular plate fins
(Didarul et al., 2007) ........................................................................................ 9

Figure 1.5: Short rectangular fins: (a) co-angular pattern, (b) zigzag
pattern (Didarul et al., 2007) ........................................................................... 9

Figure 1.6: Different heat sink models: (A) micro-plate channel (B)
circular pins (C) offset strip fins (D) jet impingement cooling (Ndao
et al., 2009) ...................................................................................................... 11

Figure 1.7: Heat transfer coefficient and pressure drop with inlet velocity
for plate fin and pin fin in (a) in-line array and (b) staggered array
(Yang et al., 2007) ........................................................................................... 14

Figure 1.8: Fin heat sink slices: (a) spanwise (c) streamwise distance
between the fins, (e) spanwise (f) streamwise distance between slices
(Sahin et al., 2005) .......................................................................................... 14

Figure 1.9: Jet impingement heat sink unit for cooling the CPU of a PC
(Naphon & Wongwises, 2010) ....................................................................... 16

Figure 1.10: Variation of the Nusselt number with mass flow rate for
different cooling methods (Naphon & Wongwises, 2011) .......................... 16

Figure 1.11: Straight and twisted pin heat sinks (Ramesha &
Madhusudan, 2012)........................................................................................ 18

Figure 1.12: Different types of fin heat sinks (Soodphakdee et al., 2001) .......... 18

Figure 1.13: Heat transfer coefficient versus pressure drop of various fin
geometries (Soodphakdee et al., 2001) ......................................................... 18

Figure 1.14: Schematic diagram of the different cross sections of model A

and model B (Naphon et al., 2009)................................................................ 20
 - xii -

Figure 1.15: Compact heat sinks: (a) plate-fin heat sink, (b) plate-circular
pin heat sink, and (c) plate-square heat sink (Yang and Peng, 2009) ....... 22

Figure 1.16: Nusselt numbers of compact heat sinks with variation in air
velocity (Zhou & Catton, 2011)..................................................................... 24

Figure 1.17: Streamlined patterns at Uc=10m/s, in the plane z=8 mm

(Zhou & Catton, 2011) ................................................................................... 24

Figure 1.18: (A) Frontal and (B) lateral perforated flat plate heat sinks
(Yaghoubi et al., 2009; Shaeri & Yaghoubi, 2009)...................................... 25

Figure 1.19: Different sorts of perforated FHSs: circular, square,

hexagonal, and triangular (Ismail et al., 2013) ............................................ 29

Figure 1.20: Nusselt number and fin effectivity variations for different
types of fin (Ismail, 2013) .............................................................................. 29

Figure 1.21: The test section of perforated blocks/ribs with different views
(Sara et al., 2001) ............................................................................................ 30

Figure 1.22: The angle of perforations and slots in rectangular blocks

towards flow directions (Khoshnevis et al., 2009b) ..................................... 31

Figure 1.23: Different designs of folded fin heat sinks: a) Extruded plate
fin, (b) Slit folded fin, (c) Perforated folded fin, (d) Perforated slit
(Jia et al., 2003) ............................................................................................... 32

Figure 1.24: (a) Perspective view of the heat exchanger and a single
perforated pin configuration (b) Sectional view of heating unit and
tested model assembly (Sahin & Demir, 2008b) .......................................... 34

Figure 1.25: Nusselt number and friction factor variations for single
perforated pin fins (Sahin & Demir, 2008b) ................................................ 34

Figure 1.26: Simple flowchart of literature review of different heat sink

types ................................................................................................................. 35

Figure 1.27: Different types of pin fins heat sinks ............................................... 38

Figure 1.28: The scope of the present thesis work ............................................... 39

Figure 2.1: Physical mechanism of heat transfer from hot surface to cool
surrounding air by convection and conduction, (Cengel, 2006). ............... 40

Figure 2.2: The velocity boundary layer development on a flat plate

surface, (Cengel, 2006). .................................................................................. 43

Figure 2.3: The thermal boundary layer development on an isothermal

flat plate surface, (Incropera, 2011) ............................................................. 44
 - xiii -

Figure 2.4: Boundary layer separation on a cylinder and formations

eddies in the downstream region, (Incropera, 2011) .................................. 45

Figure 2.5: Velocity profile associated with pressure gradient and

separation on a cylinder, (Incropera, 2011) ................................................. 45

Figure 3.1: (A) Plan view, and (B) solid pin fins side view, (C) Plan view,
(D) perforated pin fins side view, and (E) 3D of the perforated pin
fins heat sink being analysed ......................................................................... 51

Figure 3.2: Aluminium base plate with solid and perforated pin fins ............... 52

Figure 3.3: Drilling jig for producing perforated pin fins ................................... 53

Figure 3.4: Inserting pin fins through holes of base plate with countersunk
at the bottom of the heat sink........................................................................ 54

Figure 3.5: Schematic drawing of soldering area at the base plate of heat
sink .................................................................................................................. 54

Figure 3.6: Preparing aligned perforations of perforated pins in flow

direction .......................................................................................................... 54

Figure 3.7: Final design of (A) solid pin fins and (B) perforated pin fins
heat sinks......................................................................................................... 55

Figure 3.8: Detection of pin fin soldering zones at the base of heat sinks .......... 55

Figure 3.9: Overall rig design and experimental measurements system ........... 57

Figure 3.10: Schematic Drawing of Overall Experimental System .................... 58

Figure 3.11: Typical performance fan curve (model San Ace 36:
9GV3612P3J03) .............................................................................................. 58

Figure 3.12: Final assembly of rig design with three views ................................. 59

Figure 3.13: Installation of the heat sink with film heater into insulation
container ......................................................................................................... 60

Figure 3.14: Repeatability of pressure drop and CPU temperature with

variation inlet air velocity for solid (0P) and perforated (3P) pin
models .............................................................................................................. 62

Figure 3.15: Time evaluation of Tcase for 0P and 3P heat sinks models at
Re= 5393. Steady state is reached after 20mins .......................................... 64

Figure 4.1: Effect of pin perforations on (A) pressure drop and (B) fan
power as a function of airflow speed ............................................................ 70

Figure 4.2: Effect of pin design and inlet air velocity on the pressure drag
coefficient ........................................................................................................ 71
 - xiv -

Figure 4.3: Effect of inlet velocity on Nusselt number based on (A) total
and (B) projected surface area ...................................................................... 72

Figure 4.4: CPU temperature variation with fan power for 0P and 3P heat
sinks ................................................................................................................. 74

Figure 4.5: Experimental results of influence of fan power on Rth ..................... 74

Figure 5.1: Mesh generation for pinned heat sink ............................................... 78

Figure 5.2: y+ contour values for solid (0P), perforated (3P) and slotted
(10S) pinned heat sinks .................................................................................. 79

Figure 5.3: Conjugate heat transfer model of pin fin heat sink .......................... 82

Figure 5.4: Schematic diagram of the flow domain used in the CFD
analyses, showing eight perforated pin fins. ................................................ 86

Figure 5.5: Inlet air velocity versus the pressure drop and temperature
case of HSs for different turbulence intensities ........................................... 89

Figure 5.6: Validation of Nusselt number (NuT) and pressure drop (ΔP)
predictions with those of Zhou & Catton (2011) ......................................... 92

Figure 5.7: Comparison of thermal resistance predictions with those CFD

results of Zhou & Catton (2011), and experimental data of Jonsson
& Moshfeg (2001) ........................................................................................... 93

Figure 5.8: Validation between the experimental data of Yang et al. (2007)
and CFD analysis of heat transfer coefficient and pressure drop ............. 94

Figure 5.9: Comparison between CFD predictions of Nu/Nus with

experimental data of Sahin & Demir (2008) for pin fins with a single
perforation ...................................................................................................... 95

Figure 5.10: Effect of pin perforations on (A) pressure drop and (B) fan
power as a function of airflow speed ............................................................ 97

Figure 5.11: Effect of pin design and inlet air velocity on the pressure drag
coefficient ........................................................................................................ 98

Figure 5.12: Effect of inlet velocity on Nusselt number based on (A) total
and (B) projected surface area ...................................................................... 99

Figure 5.13: Comparison between experimental and numerical

predictions of influence of fan power on Tcase............................................ 100

Figure 5.14: Comparison between experimental and numerical

predictions of influence of fan power on Rth .............................................. 100

Figure 6.1: Solid and perforated pinned heat sink models ............................... 104
 - xv -

Figure 6.2: (A) Plan view and (B) Side view of the pin fin heat sink being
analysed ......................................................................................................... 104

Figure 6.3: Plan views of hotspot zones through (A) solid 0P, (B)
perforated 3P and (C) slotted 10S pinned heat sinks at Re=5393............ 107

Figure 6.4: Plan views of airflow field through (A) solid 0P, (B) perforated
3P and (C) slotted 10S pinned heat sinks at Re=5393 ............................... 108

Figure 6.5: Comparison between predicted flow field in PFHSs with solid
pin fins and for designs 2A and 2C with two perforations ....................... 110

Figure 6.6: Effect of pin perforations and inlet velocity on pressure drop,
fan power, and profit factor ........................................................................ 112

Figure 6.7: Plan views of pressure contour through solid 0P, perforated 3P
and slotted 10S pinned heat sinks at Re=5393 ........................................... 113

Figure 6.8: Variation of pressure drag coefficient with inlet air velocity for
solid and different perforated pinned heat sink designs .......................... 114

Figure 6.9: Effect of inlet velocity on NuT for the nine pin designs shown in
Figure 6.1 ...................................................................................................... 116

Figure 6.10: Effect of number of perforations on Nusselt number at 10m/s

for the five pin designs ................................................................................. 117

Figure 6.11: Effect of pin design and fan power on Tcase and Rth...................... 118

Figure 6.12: Temperature distribution through pinned heat sinks: 0P, 3P,
and 5P models at Re=5393 ........................................................................... 119

Figure 6.13: Effect of perforation positions on the pressure drop through

heat sinks....................................................................................................... 120

Figure 6.14: Effect of different perforation positions with inlet velocity on

NuT for the nine pin designs shown in Figure 6.1...................................... 120

Figure 6.15: Different vertical positions of the three perforations model

(3P) ................................................................................................................ 121

Figure 6.16: Variation of NuT with different perforation positions and Re..... 121

Figure 6.17: Comparisons of CPU temperature with the three

perforations in different positions .............................................................. 122

Figure 6.18: Horizontal movement percentage of perforations from the

centre (0%) to the outside of the pins (100%) ........................................... 123

Figure 6.19: Pressure drop trend with different perforation positions of

the 3P heat sink model ................................................................................. 124
 - xvi -

Figure 6.20: Comparisons of NuT with the three perforations in different

positions ........................................................................................................ 124

Figure 6.21: Effects of pin array on pressure drop with variation in

Reynolds number for solid (0P) and perforated (3P) pinned HS
models ............................................................................................................ 125

Figure 6.22: Effects of pin array on Tcase and Pfan for solid (0P) and
perforated (3P) pinned heat sink models ................................................... 126

Figure 6.23: Circular, square, and elliptic perforated pinned heat sink
models ............................................................................................................ 127

Figure 6.24: Effect of perforation shape on the pressure drop with various
inlet air velocities .......................................................................................... 128

Figure 6.25: Variation of total Nusselt number for solid and different
perforation shapes with various Re ............................................................ 129

Figure 6.26: Variation of temperature with perforation shapes and

various inlet air velocities ............................................................................ 130

Figure 6.27: Variation in mean local air velocity through different

perforation shapes of each pin .................................................................... 130

Figure 6.28: Temperature distribution through perforated pinned heat

sinks: 0P, 3CP, 3SP, and 3EP models at Re=5393..................................... 131

Figure 6.29: Distribution of design points in design variable space for the
perforation diameter, d (mm) and the position of single perforations,
y (mm) ........................................................................................................... 133

Figure 6.30: Response surface function of CPU temperature (Tcase) of the

single perforated pinned heat sink (1P) model .......................................... 134

Figure 6.31: Response surface function of fan power (Pfan) of the single
perforated pinned heat sink (1P) model ..................................................... 134

Figure 7.1: Slotted and notched pinned heat sink designs ................................ 139

Figure 7.2: (A) Plan view and Side view (B) 3D of the notched pinned heat
sink being analysed ...................................................................................... 139

Figure 7.3 Comparison between predicted flow field in PFHSs with solid
pin fins 0P and for designs 3S and 10S ...................................................... 142

Figure 7.4 Effect of (A) slotted and (B) notched pins on pressure drop with
variation in airflow speed ............................................................................ 144

Figure 7.5: Effect of (A) slotted and (B) notched pins on fan power as a
function of airflow speed ............................................................................. 144
 - xvii -

Figure 7.6: Comparisons of the profit factors with different heat sinks (A)
slotted and (B) notched pins ........................................................................ 145

Figure 7.7: Variation in pressure drag coefficient of slotted (A) and

notched (B) pins with different Re ............................................................. 146

Figure 7.8: Effect of slotted and notched pinned heat sinks on Nusselt
number based on (A) total (B) projected surface area ............................. 149

Figure 7.9: Variation in the mean local air velocity through (A) slotted
and (B) notched pins .................................................................................... 150

Figure 7.10: Effect of (A) slotted and (B) notched pins on Tcase and fan
power ............................................................................................................. 151

Figure 7.11: Temperature distribution through pinned heat sinks: 0P, 6S,
10S, and 7.5N models at Re=5393 ............................................................... 152

Figure 7.12: Distribution of design points in the design variable space for
the height, h (mm) and the width, w (mm) of the notch ........................... 153

Figure 7.13: Response surface function of CPU temperature (Tcase) of the

notched pinned heat sink model ................................................................. 154

Figure 7.14: Response surface function of fan power (Pfan) of the notched
pinned heat sink model ................................................................................ 154

Figure 7.15: Pareto curve of Tcase and Pfan for an 8x8 PHs with notched
pins, with an inlet air speed of 8m/s ........................................................... 155

Figure 7.16 Plan views of flow field through notch perforations for a wide
notch with Tcase=86.3oC and Pfan=0.0592W and a narrow notch with
Tcase=70oC and Pfan=0.0934W ...................................................................... 156

Figure 7.17 : The optimum temperature distribution of the wide and the
narrow notch pin models with an inlet air speed of 8m/s ......................... 157

Figure 7.18: The percentage total weight reduction of PHSs............................ 161

Figure 8.1: Schematic of different heat sink geometries in in-line

arrangement for top and side views ........................................................... 165

Figure 8.2: Variation of pressure drop with the number of columns and
different Reynolds numbers for solid (0P), perforated (3P), and
notched (7.5N) PHS designs ........................................................................ 167

Figure 8.3: Effect of the number of columns on the Nusselt number and
the Reynolds number for solid (0P), perforated (3P), and notched
(7.5N) PHSs ................................................................................................... 169
 - xviii -

Figure 8.4: Variation in pressure drop with the number of columns and
different Reynolds number for solid (0P), perforated (3P), and
notched (7.5N) PHS designs ........................................................................ 170

Figure 8.5: Effect of the number of columns on the CPU temperature and
the Reynolds number for solid (0P), perforated (3P), and notched
(7.5N) pinned heat sink models ................................................................... 172

Figure 8.6: Effect of the number of columns on the CPU temperature and
fan power of solid (0P), perforated (3P), and notched (7.5N) pinned
heat sink models ........................................................................................... 174

Figure 8.7: Variation in pressure drop through perforated pins (3P) with
different applied heat flux and inlet air velocities (A) constant and
(B) variable air properties ........................................................................... 176

Figure 8.8: Variation in pressure drop through perforated pins (3P) with
different applied heat flux and inlet air velocities (A) constant and
(B) variable air properties ........................................................................... 177

Figure 8.9: Variation in pressure drop through notched pins (7.5P) with
different applied heat flux and inlet air velocities (A) constant and
(B) variable air properties ........................................................................... 178

Figure 8.10: Variation in CPU temperature of 0P (top), perforated (3P,

Left), and notched (7.5N, Right) pins with different applied heat flux
and inlet air velocities .................................................................................. 179
 - xix -

Nomenclature

Ac Cross-sectional area of the flow passage of the heat sink (m2)

AP Projected heat transfer surface area (m2)

AT Total heat transfer surface area (m2)

Cp Specific heat constant at constant pressure (kJ/kg.K)

d Diameter of perforations (m)

D Diameter of pin fins (m)

Dh Hydraulic diameter (m)

F The view factor

h Height of slot or notch (m)

hP Projected heat transfer coefficient based on the total surface

area (W/m2.oC)

hT Average heat transfer coefficient based on the total surface

area (W/m2.oC)

H Height of duct (m)

J Profit factor

k Turbulent kinetic energy (m2/s2)

kair Air thermal conductivity (W/m.oK)

kins Insulation thermal conductivity (W/m.oK)

L Length of heat sinks (m)

n Number of perforations

N Number of pins

Nu Nusselt number

p Perimeter of cross duct (m)

Pd Pressure drag coefficient

 - xx -

Pfan Fan power (W)

Pin, out Inlet and outlet pressure of heat sink, respectively (Pa)

Pr Prandtl number

Prt Turbulent Prandtl number

Q Applied heating power (W)

Qconv. Convective heat rate (W)

Qelec. The total heat applied on the base of heat sink (W)

Qloss Conductive heat losses (W)

Qrad. Radiative heat losses (W)

Rth Thermal resistance (K/W)

Re Reynolds number

Sx, Sz Streamwise and Spanwise distance or longitudinal and

transverse distance, respectively (m)

Tair Ambient air temperature (K)

Tcase CPU temperature or the base temperature of heat sinks (K)

Tin, Tout Inlet and outlet air temperature (K)

Tm Average bulk mean temperature (K)

T0 Absolute bulk fluid temperature (K)

Tw Bottom surface of heat sink temperature (K)

U Inlet air velocity (m/s)

Un Uncertainty range of experimental test

Ux,Uv,Uz Velocities in x, y and z directions, respectively (m/s)

V Solid pin volume (m3)

Vhole Perforation volume (m3)

(x,y,z) Cartesian coordinates (m)

 - xxi -

w Width of slot or notch (m)

W Width of duct (m)

∆P Pressure drop (Pa)

∆X Insulation thickness (m)

Greek Symbols

µ Dynamic viscosity (N.s/m2)

μt Turbulent eddy viscosity (N.s/m2)

υ Kinematic viscosity (m2/s)

υt Turbulent kinematic viscosity (m2/s)

ε Turbulent dissipation rate (m2/s3)

ρ Density (kg/m3)

ϕ Porosity

ω Specific dissipation rate (1/s)

Abbreviations

CFD Computational Fluid Dynamics

CHS Compact Heat Sink

CPU Central Processing Unit

DoE Design of Experiments

FVM Finite Volume Method

HSs Heat Sinks

ICT Information and Communication Technology

MLS Moving Least Squares

PC Personal Computer

PCPFHS Plate-Circular Pin Fin Heat Sink

PEPFHS Plate-Elliptic Pin Fin Heat Sink

 - xxii -

PFHSs Plate Fins Heat Sinks

PHSs Pinned Heat Sinks

PPHSs Perforated Pinned Heat Sinks

PSPFHS Plate-Square Pin Fin Heat Sink

NPHSs Notched Pinned Heat Sinks

RANS Reynolds-Averaged Navier-Stokes

SPHSs Slotted Pinned Heat Sinks

SIMPLE Semi-Implicit Method for Pressure-Linked Equations

SST Shear-Stress Transport

0P Solid Pinned Heat Sink Model

3P Pinned Heat Sink with Three Perforations Model

5P Pinned Heat Sink with Five Perforations Model

3CP Triple Circular Perforated Pinned Heat Sink Model

3SP Triple Square Perforated Pinned Heat Sink Model

3EP Triple Elliptic Perforated Pinned Heat Sink Model

 -1-

1 Chapter One: Introduction

1.1 Motivation

Education, business, transportation, social media and the sectors economic

have become very dependent on Information and Communication Technology (ICT),
to which end, ICT has become the most important source of information and data in
our society (Zeadally et al., 2012). Thus, data centres, which are essentially digital
factories, have become a vital part of ICT processing, management, storage and
exchange of data and information (Pan et al., 2008). A data centre consists of four
main parts: power equipment such as power distribution units and batteries, cooling
equipment (chillers and computer room air-conditioning (CRAC) units), IT
equipment (servers, storage and network), and miscellaneous component loads
(lighting and fire protection systems) (Dai et al., 2014). Electronic component
systems that arrange processing, storing and transmission of data is the main part of
the data centre, according to Shah et al. (2008) and Greenberg et al. (2006), all of
which and create a large amount of heat, which must be removed from the ICT
components at a rate sufficient to avoid serious overheating problems and system
failures (Sahin et al., 2005). More than 30% of the heat removal costs of a typical
data centre is used in IT equipment and cooling equipment. Thus, an important part
of a server is the heat sink that is set over the CPU (Dai et al., 2014), as shown in
Figure 1.1.

The thermal effect can cause failure of mechanisms in electronic component

devices, due to metal migration, void formation, and inter-metallic growth. Actually,
one of the common factors that control the reliability of electronic products is the
maximum temperature limitation of these devices. For each 10oC increase above the
critical operating temperature (~85°C) of high-power electronics, the rate of these
failures almost doubles (Gurrum et al., 2004). Therefore, electronics thermal
management is of crucial significance, as is reflected in the market (Mostafavi,
2012). Another important factor is the cost increase of thermal management
products, which went from nearly $7.5 billion in 2010 to $8 billion in 2011, and is
predicted reach $10.9 billion by 2016; the annual rate of increase is 6.4%. Fans and
 -2-

heat sinks (HSs) as thermal management hardware components take an 84% share of
the total market. However, software, interface materials, and substrates as the other
main cooling products account for between 4% and 6% of the market (BCC
Research, 2014).

Many researchers have therefore been studying the thermal and fluid flow
through heat sinks, but there is still a lack of information about heat sinks, especially
for perforated heat sinks. This fact has motivated the exploring of the design
optimisation and analysis of thermal airflow through perforated pinned heat sinks
(PPHSs) for electronics cooling systems.

Power equipment

Cooling equipment

Miscellaneous
components

IT equipment

Room data centre

Inside the server

Pinned heat sink (PHS)

Figure 1.1: Data centre infrastructure (Tripplite, 2012), server (DeepInIt, 2013),
and pinned heat sink (Alutronic, 2015)
 -3-

1.2 Introduction to Heat Sink Technology

Finned heat sinks are classified into two main types: plate fin heat sinks
(PFHSs) and pin heat sinks or pinned heat sinks (PHSs), as shown in Figure 1.2.
Such heat sinks are manufactured and produced by several companies, both large
and small, such as Airedale in the UK, Raypak in the USA, to name of few. A set of
base tube materials that have high thermal conductivity, such as copper and
aluminium, can be employed to manufacture heat sinks depending on their cost and
ease of manufacturing. In recent years, the technology relating to heat sinks designed
for cooling electronics has become widespread and familiar, since their initial cost is
low, and they are simple to install, and have a reliable manufacturing process
(Chingulpitak, 2015).

Fin morphology has an important function in manufacturing and heat transfer

characteristics. Cylindrical, rectangular, square, elliptic, and conical or semi-conical
are the widespread uniform pin fins geometries. In addition, pins offer a practical
means of achieving a large heat transfer area without excessive primary surface area
and act as turbulence promoters, thus further enhancing heat transfer rates by
breaking up the thermal boundary layer for many applications, such as cooling
electronic devices, including processes that use gas or liquid coolants (Denpong,
2001; Zhou & Catton, 2011; Naphon et al., 2009; Brigham & Van Fossen, 1984).
Therefore, it seems that it is a suitable time to employ this technology in traditional
heat sinks and in industrial applications as well.

In general, pin fin layouts are made up of a network of solid pins mounted
directly on the heat sink surface. Either a staggered or an in-line arrangement is
usually configured for arrays of pins with the working fluid flowing parallel or
perpendicular to the pin axes.

1.3 Importance of Electronics Cooling

In many engineering applications, the power dissipation creates heat as a by-

product, which may cause system failures in these devices due to serious
overheating. This is mainly due to the certain temperature limits that are required for
almost all applications to work within suitable conditions. Currently, as electronic
devices decrease in size, their thermal power losses increase (Mostafavi, 2012).
 -4-

Additionally, the forced convection of heat sinks covers a wide range of industrial
applications in order to overcome the damaging effects of overheating or burning.
Hence, it is very important to consider the cooling system for electronic components.

The main industrial applications of heat sinks are cooling of tiny electronic
components, electronic boards and components, the central processing unit (CPU) of
personal computers and data centres, internal combustion (IC) engine cooling (fins
in a car radiator), gas turbine blade coolant path, sophisticated electronic chips,
electrical appliances (computer power supplies, substation transformers, etc.), the
aerospace industry, and cooling of fuel elements in nuclear reactors (Prashanta,
1998; Sahin & Demir, 2008a; Sahin & Demir, 2008b; Amol & Farkade, 2013; Sara
et al., 2000; Sara et al., 2001).

Plate and pin fins are commonly used for cooling the CPUs of a personal
computer and electronic components devices (Dempong, 2001; Kim & Kim, 2009;
Yakut et al., 2006a; Zhang et al., 2005; Yakut et al., 2006b; Naphon & Knonseur,
2009); Naphon & Wiriyasart, 2009; Naphon & Wonwises, 2010; Naphon, 2011;
Konsue, 2012; Diani et al. (2013), integrated circuit chips in electronic equipment,
compact heat exchangers, and cooling of advanced gas turbine blades (Jonsson &
Moshfegh, 2001; Yang et al., 2007; Jeng & Tzeng, 2007; Sahin et al., 2005).

According to the author’s knowledge, the fin perforations might play an

important role in the thermal airflow through heat sinks; in other words, the cooling
performance will enhance and the pressure drop will reduce. It is possible those heat
sinks are useful for cooling electronic applications and for IC engine cooling such as
substation transformers, computer power supply, and fins in a car radiator
(Prashanta, 1998, Sahin & Demir, 2008a; Sahin & Demir, 2008b; Amol & Farkade,
2013; Sara et al., 2000; & Sara et al., 2001).

1.4 Liquid and Air Cooling of Data Centres

Generally, electronic systems in data centres are cooled by liquid or air

(Anandan & Ramaligam, 2008).

Liquid cooling such as water, nanofluids, polymers, and dielectric liquid

(Hydrofluoroethers, HFE) can be used to cool the heat sinks and servers of racks in
data centres. Direct contact liquid cooling techniques, such as immersing servers into
 -5-

dielectric liquid (Tuma, 2010; Almaneea, 2014) may be used. Ramifications of

immersion on data centre cooling and energy performance can be found in Chi et al
(2014). Another technique to cool data centres is indirect contact liquid cooling via
bringing the cooled liquid to heat sinks on the top of the chips or alternatively to the rack
or into the server as a heat exchanger on the front or rear of the rack (Villa, 2006). The
main advantages of this method are the heat transfer rate enhancement is greater than
that of the air-cooling method since the thermal conductivity and thermal capacity of
liquids are superior to those of air. In addition, dielectric liquids act as electrical
insulators without any electrical discharge (Naidu & Kamaraju, 2009; Alkasmoul,
2015). However, the main disadvantages of the pressure drop and pumping power of
liquids is higher compared with that of air because the viscosity and density of
liquids are larger than those of air. Furthermore, liquid cooling are risk of the liquid
leaking, which may damage the server’s electronic components, resulting in data
centre loss; the risk of condensation forming, which may lead to a failure in the
system; the high cost of maintenance and installation; and an increase in
infrastructure such as pipe work, leak detection, and installation of insulation (Villa,
2006; Naidu & Kamaraju, 2009).

Due to all the above disadvantages of liquid cooling, the most common method
of heat dissipation for thermal control of electronics is air cooling. Reduced cost, the
availability of air, and the simplicity of design are the main benefits of this cooling
method. As an example of an active air-cooled device, heat sinks with a fan or
blower are commonly employed. An amount of heat is dissipated from the heat
source to environmental air utilising a heat sink as a heat exchanger, which is a vital
practice employed in air-cooling systems. This transfer mechanism is easy, simple
and leads to reduced cost (McMillin, 2007). However, the heat transfer rate of the
air-cooling method is lower than that of the liquid cooling, as indicated previously.

In this technique, the heat transfer rate of the heat sink can be augmented,
either by increasing the fan speed or the surface temperature of the heat sink. As the
fan speed increases, however, the fan’s reliability reduces and it consumes a lot more
power and the noise level increases to undesirable levels, particularly for the office
or home consumer. Increasing the temperature is also unacceptable because it
reduces the reliability of the central processing units (CPUs) and that leads to earlier
 -6-

chip short circuit (McMillin, 2007). Hence, increasing fan speed and increasing the
temperature are not a favoured approach.

Therefore, these challenges need to be addressed by inventing an effective air

cooling solution that has direct influences on the reliability, power, and performance
of electronic devices. In this study, active air-cooling of perforated pinned heat sinks
(PPHSs) is investigated as a new technique (see sections 6.3 & 6.4.1) to cool central
processing units (CPUs), enhance heat transfer rate, and reduce fan power
consumption.

Due to the importance of the fin heat sink applications, which impact on the
forced heat transfer and fluid flow enhancement (and they have many serious
applications, especially to cool electronic devices such as large scale datacom
equipment and PC desktops), it is important to conduct a literature review that relates
to this interesting subject. In this chapter, many previous studies, both numerical and
experimental works, are reported, split into six groups based on the type of fins:
solid plate fins (A), solid pins (B), compact plate-pins (C), perforated plate (D),
perforated pins (E), and perforated folded fins (F) heat sinks, as shown in Figure 1.2.

A B

C D

E F

Figure 1.2: Different types of fins: (A) solid plate fins, (B) solid pins, (C) compact
plate-pins, (D) perforated plate, (E) perforated pins, and (F) perforated folded
fin heat sinks
 -7-

1.5 Solid Plate Fin Heat Sinks (SPFHSs)

The most widely used heat sink designs in industrial applications are those
based on rectangular plate fin heat sinks (PFHSs), Figure 1.2A, due to their simple
structure and ease of manufacture. These have been widely studied, and several
researchers have used experimental and numerical methods to remove the intrinsic
limitation that the air flow through parallel heat sink channels is smooth, thus
limiting the achievable heat transfer rate.

In this section, the reviewed literature can be categorised into two types of
work: experimental and numerical studies on solid plate fin heat sinks.

1.5.1 Experimental Studies

Plate fins as a flat plate, based on the literature reviews, single and multiple
cross-cut plate fins (strip fins) have been investigated by many experimental works
to study the effects of several parameters on the heat transfer and turbulent flow of
solid fin heat sinks. Such parameters are the height, width, number of fins, the
streamwise and spanwise distance between fins, and the type of material used in the
fin heat sink. Air and water are both used as a coolant in these studies.

It is indicated that the thermal resistance (see section 2.5.6) of single cross-cut
fin heat sinks is lower than that of the multiple cross-cut fins, plate fins, and square
pin fin heat sinks. This may be because the total wetted surface of the cross-cut fins
(see section 2.5.5) is larger than that of other types of fins, in addition to the spacing
between fins being suitable for airflow to pass through easily that leads to demolish
the growth of the boundary layer over the heat sink. Thus, it would be beneficial to
study the optimum thermal and airflow performance of cross-cut fins.

Air Cooling

Air is used as a coolant in the next three studies: Kim & Kim (2009), Didarul
et al. (2007), and Naphon & Khonseur (2009). The effects of cross-cut fins are used
for cooling electronic device applications are examined by Kim & Kim (2009). The
findings show that the thermal resistance of single cross-cut heat sinks outperforms
on the multiple cross-cut heat sinks. In addition, the comparison of the thermal
resistance of these heat sinks with pin and plate fin heat sinks indicates that the
 -8-

cross-cut heat sinks offer less thermal resistance than plate fin HSs and square pin
HSs by 5–18% and 14–16%, respectively.

Generally, if the dimensionless fan power (x-axis of Figure 1.3) is tiny and the
dimensionless heat sink size (y-axis of Figure 1.3) is large, an optimized plate fin
heat sink is recommended. However, the optimum pinned heat sink is suggested as
the dimensionless fan power is large and the dimensionless size of the heat sink is
tiny. The area in between the optimized plate fin and optimized pinned heat sinks is
represented the optimized cross-cut heat sinks.

Figure 1.3: Contour map of the thermal ratio for optimised plate, pin, and
cross-cut FHSs (Kim & Kim, 2009)

Didarul et al. (2007) indicated the effects of the direction of the short
rectangular plate fin, Figure 1.4, on the heat transfer rate and flow inside a duct for
turbulent airflow. The characteristic considered in this study was that the directions
of the fins were co-angular and zigzag, Figure 1.5. They observed that the optimum
improvement of local heat transfer coefficient (hx) is at 20o angle. In addition, the
average heat transfer coefficient (have) is largest for the zigzag fin model and it is
four times more than that without fins. However, the friction factor of the zigzag
model is larger than that for the co-angular pattern. These fins are utilised to cool the
trailing edge region and the internal passage of turbine blades.
 -9-

Figure 1.4: Test section and direction of short rectangular plate fins
(Didarul et al., 2007)

Figure 1.5: Short rectangular fins: (a) co-angular pattern, (b) zigzag pattern
(Didarul et al., 2007)
The effect of the channel height and the width of the microchannel were
investigated by Naphon & Khonseur (2009) with laminar airflow. They found that
the heat sink temperature decreases and Nusselt number (see section 2.5.5) increases
with increasing the channel height decreasing channel width. In addition, the shape
and the size of rough irregularities on the microchannel surface will influence the
pressure drop.

Liquid Cooling

Zhang et al (2005) reported that liquids can be utilised to cool electronic

system packages for two sizes of chip at 12×12mm and 10×10mm using micro-
rectangular plate fins with de-ionised water as a coolant. In general, the experimental
data indicates that pressure drop increases while chip temperature and thermal
resistance decreases with increasing flow rate for both chip sizes. For the 10×10mm
chip, however, the overall thermal resistance is higher than that of the 12×12mm
chip.
 - 10 -

1.5.2 Numerical Studies

Heat sinks that are used in the cooling of electronic devices, microchips, and
other systems consider the optimum design for fin array geometry. Heat transfer and
turbulent fluid flow have been presented numerically using solid plate fin heat sinks.
The governing equations Navier-Stokes and energy equations with k-ε turbulence
models are chosen by most of the researchers via employing the finite volume
method. The next papers in this section deal with this topic. The numerical and
experimental data are consistent in that the strip fins have achieved the smallest
thermal resistance.

The optimum design of parallel flat plate fin HSs was studied by Arularasan
and Velraj (2008) with a turbulent airflow. The findings indicate that the optimum
plate fin heat sink design based on the base temperature, thermal resistance, and
pressure drop is found at the specific parameters of the fin height, fin thickness, pitch
of the fin and the base height.

The Taguchi method is used to predict the optimum cooling design of parallel
plate fin HSs used in desktop PC CPUs by Ko-Ta (2005). It is indicated that two
design parameters have an important effects on the cooling performance of this heat
sink: the air speed and the fin flake gap. The lowest value of the base temperature is
decreased by 8oC and the temperature reduction is nearly 15%.

Velayati & Yaghoubi (2005) studied the effect of different fin blockage ratios
(D/W= fins thickness/fins spacing) and Reynolds numbers on the turbulent flow and
heat transfer characteristics of plate fin heat sinks. They found that the D/W and
Reynolds highly influence the separation flow, reattachment over the plate surface,
and the recirculation downstream of the plate. Thus, the Nu increases and the friction
factor decreases when both these parameters, D/W and Re, are increased. In addition,
fin efficiency (qwith fins/qwithout fins) enhances when D/W and Re are decreased.

The optimum design of different fin heat sinks was theoretically investigated
by Ndao et al. (2009) by using water and the dielectric liquid, HFE-7000. The heat
sink models are micro-plate channel, in-line and staggered circular pin HS, strip fin
HS, single and multiple impinging jet, shown in Figure 1.6. These heat sinks are
applied in electronic devices and chips. This optimisation is carried out in two steps:
simultaneous minimisation of the total thermal resistance (Rth,T, based on the total
 - 11 -

wetted surface area) and the pumping power consumption for each of these heat
sinks. The data indicates that the strip fins HS has the lowest thermal resistance of
the cooling devices, followed by the staggered and in-line circular pin HSs.
Furthermore, the micro-plate HS offers the lowest thermal resistance at relatively
very low pumping power.

Figure 1.6: Different heat sink models: (A) micro-plate channel (B) circular pins
(C) offset strip fins (D) jet impingement cooling (Ndao et al., 2009)

1.6 Solid Pinned Heat Sinks (SPHSs)

Although many optimisation reports have investigated plate fin heat sinks, see
e.g. Chiang (2005) and other previous studies such as Velayati & Yaghoubi (2005),
Arularasan and Velraj (2008), they cannot remove the intrinsic limitation that stops
air flowing through the heat sink channels is smooth, due to the parallel plate
arrangement, leading to the development of a boundary layer and limiting the
achievable heat transfer rates. Pinned heat sinks (PHSs), as shown in Figure 1.2B,
can be an effective alternative to plate fin HSs since they have the advantage of
hindering the development of the thermal boundary layer on smooth surfaces that is
responsible for limiting the heat transfer rates in plate fin designs (Zhou & Catton,
 - 12 -

2011). Pinned heat sinks play important role as turbulence promoters lead to enhance
heat transfer rates by disrupting boundary layer with greater pressure drop compared
with plated fin heat sinks (Jonsson & Moshfegh, 2001)

The major difference between plate fins and pin heat sinks is that the pressure
drop and heat transfer rate of pinned HSs are higher than those of plate fin HSs. In
addition, the thermal resistance and the average temperature of pinned HSs are lower
compared to plate fin HSs. In the next studies, by Jonsson & Moshfegh (2001) and
Yang et al. (2007), various cross-sections of pins, such as square, circular,
hexagonal, diamond and elliptic, are investigated with air and water coolants.

1.6.1 Experimental Studies

It can be observed that several parameters are considered in these studies in

order to report the effects of a parameter studies on the heat transfer and turbulent
flow through solid pinned heat sinks. These parameters are: cross-section of pin fin
shape, which can be circular; square; elliptic; diamond; hexagonal pin in in-line and
staggered arrangements; the height, width and number of fins; pin heat sink material;
and the streamwise and spanwise distance between pins. Air, water, and nanofluids
(coolants seeded with nano sized particles) are utilised as a coolant in these
experimental works.

Air Cooling

Vanfossen & Brigham (1984), Tanda (2001), Jeng & Tzeng (2007), Jonsson &
Moshfegh (2001), Yang et al. (2007), and Sahin et al. (2005) have all studied air
cooling. The important outcomes illustrate that the circular and elliptic pin shapes
have the higher heat transfer rate enhancement and lower thermal resistance.
Additionally, the pin density, which means the increasing number of pin fins, leads
to improvement the heat transfer rate while the pressure drop through solid pinned
heat sinks increases. Commonly, the staggered pin array achieves a higher heat
transfer rate and pressure drop compared with the in-line array.

To explain the effect of the in-line and staggered pin arrangements on the heat
transfer rate and pressure drop through PHSs, Tanda (2001) and Jeng & Tzeng
(2007) investigated this subject. Tanda (2001) studied diamond-shaped element pins,
which are useful for engineering applications such as electronic devices, compact
heat exchangers, and in cooling of advanced gas turbine blades, whilst Jeng & Tzeng
 - 13 -

(2007) examined square PHSs. Both studies indicated that the Nusselt number and
pressure drop of PHSs in the staggered array is the largest. Furthermore, Jeng &
Tzeng (2007) compared square pins with open article of circular pin fins and explain
that the pressure drop and Nusselt number of square pins and circular pins for both
in-line and staggered arrays depend on the spacing pins values and Reynolds
number. Generally, the staggered square pin arrangements have larger pressure drops
than the circular and square pins with in-line array arrangements.

In the next two articles, Jonsson & Moshfegh (2001) and Yang et al. (2007),
pin heat sinks are used for turbine blade and electronic device cooling. The pins’
shapes affect the heat transfer and pressure drop in in-line and staggered arrays, as
explained below.

Jonsson & Moshfegh (2001) investigated the different configurations of fins:

plate fins, strip fins, square pin, and circular pin, in in-line and staggered arrays, all
of which influence the Nusselt number and pressure drop. It is identified that Nusselt
number and pressure drop depend on the height and thickness (diameter) of the pins
and the distance between them, as well as the height and width of the wind tunnel. In
addition, the lowest pressure drop is observed at the plate fins due to their fin length.
Furthermore, the circular PHSs have a lower pressure drop than that of the square
PHSs.

The effects of the shape and density of PHSs with in-line and staggered
arrangements on heat transfer and pressure drop are reported by Yang et al. (2007).
The cross-section pins are circular, elliptic, square, and flat plate rectangular fins.
The experimental data imply that the highest average heat transfer coefficient occurs
at the staggered arrangement of the circular PHS. Furthermore, the thermal
resistance based on the projected area is smallest at the circular pins in-line, Figure
1.7. For staggered arrays, however, the lowest pressure drop is at the elliptic pin, and
this pin has a slightly higher performance than that of the circular pin. In general, the
average heat transfer coefficient and pressure drop increase with increasing pin
density.

Sahin et al. (2005) investigated the effects of geometric parameters of the HS

fins, as shown in Figure 1.8, on Nusselt number and friction factor. This kind of heat
sink is utilised for electronic cooling equipment. They explained that the optimum
design for the slices fin is obtained at 15mm fin width; 15o angle of attack; 100mm
 - 14 -

fin height; 20mm spanwise distance between fins; 15mm streamwise separation
between fins; 20mm streamwise separation between slices; 20mm spanwise distance
between slices; and 4m/s fluid velocity.

Figure 1.7: Heat transfer coefficient and pressure drop with inlet velocity for
plate fin and pin fin in (a) in-line array and (b) staggered array
(Yang et al., 2007)

Figure 1.8: Fin heat sink slices: (a) spanwise (c) streamwise distance between
the fins, (e) spanwise (f) streamwise distance between slices (Sahin et al.,
2005)

In the following two studies, Yakut et al. (2006a, 2006b), the results of using
hexagonal pin fins for cooling the CPU of a personal computer and electronic
component devices are reported. They have used the Taguchi optimisation design
method to explain the influence of the height, width of the hexagonal fins, and
spacing between fins on the thermal resistance and pressure drop (Yakut et al.,
2006a) and on the Nusselt number and friction factor (Yakut et al., 2006b).
Commonly, it can be observed that the pin height is the most effective parameter on
 - 15 -

Nu and thermal resistance while pin width is the most effective parameter on ΔP and
friction factor.

Liquid Cooling

Liquids such as water and Nanofluids can also be utilised to cool electronic
system packages. The heat transfer rates increase and the thermal resistances
decrease once TiO2 nanofluid coolant is used, in comparison with water-cooling for
the same heat sink and under the same boundary conditions such as same applied
heat flux, concentration of nanofluid, and inlet mass flow rate and temperature
(Naphon & Nakharintr, 2013). In this literature, it is possible to utilise the jet cooling
method to cool the CPU of a personal computer (PC) and enhance the CPU
temperature. Heat transfer rate and CPU temperature enhance with increasing mass
flow rate and when decreasing both nozzle diameter and channel width.

Naphon & colleagues (2010, 2011, and 2013) have produced three important
papers relating to mini-pin heat sinks using laminar water and nanofluid flow as a
coolant to cool the CPU of a PC. In the first two papers (2010 and 2011) employed a
jet flow techniques (parallel flow method) while their other one Naphon &
Wongwises (2013) used the traditional cross-flow method. Generally, the authors
found that the nanofluid achieve a significant enhancement in heat transfer rate and
Nusselt number while the pressure drop is higher compared with air- and water-
cooling.

Naphon & Wongwises (2010) investigated the jet impingement heat transfer
by utilising mini-rectangular pin heat sinks, which are constructed from copper, to
cool the CPU of a PC. This study used de-ionised water as a coolant and the PC was
examined with no load and with full load operating conditions. They indicated that
CPU temperature reduces when the channel width and the nozzle diameter decrease.
Furthermore, the largest CPU temperature drops and energy consumption increases
take place when the CPU is working under full load conditions. Naphon &
Wongwises (2011) reported the jet nanofluid effect on cooling the CPU by utilising
mini-channel HSs, Figure 1.9. TiO2 particles were used as nanofluid coolant. Using
the jet nanofluid lowered the average temperatures of the CPU by nearly 3% and
6.25% than those of the jet water and the conventional cooling system, respectively.
As a result, the Nusselt number for the jet nanofluid is higher than that for the two
other techniques, jet water and conventional water cooling system, Figure 1.10.
 - 16 -

Maybe the nanofluid can capture and transfer more heat since their thermal
conductivity and thermal capacity are higher.

Naphon & Nakharintr (2013) studied the effect of the channel height on the
heat transfer rate of mini-rectangular fin heat sinks with nanofluid (TiO2) as a
laminar flow. In this study, heat transfer rate and Nusselt number enhance with
increasing channel height. Comparing the results with water indicate that the heat
transfer rate and Nusselt number of the nanofluid are higher than those of the water.
In addition, the thermal resistance of the heat sink with the nanofluid is lower than
that of the water. However, the pressure drop of both nanofluid and water is
approximately the same in this study.

Figure 1.9: Jet impingement heat sink unit for cooling the CPU of a PC
(Naphon & Wongwises, 2010)

Figure 1.10: Variation of the Nusselt number with mass flow rate for
different cooling methods (Naphon & Wongwises, 2011)
 - 17 -

1.6.2 Numerical Studies

In this part, the literature review discusses the enhancement of heat transfer
with laminar and turbulent fluid flow for solid fin heat sinks numerically by using
different fin shapes. Turbulent flow is in common use while laminar flow is
specifically utilised according to the application’s requirements. Several kinds of
commercial CFD software program are utilised to solve the governing equations,
Navier-Stokes and energy equations with k-ε and k-ω turbulence models, which are
chosen by most researchers via employing the finite volume and the finite elements
methods.

The main conclusions indicate that the circular pinned heat sinks have a larger
Nusselt number and lower friction factor than most other types of fin heat sinks such
as plate fins, strip plate fins, elliptic pins, and square pins in in-line and staggered
arrays under laminar airflow. The elliptic and circular pins, however, have the lowest
pressure drop therefore requiring lower pumping power values under laminar flow
conditions.

Air Cooling

In the next two works, by Ramesha & Madhusudan (2012) and Soodphakdee
et al. (2001), laminar airflow and heat transfer characteristics are numerically
reported.

Ramesha & Madhusudan (2012) investigated the effect of pin heat sink profile
on the laminar forced convection heat transfer. These pin fins, which are useful for
electronic cooling applications, are square twisted with various attack angles of
airflow direction, as shown in Figure 1.11. The outcomes indicate that the twisted
pins enhance the heat transfer rate of the heat sink especially at 30 o, 45o, and 60o
twisted angles by comparing the performance of a straight pin fin heat sink at 0 o
twisted. In addition, the pressure drop of the twisted pins at 30o and 45o improves
and is nearly similar to the straight pins.

The effect of cross-section fins on laminar forced convection heat transfer and
pressure drop has been investigated by Soodphakdee et al. (2001). The shapes of
these cross sections are plate fins, circular, elliptic, and square pins in in-line and
staggered arrays, as shown in Figure 1.12, and these fins can be applied in integrated
circuit chips. The findings explain that elliptic fins have the highest heat transfer
 - 18 -

coefficient at lower pressure drop and pumping power values. At larger pressure
drop and pumping power values, however, the circular pin fins possess the highest
heat transfer coefficient, as shown in Figure 1.13.

Figure 1.11: Straight and twisted pin heat sinks (Ramesha & Madhusudan, 2012)

Figure 1.12: Different types of fin heat sinks (Soodphakdee et al., 2001)

Figure 1.13: Heat transfer coefficient versus pressure drop of various fin
geometries (Soodphakdee et al., 2001)
 - 19 -

Mohan & Govindarajan (2010) reported the optimum forced convection heat
transfer and temperature distribution through two kinds of heat sink: plate fins and
pins HSs, which are adequate for the CPUs of desktop computers. They found that
the CPU temperature of the heat sink decreases when the base plate thickness and
thickness of the fin increase. If copper is selected as the base plate material rather
than aluminium, the thermal resistance of the heat sink reduces as expected, while
the heat sink will be more expensive and heavier compared with when using
aluminium. Thus, this study demonstrated the practical compromise that has to be
struck between a low thermal resistance when using copper as the base plate
material, which is costlier and heavier, and a higher thermal resistance for
aluminium, which is cheaper and lighter.

Liquid Cooling

The following researchers, Naphon et al. (2009 and 2011) and Mohan &
Govindarajan (2010) have used numerical methods to study turbulent flow and heat
transfer in heat sinks.

Naphon et al. (2009 and 2011) report on two experiments using forced heat
transfer and turbulent fluid flow for mini-square PHS. The first one studied variable
channel width, which is used for the CPU of a PC, and a de-ionised water coolant
was used to explain the flow structure and behaviour of the working fluid. The
findings explain that the flow pattern, pressure and temperature distribution are not
uniform over the mini-heat sink. That is because all these results depend on liquid
velocity, which is non-uniform through heat sinks. In addition, the direction and
distribution of velocity at the entrance region of the mini-heat sink is dependent on
the liquid flow pattern at the inlet plenum (Naphon et al., 2009). The second work
studied the effect of the outlet port position on jet impingement heat transfer and
fluid flow of two models, A and B, which have four different outlet port positions
(Naphon et al., 2011), Figure 1.14, for the same mini-square fin heat sink as in the
last report. The numerical results showed that the flow velocity and the temperature
distribution of coolant fluid through the second design (B) are uniformly better than
in the first model (A). This means that both heat transfer rate and the overall
performance of the second model (B) are higher than that in the first model (A).
Thus, the uniformity of temperature distribution has an important effect on the
thermal performance of the mini-heat sink.
 - 20 -

Based on the previous literature review, the main advantages and

disadvantages of the plate fin heat sinks and pinned heat sinks are shown in Table
1.1

Figure 1.14: Schematic diagram of the different cross sections of model A and
model B (Naphon et al., 2009)

Table 1.1: The comparison between the plate fin heat sinks and pinned heat
sinks
Plate fin heat sinks (PFHSs) Pinned heat sinks (PHSs)
The most widely used in industrial applications
Air, water and Nanofluids are used to cool different engineering devices
Relatively complex structure and
Simple structure and ease of manufacture
manufacture
Different type of pin configurations:
Parallel plate fins only circular, square, elliptic, strip in in-line and
staggered arrays
The intrinsic limitation that the air flow
Act as turbulence promoters lead to break
through parallel heat sink channels that is
up a boundary layer
smooth
Hindering the development of a boundary
The development of a boundary layer easily
layer
Limiting the achievable heat transfer rate Enhancement heat transfer rates
Lower pressure drop and fan power Greater pressure drop and fan power
Higher the base average temperature Lower the base average temperature

Higher thermal resistance to some extent Lower thermal resistance to some extent
 - 21 -

1.7 Plate-Pin Fin Heat Sinks (PPFHSs) or Compact Heat Sinks

(CHSs)

Plate-pin fin heat sinks are a kind of compact heat sinks (CHSs), as shown in
Figure 1.15B and C, and have been reported on only in relation to turbulent airflow.
Compact heat sinks (CHSs) consist of some pins among plate fins in in-line and
staggered arrangements. As more pins are present among the plate fins, the boundary
layer growth through the heat sink is inhibited because the pins act as obstructions.
The benefits of compact heat sinks are reduction of the CPU temperature and
thermal resistance and enhancement of the Nusselt number, compared with plate fins
and pin HSs. However, these pins will impede airflow, which leads to a pressure
drop, and fan power for compact heat sinks is huge in comparison with other plate
fins and pin HSs.

In the next literature surveys, all types of compact heat sinks (CHSs) are
applied to cool electronic components under a turbulent airflow.

Yu et al. (2003, 2004, and 2005) conducted numerical and experimental

investigations into the thermal airflow through plate-circular pin fin heat sinks
(PCPFHSs), which consist of some circular pin fins among plate fins. The results
indicate that the thermal resistance of the PCPFHS is nearly 30% smaller than that of
the plate fin heat sink (PFHS). However, the pressure drop of the PCPFHS is much
higher than that of the PFHS. The performance profit factor (Q/Pfan) of the PCPFHS
is about 20% higher than that of the PFHS.

Yang & Peng (2009a and 2009b) produced two papers relating to the compact
heat sink. Thermal characteristics and pressure drop of the plate-circular pin fin heat
sink (PCPFHS) in in-line and staggered arrangements are considered with a mixed-
height design of pins, as shown in Table 1.2. The results indicate that the Nusselt
number enhancement of the PCPFHS is over 30% superior to that of the plate fin
heat sink (PFHS). However, the pressure drop of the PCPFHS is nearly 110% higher
than that of the PFHS. For the in-line arrays design, the profit factor is higher than
for the staggered arrays model. The profit factor of Type-3 is the highest while the
largest Nu is for Type-4 (Yang & Peng, 2009a). Yang & Peng’s (2009b) second
report deals with the effects of pin shape and arrangement on the thermal and
hydraulic characteristics of compact heat sinks utilising circular and square pin fins
 - 22 -

between plate fins. These compact heat sinks are called the plate-circular pin fin heat
sink (PCPFHS) and the plate-square pin fin heat sink (PSPFHS), as shown in Figure
1.15. The findings show that the profit factor of the PCPFHS outperforms the
PSPFHS by approximately 7%. In addition, the thermal resistance and pressure drop
of the PCPFHS are about 10% and 90% respectively smaller than those of the
PSPFHS.

Figure 1.15: Compact heat sinks: (a) plate-fin heat sink, (b) plate-circular pin
heat sink, and (c) plate-square heat sink (Yang and Peng, 2009)

Table 1.2: The practical examples of the heat sinks dimensions

(Yang and Peng, 2009)

Kumar & Bartaria (2013) assessed the thermal characteristics and pressure
drop of the plate-elliptic pin fin heat sink (PEPFHS), which means some elliptic pins
distribute between plate fins in an in-line arrangement with three different minor
radiuses of elliptic pins. The results indicate that the thermal resistance and the
Nusselt number of the PEPFHS enhance as the minor radiuses of the elliptic pins
increase. Furthermore, the Nusselt number of the PEPFHS is higher than that of the
plate pin (PFHS) while the pressure drop of the PFHS is lower than that of the
PEPFHS.
 - 23 -

The results of using more different plate-pin fin heat sink models with various
cross-section types of pin-fin, square, circular, elliptic, NACA 0050 profile, and
dropform are by reported Zhou & Catton (2011) to enhance thermal and hydraulic
characteristics of this kind of heat sink. The numerical data, which are obtained from
the k-ω turbulent model as provided in ANSYS CFX-12.1 program, illustrated that
PPFHSs improve the Nusselt number by up to 85% while a maximum pressure drop
of 525% is reached in comparison with plate fin heat sinks (PFHSs), as shown in
Figures 1.16 and 1.17.

Yuan et al. (2012) investigated the thermal hydraulic characteristics of the

compact plate-circular pin fin heat sink (PCPFHS) in in-line and staggered
arrangements to find its potential application in the CPU of a PC. Heat sink
dimensions and boundary conditions are similar to the previous papers (Yang &
Peng, 2009a and 2009b) with mixed pins; the diameter design of the PPFHS is
shown in Table 1.3. They proposed that all these PCPFHS models achieve the
cooling requirement of a desktop PC CPU at less than 60W as a heating power and
with a maximum temperature of 85oC. The pressure drop over PPFHSs increases
while the thermal resistance and the profit factor will significantly decrease as pin
diameter and air velocity increase. However, the effects of pin distance and pin
array of this compact HS were less remarkable.

Table 1.3: Different pin diameter combinations for four types of PPFHS
(Yuan et al., 2012)
 - 24 -

Figure 1.16: Nusselt numbers of compact heat sinks with

variation in air velocity (Zhou & Catton, 2011)

Figure 1.17: Streamlined patterns at Uc=10m/s, in the plane z=8 mm

(Zhou & Catton, 2011)

1.8 Perforated Fin Heat Sinks (PFHSs)

The main reason for interest in this subject is that forced convection fins have
various applications, from cooling of tiny electronic components to cooling of fuel
elements in nuclear reactors. Furthermore, according to the author's knowledge and
the next literature reviews in this section, the fin perforations play an important role
by way of improving the thermal and flow characteristics of heat sinks and vanishing
the vortexes and boundary layers behind solid plate fins and pin heat sinks. In
addition, devices with these perforated fins will be lighter in weight and material will
 - 25 -

also be saved in their design (Yaghoubi et al., 2009). Only air is used as a coolant in
the following works.

The numerical studies calculated NuT based on total wetted surface area of the
perforated fins is lower than that of solid fins heat sink. Hence, we recommend
determining the projected Nusselt number (NuP), based on surface area of only the
heat sink base, L×W: where L, and W are length and width of the heat sink,
respectively, as this may be a more effective measure of cooling capacity for a given
heat sink size. The CPU temperature should not exceed the reference critical
temperature of 85oC (Gurrum et al., 2004; Yuan et al., 2012). Furthermore, it should
be considered to minimise CPU temperature and fan power consumption in order to
select the optimum heat sink design.

1.9 Perforated Plate Fin Heat Sinks

Either perforation can be along the length of the plate fins as a small channel
(frontal perforations) Figure 1.18A, or on the side of the plate fins as lateral
perforations, Figure 1.18B. They are able to enhance thermal airflow of these heat
sinks compared to the equivalent solid fin heat sinks.

A B

Figure 1.18: (A) Frontal and (B) lateral perforated flat plate heat sinks
(Yaghoubi et al., 2009; Shaeri & Yaghoubi, 2009)

1.9.1 Plate Fins with Lateral Perforations

The first section deals with several experimental reports on lateral circular
perforated plate fin heat sinks. The main conclusion is that the Nusselt number and
friction factor of perforated plate fins are larger than those of the solid fins. For
instance, Dhanawade et al. (2010, 2014, and 2014) have produced three studies on
lateral perforation PFHSs. The first one investigates the effect of lateral circular
 - 26 -

perforated plate fins on forced convection heat transfer (Dhanawade & Dhanawade,
2010), and found that, at low applied heat flux levels up to 14000W/m2, the Nusselt
number for the 12mm perforation diameter is larger than that for the 10mm
perforation diameter. However, at high heat flux levels up to 20000W/m2, the largest
Nusselt number is for the 10mm perforation diameter.

Ganorkar & Kriplani (2012) produced another study explaining the effect of
the lateral circular perforated plate fins on the heat transfer rate. This kind of HS is
used to cool electronic applications and in IC engine cooling such as substation
transformer, computer power supply, and fins in a car radiator. The effects of the
lateral perforated plate fins’ shape on forced convection heat transfer and friction
factor (f) are investigated in another report by Dhanawade et al. (2014). Evidently,
the data point out that the Nu and f of the perforated fins are higher compared to
solid fins and they increase with increases in the perforations’ diameter. The
𝑄𝑝𝑒𝑟𝑓𝑜𝑟𝑎𝑡𝑒𝑑 𝑓𝑖𝑛𝑠 −𝑄𝑠𝑜𝑙𝑖𝑑 𝑓𝑖𝑛𝑠
effectiveness of the square perforated fins, , is nearly the
𝑄𝑠𝑜𝑙𝑖𝑑 𝑓𝑖𝑛𝑠

same as that of the circular perforated fins, while, with respect to the friction factor,
the circular perforated fins have the lowest value. Dhanawade et al. (2014) have
developed their previous work utilising the Taguchi design experimental method for
optimum design of the thermal performance of circular lateral perforated PFHSs.
They found that the most vital parameters are Re, perforation porosity, and then fin
thickness, respectively. The highest level of effectiveness for the perforated fins is
nearly 19%, noted at Re=87000, 0.22 porosity, and 5mm of fin thickness. The
findings show agreement with the results of Ganorkar & Kriplani (2012).

According to numerical studies, several factors such as average friction factor,

Nusselt number based on the total wetted surface area (NuT), and fin weight reduce
as increasing the number of perforations. However, the percentage of heat transfer
enhancement or fin effectiveness (ɛ=qwith fins/qwithout fins) decreases incrementally with
the number of perforations up to eight holes and then this enhancement increases as
the perforations rise up to 50 holes, according to work by Yaghoubi et al. (2009) and
Shaeri, et al. (2009). They investigated thermal and airflow characteristics of square
lateral perforated PFHSs at variable porosity under laminar and turbulent airflow.
Under the laminar flow conditions, the perforated fins effectiveness is nearly the
same value as that of the solid fins, even though the perforations have increased in
 - 27 -

number, whereas, for the turbulent flow, heat transfer rate increases when increasing
the number of perforations.

1.9.2 Plate Fins with Longitudinal (Frontal) Perforations

The thermal and hydraulic characteristics of perforated plate fin HSs have only
been numerically reported with laminar and turbulent airflow; there is no
experimental work. Either k-ε standard or RNG models are utilised in the following
literature to solve the governing equations. Similarly to lateral perforation plate fins,
total drag (friction and pressure drag), Nusselt number based on the total wetted
surface area (NuT) and the weight of the fins reduce as the number of these
longitudinal perforations along the length of the plate fins increases. Fin
effectiveness is enhanced via these perforations, which alleviate the recirculation
zones that are behind the plate fins for both laminar and turbulent airflow. For
example, Shaeri & colleagues (2009 and 2012) have presented work related to the
perforated PFHSs in the presence of laminar and turbulent airflow.

The laminar flow and heat transfer characteristics have been numerically
investigated by the following researchers.

The effects of the number of perforations with variable porosity on the heat
transfer rate and laminar airflow have been investigated by Shaeri & Yaghoubi
(2009). Numerical data explain that the average friction coefficient, pressure drop,
average Nusselt number (NuT) and the weight of the fins decrease, but the
effectiveness of the perforated fins increases when the number of perforations
increases. Perforated plate fins reduce the shape and the size of recirculation zones
(wakes) behind these fins compared with solid fins. The effects of size and number
of perforations of a flat plate of the same porosity on thermal performance and
laminar airflow have been studied by Shaeri & Jen (2012). The outcomes illustrate
that the total drag, friction and pressure drag stay nearly constant for all kinds of
perforated and solid fins because the airflow has a low velocity inside those
perforations. Conversely, the thermal entrance length (the distance of thermal
boundary layer inside the perforations) is smaller with a larger number of
perforations than with a smaller number perforations, by which means the heat
transfer rate of fins with a smaller number of perforations (larger perforation sizes)
improves by approximately 80% compared with solid fins.
 - 28 -

The following researchers report turbulent airflow and heat transfer

characteristics numerically.

Shaeri & Yaghoubi (2009) have reported the influence of perforations with a
variable porosity in perforated plate fins on the heat transfer rate and turbulent
airflow. The results indicate that the rising number of perforations influences: the
size of the wakes that form behind the fin; the length of the recirculation zone around
the lateral surfaces of the fin; total drag; skin friction coefficient; and the weight of
the fins decreases. Fin effectiveness of perforated fins with three perforations is
almost 65% higher than that of the solid fin. On the other hand, Shaeri & Jen (2012)
report the effects of size and number of perforations for the same porosity on thermal
performance and level of turbulent fluid flow. The results prove that the friction drag
of the perforated fins is higher but the pressure drag and the total drag of the
perforated fins are smaller than those of the solid fins. Furthermore, fin effectiveness
increases with increasing number of perforations; in other words, heat transfer rate
enhances with decreases in perforation size at constant porosity.

1.9.3 Effect of Differently Shaped Perforations

Concerning the shape of the perforations along the plate fins, Ismail et al.
(2013 and 2014) have only numerically demonstrated this with laminar and turbulent
airflow.

The effects of circular and square perforations along the plate fins on the
thermal and turbulent airflow performance have been considered by Ismail et al.
(2013). The results show that the heat transfer rate of the perforated fins is nearly the
same for both the circular and square perforations, while the pressure drop is lower
for the circular perforated fins. In addition, as the number of perforations increases
from two to three, fin effectiveness is almost the same but pressure drop decreases.
Ismail et al. (2013 and 2014) have developed this study via considering more
perforation shapes in an investigation into the effects of perforation shapes on the
thermal and hydraulic performance under laminar and turbulent airflow. Circular,
square, triangular, and hexagonal perforation shapes have the same surface area, as
shown in Figure 1.19. Commonly, the results are the same for both laminar and
turbulent airflow. The hexagonal and circular perforations have higher heat transfer
performance enhancement (HTPE) and lower pressure drag coefficient than the other
 - 29 -

perforations, Figure 1.20. In addition, the maximum Nusselt number, NuT, still
occurs for the solid plate fins.

According to the shapes of the fins with lateral perforations, Ismail et al.
(2014) have demonstrated the effects of number and shape of lateral perforations,
circular, square, triangular, and hexagonal, on the turbulent airflow and heat transfer.
RANS-based modified k-ω turbulent flow has been considered. They indicate that
the shapes of the perforations have a significant role in enhancing the cooling and
hydraulic performance. Hexagonal perforated fins, however, have the largest
effectiveness and heat transfer performance enhancement (HTPE) of the perforated
fins. As indicated earlier, solid fins have the maximum Nusselt number, NuT, and the
largest friction coefficient and this decreases with increasing in the number of
perforations.

Figure 1.19: Different sorts of perforated FHSs: circular, square, hexagonal,

and triangular (Ismail et al., 2013)

Figure 1.20: Nusselt number and fin effectivity variations for different
types of fin (Ismail, 2013)
 - 30 -

1.9.4 Perforated Ribs and Blocks as Fins

The experimental testing of the other types of perforated blocks as fin heat
sinks, ribs or baffles towards the flow direction is investigated in this section. These
perforations have differently shaped perforations. For instance, turbulent forced
convection heat transfer and friction loss of a single baffle that has perforations in
different positions, of different sizes, and with inclined orientations inside the
rectangular channel have been investigated by Dutta and Dutta (1998). The results
point out that both local and average Nusselt numbers increase when increasing the
angle of baffle orientation and baffle size, and with a decreasing number of circular
perforations. With regard to the position of the baffle, when it is located at the start
from the heat source, the Nusselt number is higher than that of the baffle, which is
placed far away of the heat source. Furthermore, friction factor ratio decreases as the
angle of baffle decreases and circular perforation density increases.

Sara et al. (2000 and 2001) have produced two works related to solid and
perforated blocks, which are used in many practical applications. These works are
focused on the thermal performance efficiency (η=ha/hs, where ha and hs are the
convective heat transfer coefficient with and without blocks, respectively) of these
perforated block types with turbulent airflow, Figure 1.21. The results show that the
performance efficiency and Nusselt number of the perforated blocks are greater than
the solid blocks and they increase by nearly 30%-60% as increasing the perforation
inclination angle, perforation open-area ratio, and perforation diameter. Additionally,
friction factor and pressure drop of the perforated blocks are lower than those of the
solid ones. Therefore, the gained energy performance of the perforated blocks
compared to the solid blocks is up to nearly 77% due to the enhanced Nusselt
number and the reduced pressure drop of the perforated blocks.

Figure 1.21: The test section of perforated blocks/ribs with different views
(Sara et al., 2001)
 - 31 -

With respect to numerical reports of perforated ribs as fins, it is indicated that

the numerical data are in agreement with the previous experimental reports. For
example, Khoshnevis et al. (2009a) studied the effects of circular perforated ribs
with various attack angles towards the flow direction on the thermal airflow of heat
sinks inside a rectangular channel. However, the effects of two kinds of perforation,
circular and slotted perforated ribs shown in Figure 1.22, were reported in another
study by Khoshnevis et al. (2009b). The Nusselt number enhances as the perforation
inclination angles, perforation diameter and perforation open-area ratio increase.
Furthermore, pressure drop reduces with increasing perforation diameter and open-
area ratio, but it is not affected by perforation inclination angles. Generally, the
Nusselt number and pressure drop of the perforated ribs are slightly enhanced
compared to slotted ribs with the same open-area ratio.

Figure 1.22: The angle of perforations and slots in rectangular blocks towards
flow directions (Khoshnevis et al., 2009b)

1.10 Perforated Folded Fin Heat Sinks (PFFHSs)

The thermal resistance of several triangular folded fin heat sinks is investigated
by Jia et al. (2003, 2004 and 2007). The fin types are: extruded plate fin (a model),
slit folded fin (b model), perforated folded fin (c model), and perforated slit folded
fin (d model), as shown in Figure 1.23, and they are tested for the same boundary
conditions such as applied heat flux, inlet air velocities and inlet air temperature. The
experimental results indicated that the thermal resistance of the new triangular folded
fins design (b, c, and d models) is superior to that of the traditional plate fins (a
model). The most effective for application in high-powered electronic devices are the
slit folded fin (b model) and/or perforated slit folded fin (d model) heat sink models.
The thermal resistance of the slit folded fin (b model) and the perforated slit folded
 - 32 -

fin (d model) is nearly 18% and 20% respectively less than that of conventional plate
fin heat sinks (a model) at a fixed fan power. In addition, the cooling performance of
these heat sinks depends remarkably on the increasing fin height, number of slits for
the perforated slit folded fin, decreasing fin pitch, and Reynolds number.

Figure 1.23: Different designs of folded fin heat sinks: a) Extruded plate fin, (b)
Slit folded fin, (c) Perforated folded fin, (d) Perforated slit (Jia et al., 2003)

1.11 Perforated Pinned Heat Sinks (PPHSs)

Relatively few studies have considered the effect of perforations on the heat
transfer and pressure drop of perforated pinned heat sinks (PPHSs), shown in Figure
1.24 which is investigated experimentally in the following literature survey, rather
than through numerical reports. It is indicated that pin perforations offer considerable
benefits by enabling the heat transfer to be improved while at the same time reducing
both the pressure drop across the heat sink and the fan power required to pump the
air through it. In addition, reduction in the weight of the pinned heat sink can be
obtained via these perforations. These perforated PHSs can be classified into two
types, single and multiple perforations.

1.11.1 Single Perforated Pinned HSs

PHSs with only one perforation are called single perforated PHSs. The effects
of square and circular cross-section perforated pinned heat sinks in an in-line array
have been reported by Sahin & Demir (2008a and 2008b), while Amol & Farkade
(2013) considered the effect of a staggered arrangement of circular cross-section
 - 33 -

perforated pinned heat sinks. The various parameters with Reynolds number, such as
turbulent airflow, clearance ratio (C/H) and inter-fin spacing ratio (streamwise
distance) in the flow direction, were studied in these three reports to investigate the
Nusselt number and pressure drop of perforated pinned HSs where C is the distance
from the tip of the pins to the upper surface of the wind tunnel, and H is the height of
the pins. In addition, this perforation is just a single circular perforation located near
the bottom of the fin. These studies have found consistently that a single perforation
leads to an enhancement of Nusselt number and a reduction in pressure drop
compared to the equivalent solid pin system, as shown in Figure 1.25. For example,
Sahin & Demir (2008a) have found that the enhancement efficiencies of square
cross-section perforated pinned heat sinks vary between 1.1 and 1.9, while the
enhancement efficiencies of circular cross-section perforated pinned heat sinks are
the highest, varying from 1.4 to 2.6 depending on the inter-fin spacing ratio and
clearance ratio (Sahin & Demir, 2008b). In addition, the projected Nusselt number,
NuP, is enhanced and the friction factor increases when reducing both clearance ratio
(C/H) and streamwise distance.

It can be concluded that the main outcomes of this design are that localised jet
flows through the perforations increase local heat transfer by alleviating the
recirculation zones that form behind solid pins, and increasing shear-induced mixing
leads to enhance thermal airflow and reduce pressure drop through perforated pinned
heat sinks. To select the optimum design, the Taguchi experimental design method
design is used in these studies utilising the ANOVA-TM software package to
evaluate the effect of each parameter on the optimisation criterion. The trade-offs
among goals are considered and the optimum design occurs as pin height and pitch
are 50mm and 3.417, respectively at Re=42000 (Sahin & Demir, 2008).

As indicated in the previous three reports, the perforated pinned heat sinks can
be used for large heat exchange applications because the dimensions of the heat sink
are 250×250mm, which is large, and the aspect ratio of height to diameter, H/d, is
greater than four (Vanfossen & Brigham, 1984). However, it is difficult to apply this
size of perforated PHSs for cooling electronics systems due to restrictions in the size
of these systems. Thus, a mini-perforated pinned heat sink design is required to
enhance heat transfer rate and at same time reduce fan power consumption to drive
air through PHSs, and that leads to the desirable benefit of reducing the CPU
 - 34 -

temperatures of the heat sink in the case of a fixed heat sink size, which is our goal
in this study.

Figure 1.24: (a) Perspective view of the heat exchanger and a single perforated
pin configuration (b) Sectional view of heating unit and tested model
assembly (Sahin & Demir, 2008b)

Figure 1.25: Nusselt number and friction factor variations for single perforated
pin fins (Sahin & Demir, 2008b)

1.11.2 Multiple Perforated Pinned HSs

Based on the literature review and our knowledge, the combination of

experimental and numerical studies relating to the benefits of single and multiple
perforated pinned heat sinks for electronic cooling applications has not yet been
reported. Hence, illustrating the comprehensive thermal airflow of this kind of heat
sink has motivated a full study of the benefits of multiple perforated PHSs, as shown
in previous Figure 1.2E and 1.27.
 - 35 -

The expected benefits of multiple pin perforations may enhance the heat
transfer rate (increasing NuT and NuP) while reducing the fan power consumption,
which is required to overcome the pressure drop across the heat sink. The
minimisation of CPU temperature and thermal resistance are the other important
factors for thermal management of systems containing electronic components,
together with minimising the fan power consumption. The additional benefit of a
reduction in the weight of the pinned heat sinks is important to reduce the cost and
save material.

The previous studies can be summarised by the flowchart illustrated in Figure

1.26.

Heat Sinks (HSs)

Numerical &
Solid Plate Fins Solid Compact few
HSs HSs Experimental
Experimental Studies
& Numerical
Studies
Solid Pin Fins Perforated Fins
HSs HSs

Perforated Plate Perforated Pin

Fins HSs Fins HSs

Experimental Lateral
& Numerical Only Singular
Perforated Plate
Studies Perforated Pin Fins
Fins HSs
HSs

Longitudinal
Perforated Plate
Fins HSs Only
Numerical Experimental
Studies Studies
Perforated
Shapes

Experimental
Perforated Ribs
& Numerical
& Blocks Fins
Studies

In the current study: Experimental & Numerical investigation of multi & different
perforated shapes pinned heat sinks

Figure 1.26: Simple flowchart of literature review of different heat sink types
 - 36 -

1.12 The Aims and Objectives of the Current Study

According to the literature review, as indicated previously that many

optimisation reports have investigated plate fin heat sinks, see e.g. Chiang (2005),
but they cannot remove the intrinsic limitation that air flows, which is smooth
through the heat sink channels. This is due to the parallel plate arrangement, limiting
the achievable heat transfer rates. Pinned heat sinks (PHSs) can be an effective
alternative to plate fin heat sinks since they have the advantage of hindering the
development of the thermal boundary layer on smooth surfaces responsible for
limiting the heat transfer rates in plate fin designs (Zhou & Catton, 2011). However,
this the heat transfer enhancement of pinned heat sinks is always accompanied by a
substantial increase in fan power losses (pressure drop). Hence, in most pinned HS
applications, both the heat transfer and pressure drop characteristics should be
considered.

Based on the author’s knowledge, very few experimental studies have been
reported; only three papers have examined the thermal airflow characteristics of a
single circular perforation at the bottom of a pin fin HS (Sahin & Demir, 2008a;
Sahin & Demir, 2008b; Amol & Farkade, 2013). The perforations are a useful air-
cooling technique to enhance the thermal airflow characteristics of the pinned heat
sink. Furthermore, there exists neither numerical data with respect to the use of
perforated pin fins nor combination of experimental and numerical works relating to
notched and slotted pin fins for heat sink applications.

As a result of that, the main aim of this study is a numerical and experimental
investigation of different configurations of perforated, notched and slotted pinned
heat sinks that are presented to enhance the heat transfer rate, reduce CPU
temperature, and decrease the fan power to overcome the pressure drop through
pinned HSs. Then, the optimum thermal airflow characteristics of PHSs design such
as perforations dimensions are examined to obtain the lowest CPU temperature and
fan power consumption through a heat sink. In addition, the application
specifications of pinned heat sinks is reported for active air-cooling of electronic
systems since, at a smaller scale, convective heat transfer to air as it flows over a
network of fins is also the most common approach to cooling microelectronics due to
its low cost, availability, relatively simple structure and easy manufacturing (Zhou &
 - 37 -

Catton, 2001). Finally, the weight of these heat sinks will be lighter when using
aluminium and perforations.

The types of pin fin heat sinks that will be studied in this thesis are, as shown in
Figure 1.27:

1. Circular perforated pin fins are aligned in the direction of flow; the locations
and number of holes can be changed as follows: single (1P), double (2P),
triple (3P), and five perforations (5P).
2. The shape of these perforations can be changed to square (3PS), and elliptic
(3PE).
3. Slotted pin fins (SPHSs) are aligned in the direction of flow, and the slot
height can be 3S, 6S, and 10S with constant slot width.
4. Notched pin fins (NPHSs) are arranged in the direction of flow, and the notch
height can be 2.5N, 5N, and 7.5N with constant notch width.

To reach the specified aims, this study is divided into five objective parts:

1. To design, fabricate, and examine experimentally the thermal airflow

characteristics of perforated and solid pin fin heat sinks to be used for active
air-cooling of electronic systems.
2. To investigate numerically the thermal airflow characteristics of solid and
perforated pinned heat sink devices in order to validate the CFD approach
against the experimental results.
3. To investigate numerically the thermal airflow characteristics of various
configurations of perforated, notched and slotted pinned heat sink devices to
demonstrate how the thermal airflow characteristics of these models enhance
pinned heat sinks compared with solid pin fins.
4. The optimal variable design of perforated and notched pinned heat sink
models are considered to achieve the multi-objective function that is
represented to minimise CPU temperature and fan power consumption and
select the optimum pinned heat sink design
5. Lastly, to consider the limitations in the application of pinned heat sinks
based on the pin density and the supplied heat flux for investigating the
capability of these pinned heat sink designs to be used in the desktop PC
CPU for waste heat dissipation. Furthermore, to evaluate the allowance level
of applied heating power on these pinned heat sink models.
 - 38 -

D= 2mm for each pin d= 1mm

for each perforation

0P-Solid Fin 1AP-One 1BP-One 1CP-One 2AP-Two 2BP-Two 2CP-Two 3P-Three 5P-Five
without Bottom Centre Top Hole Bottom Top Holes Separated Holes Holes
Holes Hole Hole Holes Holes

A- Circular Perforations – each holes has a diameter= 1mm and

each pin diameter=2mm

d= 1mm

h= 1mm, h= 1.5mm,
w= 1mm w= 1mm

3PC- Circular Holes 3PS- Square Holes 3PE- Elliptic Holes

B- Circular, Square, and Elliptic Perforations

h= 3mm,
h= 6mm, h= 10mm,
w= 1mm
w= 1mm w= 1mm

3S 6S 10S
C- Slotted Pin Fins, SPHSs

h= 2.5mm, h= 5mm, h= 7.5mm,

w= 1mm w= 1mm w= 1mm

2.5N 5N 7.5N

C- Notched Pin Fins, NPHSs

Figure 1.27: Different types of pin fins heat sinks

 - 39 -

Finally, the scope of the current work can be represented as shown in Figure
1.28.

Chapter 2: The principle concepts of convection heat transfer such as heat

transfer mechanism, velocity and thermal boundary layer, boundary layer
separation and hydraulic and thermal characteristics are explained.

Chapter 3: The fabrication steps, rig design, and apparatus of perforated & solid
PHSs are described. In addition, measurement devices and test procedures to
measure the significant characteristics for calculating thermal airflow
characteristics of those pinned HSs are explained.

Chapter 4: The main benefits of pressure drop, fan power, CPU temperature, &
heat transfer rate from using the new perforated PHS with multiple perforations
are investigated experimentally.

Chapter 5: The numerical simulation details for the PHSs are described. For
example, each of numerical solution procedures, boundary conditions,
assumptions, and the airflow and thermal characteristics (pressure drop, fan
power, Nusselt number, thermal resistance, and temperature base of heat sinks)
are explained.

Chapter 6: Evaluation of the thermal airflow characteristics of perforated heat

sinks to discover how these pin fins designs can reduce the hot spots inside the
heat sink and enhance airflow through it utilizing complementary experimental
and numerical simulation models. The optimum perforated PHS designs are
considered.

Chapter 7: The predicted CFD simulation of slotted and notched PHSs are
discovered in detail concerning their heat transfer and flow characteristics to
ensure how these pin fins designs can reduce the hot zones inside the heat sink
and enhance airflow through it compared with solid pin fins. The optimum
notched pin designs are described.

Chapter 8: In this section, the effects of pin density and applied heat flux are
considered based on the values of pressure drop, fan power, Nusselt number, &
CPU temperature of PHSs.

Chapter 9: The main conclusions and recommendations are explained.

Figure 1.28: The scope of the present thesis work

 - 40 -

2 Chapter Two: The Fundamental of Convection Heat

Transfer

2.1 Introduction

In this chapter, the basic concepts of fluid flow and heat transfer are illustrated.
The basic concepts are included the physical mechanism of convection heat transfer,
the types of fluid flows, the velocity and thermal boundary layers, and the boundary
layer separation. In addition, the hydraulic and the heat transfer characteristics of
heat sink that are investigated in the current study.

2.2 Physical mechanism of convection heat transfer

Heat transfer through fluids (liquids or gases) can be by conduction or

convection depending on the presence or absence of any bulk fluid motion. In the
case of bulk fluid motion, heat transfer occurs by convection, as shown in Figure 2.1
(a) and (b), while heat transfer occurs by conduction in the absence of bulk fluid
motion, Figure 2.1 (c).

In reality, convection heat transfer involves fluid motion and heat conduction.
Heat moves from a hot surface to an adjacent cooler fluid layer by conduction, and
then this heat transfers to the next cooler fluid layer by fluid motion, and so on.
Thus, the rate of convection heat transfer is much higher than that of by conduction,
(Cengel, 2006).

Figure 2.1: Physical mechanism of heat transfer from hot surface to cool
surrounding air by convection and conduction, (Cengel, 2006).
 - 41 -

The convection heat transfer, by experience, depends on the fluid properties

such as dynamic viscosity (µ), thermal conductivity (k), thermal capacity (Cp), and
density (ρ) and the fluid velocity (U). Furthermore, it depends on the geometry, solid
surface roughness and the type of fluid flow. Therefore, the heat transfer by
convection is a complex mechanism, (Cengel, 2006). The rate of convection heat
transfer increases with increasing temperature difference between a hot surface and a
cold fluid. This rate can be defined by Newton’s law of cooling:

Q̇conv = hAs (Ts − T∞ ) (2.1)

which relates the average convective heat transfer coefficient (h), the heat transfer
surface area (As), the surface temperature (Ts) and the ambient fluid temperature
(T∞).

2.3 The basic concept of fluid flow types

Since convection heat transfer is accompanied with fluid mechanics, the

common general categories of fluid flow are explained below to understand fluid
flow behaviour that effects the enhancement of convection heat transfer, (Cengel,
2006).

2.3.1 Viscous and Inviscid Flow

When the viscosity of a fluid is considered and its effects are significant due to
an internal resistance of a fluid to flow, that is called viscous flow. However,
inviscid flow is assumed no viscosity and its effects is very trivial in some flows and
can be ignored.

2.3.2 Internal and External Flow

If a fluid is forced to flow inside a channel, duct and pipe and it is confined
by a surface, this is called internal flow. However, external flow can be defined as
when fluid is forced over or around an object and without restriction by adjacent
surfaces of an object.

2.3.3 Compressible and Incompressible Flow

Certain gas flows involve substantial variations in the fluid density, and these
are known as compressible flows. For example, high-speed aircraft, rocket motors
and jet engines are relevant to compressible flow. Liquid densities are essentially
 - 42 -

considered constant and thus classified as incompressible flow. Air flows are also
commonly modelled as incompressible flow if the flow speed is sufficiently low.

2.3.4 Laminar and Turbulent Flow

If a fluid flows in parallel flow with smooth streamlines and orderly flow
without interaction between the fluid flow layers, this is called laminar flow. For
example, the flow with low speed and high viscosity such as oils. In contrast,
turbulent flows involve chaotic fluctuations in the local fluid velocity, resulting in
disruption between the fluid layers, and it is not an orderly flow. The process of a
laminar fluid flow that is becoming fully turbulent flow is called transient fluid flow.
Such flows occur at high speed and with low viscosity fluids such as air.

2.3.5 Natural and Forced Flow

Based on how the fluid moves, if a fluid is forced to flow inside or over a pipe
by a fan or a pump that is classified as forced fluid flow or forced convection, as
shown in Figure 2.1 (a). However, the buoyancy force effect is a response to a fluid
motion where warmer fluid (lighter fluid) rises up and cooler fluid (denser) goes
down; this is called natural convection (thermosiphon effect), as shown in Figure 2.1
(b).

2.3.6 Steady and Unsteady Fluid Flow

Steady flow is the type of fluid flow in which the fluid characteristics
(velocity, pressure, etc) at a point are independent of time. While, the unsteady flow
is the type of fluid flow in which the fluid characteristics (velocity, pressure, etc.) at
a point change with respect to time.

2.4 The concept of boundary layers

The concept of boundary layers is important to understand the convection heat

transfer between a surface and a fluid flowing over it. Velocity and thermal boundary
layers are described in this section.

2.4.1 Velocity Boundary Layer (δu)

Figure 2.2 shows the velocity boundary layer of fluid flowing over a flat plate.
The x-axis represents the fluid flow direction over the surface of a flat plate from the
leading edge of the plate, and the y- axis represents the normal flow direction from
 - 43 -

the plate surface. The velocity of fluid (V) at the leading edge of the plate in x-
direction is uniform velocity. It can be imagined that the fluid consists of many
adjacent fluid layers on top of each other. The velocity of the fluid particles in the
first layer next to the surface plate is zero due to the no-slip condition. This layer
then will affect the motion of the next adjacent fluid layer due to the friction force
between the fluid particles of these two neighbouring layer at different velocities and
this act to the fluid particles motion in the next layer, and so on until. The velocity
reaches the free-stream velocity (u∞) at a certain distance from the surface of the
plate. This distance is known as the boundary layer thickness (δu) and is defined as
the distance at which u=0.99u∞. The velocity boundary layer (δu) involves four flow
regions in which the fluid viscous: the fluid flow velocity is zero at the surface of flat
plate. The laminar sublayer (viscous sublayer) is a very thin layer above the flat plate
surface. The buffer layer is a layer just next the laminar sublayer and a flow begins
to develop to turbulent flow. The third region is the turbulent layer. The free stream
region is far away from the surface, where u=u∞, (Cengel, 2006).

Figure 2.2: The velocity boundary layer development on a flat plate surface,
(Cengel, 2006).

2.4.2 Thermal Boundary Layer (δth)

Figure 2.3 shows the thermal boundary layer of cool fluid flowing at a specific
uniform temperature (T∞) over a hot flat plate (Ts). The thermal boundary layer is
similar to the velocity boundary layer and the former will develop due to the
temperature difference between the fluid flow and the surface plate. The hot surface
of the plate will achieve thermal equilibrium with the fluid layer, adjacent to the
surface. The energy of the fluid particles will be exchanged with the particles of the
adjoining fluid layer, and so on. The temperature gradients of the thermal boundary
layer are represented by:
 - 44 -

(𝑇𝑠 − 𝑇) = 0.99(𝑇𝑠 − 𝑇∞ ) (2.2)

The thickness of the thermal boundary layer increases with increasing distance
from the leading edge in the flow direction, since the effects of heat transfer
penetrate farther into the fluid flow. The relation between conditions and the
convection heat transfer at any distance x from the leading edge are represented by
applying Fourier’s law at the interface between the solid surface plate and the fluid
layer as y=0:
𝑑𝑇𝑓 𝑑𝑇𝑠
𝑘𝑓 | = 𝑘𝑠 | (2.3)
𝑑𝑦 𝑦=0 𝑑𝑦 𝑦=0

where kf and ks are the thermal conductivity of fluid and solid flat plate, respectively,
(Incropera, 2011).

Figure 2.3: The thermal boundary layer development on an isothermal flat

plate surface, (Incropera, 2011)

2.4.3 Boundary Layer Separation

To understand the phenomenon of boundary layer separation, consideration

fluid flow around a cylinder is very important for engineering applications. For
example, shell-and-tube heat exchangers, bundle circular tubes heat exchangers,
circular pinned heat sinks, etc.

The upstream fluid velocity (V) around a cylinder and the free stream velocity
(u∞) that depends on the distance (x) from the stagnation point are considered, as
shown in Figure 2.4. The fluid velocity is equal to zero at the stagnation point (θ=0).
As the fluid flow accelerates due to the favourable pressure gradient (du/dx > 0 as
dp/dx < 0), the fluid flow reaches to the maximum value at dp/dx=0 and then it
decelerates due to the adverse pressure gradient (du/dx < 0 as dp/dx > 0), as shown
 - 45 -

in Figure 2.5. The fluid velocity gradient becomes zero at the surface when the fluid
flow decelerates, this point is called “separation point”. At this point, the momentum
of fluid is not sufficient to overcome the pressure gradient and the continued fluid
movement downstream is impossible. In addition, the oncoming fluid flow prevents
flow back upstream. Thus, boundary layer separation must happen. This is the main
reason the boundary layer separates from the surface and reversed flow and vortices
are formed just behind the cylinder at the downstream region, (Incropera, 2011).

Figure 2.4: Boundary layer separation on a cylinder and formations eddies in

the downstream region, (Incropera, 2011)

Figure 2.5: Velocity profile associated with pressure gradient and separation on
a cylinder, (Incropera, 2011)
 - 46 -

2.5 Hydraulic and Heat Transfer Characteristics

Airflow and heat transfer characteristics including Reynolds Number, pressure

drop, fan power, profit power factor, pressure drag coefficient, Nusselt number,
thermal resistance, average temperature base case heat sinks (CPU temperature),
temperature and velocity air distribution along pin fin heat sinks, are important
parameters, to evaluate pinned heat sinks designs, which can be obtained from the
ANSYS FLUENT post processing options. These factors are defined below.

2.5.1 Reynolds Number (Re)

Reynolds number is the ratio between inertial forces and viscous forces and is
defined as:

UDh
Re  (2.4)


Ac ( H .W )
Dh  4 2 (2.5)
p (H  W )

where U: the air inlet velocity, Dh: duct hydraulic diameter , ρ (kg/m3),and μ (kg/m.s)
are the density and viscosity of air. In the present study, the inlet velocities are varied
from 6.5m/s to 12m/s and the range of Reynolds numbers is 3500-6580.

2.5.2 Pressure Drop (ΔP)

Pressure drop (Pa) is defined as the difference in pressure between inlet and
outlet airflow of test section (heat sink).

P  Poutlet  Pinlet (2.6)

where ∆P is the pressure drop over the heat sink, and Pinlet, outlet are inlet and outlet
pressure of the airflow in the test section.

2.5.3 Fan Power (Pfan) and Profit Power Factor (J)

Fan power (W) is the required power to drive the air through the heat sink and
can be evaluated as Sparrow et al. (1980) and Yuan et al. (2012) by:

Pfan  UAc P (2.7)

 - 47 -

where Ac: cross sectional area of the flow passage of the heat sink =h.Sz.(N-1) (m2),
h: pin fins height (m), Sz: spacing between pins (m), N: number of pins in a row. In
this study, fan efficiency is assumed 100% (Yuan et al., 2012).

The profit factor (dimensionless) is another factor to compare between heat sink
designs (Yu et al., 2005)

Q
J (2.8)
Pfan
where Q: the applied heating power on the base heat sink surface (W).

2.5.4 Pressure Drag Coefficient (Pd)

It is dimensionless and used for the drag or resistance quantity of an object

against fluid flow and found as:

Pd= ∆P/0.5ρU2 (2.9)

2.5.5 Nusselt Number (Nu)

The Nusselt number of the pin-fins array is the ratio between the heat transfer
rates of convection and conduction. Previous researchers have calculated heat
transfer coefficient based on either the projected, AP, or total, AT, surface area of the
heat sink and these are related to one another via the relationship (Sara, 2003; Sahin
& Demir, 2008):

A 
hP  hT  T  (2.10)
 AP 
Qconv
hT  (2.11)
T  Tin
AT [Ts  ( out )]
2
where Qconv: power applied to the base (W), hT: the total heat transfer coefficient
(W/K.m2), hP: the projected heat transfer coefficient (W/K.m2), AT: total surface area
(m2), AP: projected surface area (m2)Ts: the upper surface of heat sink temperature
(oC), Tin, out: inlet and outlet air temperature (oC).

The Nusselt number (NuT) based on the total surface area of the pin-fins is:

hT . L
NuT  (2.12)
k air
 - 48 -

While the projected Nusselt number (Nup) based on the projected surface area of the
pin fins is:
hP . L
Nu P  (2.13)
k air
where L: length heat sink in flow direction (m), kair: is the thermal conductivity of air
(W/K.m).

2.5.6 Thermal Resistance (Rth)

The thermal resistance (K/W) of the heat sinks Rth is an object or material
resists to a heat flow through heat sink and it is defined by:

𝑅𝑡ℎ = ∆𝑇/𝑄̇ (2.14)

The temperature difference ∆T is defined as the difference between the average
temperature on the base (Tcase) and the inlet air temperature (Tin) (Jonsson &
Moshfegh, 2001).

2.5.7 Porosity (Ø)

The porosity of perforated pin fins has been calculated from the void volume
of perforations divided by the volume of solid pin fin:-

Vhole
Porosity ( )  (2.15)
V
where Vhole, is perforations, slots, and notches void volume, and V solid pin volume.
 - 49 -

3 Chapter Three: Experimental Methods

3.1 Introduction

This chapter focuses on two important elements of the work:

1. The description of the fabrication procedure of the heat sinks and the
integration of these heat sinks into a measurement section.

2. The equipment and test procedures to measure the significant characteristics

such as the local (inlet and outlet) air temperatures; variation of the upper and
lower heat sink surfaces temperatures; ambient air temperature: inlet and
outlet local pressure differences (pressure drop); and inlet air velocities for
calculating thermal and airflow characteristics of solid and perforated pin fins
heat sinks. These heat sinks are designed, fabricated, and tested during this
study.

The main goal of the experimental work is an investigation into the benefits of
pin fin perforations on the heat transfer and fan power in pinned heat sinks (PHSs)
for cooling electronics packaging. Experimental data is presented, for the first time,
on the benefits of using multiple perforations and the data used to validate a
corresponding Computational Fluid Dynamics (CFD) model of the conjugate heat
transfer problem in the Chapter 4.

3.2 Experimental Objectives

The principal objectives of the experimental work are:

1. Design solid (0P) and novel perforated pinned heat sinks (3P).

2. Fabricate the aluminium heat sinks.

3. Experimentally determine the forced convection conjugate heat transfer and

pressure drop for air flows over solid and perforated pin fin heat sinks.
 - 50 -

3.3 Heat Sink and Test Section Descriptions

Two types of aluminium heat sinks have been designed and fabricated; solid
and perforated pinned heat sinks (Figure 3.1) that can be supplied with a heat load of
approximately 24000W/m2 in line with Yuan et al. (2012) using a thin film heater.
As follows Zhou & Catton (2011), the pin fins have a circular cross-section of 2mm
and are spaced uniformly on the upper surface of an aluminium base plate of
50mmx50mmx2mm. The height of these pin fins is 10mm located on an 8x8 array
with a constant spacing between the streamwise and spanwise directions of 6.5mm.
The perforated pin fins have three perforations of 1mm diameter. These perforations
are aligned in the direction of the airflow and distributed up the length of the pins.
Pin designs were studied with both 0 and 3 perforations with corresponding different
porosity (ϕ=Vhole/Vpin) of 0, and 0.15 where Vhole, and Vpin are the perforations
volume and pin volume, respectively.
 - 51 -

A B

D
C

d=1

Three perforations for

each pin fin.
The distance between the
centres of these
perforations is equal at
2.5mm.

Figure 3.1: (A) Plan view, and (B) solid pin fins side view, (C) Plan view, (D)
perforated pin fins side view, and (E) 3D of the perforated pin fins heat
sink being analysed
 - 52 -

3.3.1 Heat Sink Fabrication

The aluminium heat sink consists of two main parts; (I) the base plate (II) pin
fins, as shown in Figure 3.2. The base plate of heat sink dimensions used in this
study are 50mm x 50mm and 2mm thickness for both types of pin fins; under study.
Each pin was cut from 2mm aluminium bar using a rivet cutter to a length of 12mm.

Two heat sinks have been designed and fabricated from aluminium, the first
one with solid pins (0P) and the second with perforated pins (3P). The fabrication of
heat sinks formed from 64 pin fins in 8x8 in-line arrangement with a constant
spacing between the pins in two directions; streamwise and spanwise of 6.5mm is
two stages. The first description is about the production of perforated pin fins and the
second stage describes the assembly into solid and perforated heat sinks.

Manufacture of perforated pins: Sixty-four solid pins have been drilled with
three perforations each of 1mm diameter with a constant centre to centre spacing
between these perforations of 2.5mm in a vertical direction of a pin to produce the
perforated pin fins (3P). To aid in the manufacture, a steel drilling guide was first
constructed with 3×1mm guide holes, Figure 3.3. To manufacture a single pin, the
aluminium bar was inserted until the end was flush with the guide outlet. Three holes
were then drilled using the guide to ensure the spacing and alignment of these holes.
Finally, the pins were cut to length using a rivet cutter.

Solid Pin
Aluminium Base Plate
50x50x2mm
Perforated Pin

Figure 3.2: Aluminium base plate with solid and perforated pin fins
 - 53 -

Three perforations
Ø≈1mm

Hole of ~2mm to
insert solid pin

Figure 3.3: Drilling jig for producing perforated pin fins

Forming the heat sinks: The second fabrication part is a manufacturing of solid
and perforated heat sinks. Two base plates were prepared by drilling 64 holes of
1.9mm diameter in which a pin fin can be inserted for each one through these holes.
The holes at the bottom of the base plate are countersunk to a depth of 1.5mm with
the widest diameter of 6mm, Figure 3.4. The main purpose of this is allowing the
brazing alloy to flow more easily around the pin fins inside those holes. Besides,
enlarging the soldering area gives a greater interaction between pin fins and the base
plate of the heat sink from a thermal perspective, as shown in Figure 3.5. This
minimises any resistance to heat transfer from the bottom of heat sink passes through
pin fins to the surrounding air. The individual pins were brazed onto a square
(50mm) base plate that was predrilled with a regular array of holes spaced on 6.5mm
centres. During the brazing process, a Fibre based heat resistant mat, Figure 3.6, is
used to hold and avoid any movement of the pin fins. After the brazing has been
completed, the bottom surface of the heat sink is smoothed and polished with emery
paper to avoid any extra material on the lower surface of the heat sink from the
soldering process.

With respect to the perforated pin fins, copper wires of 0.8mm diameter are
passed through the holes of perforated pins prior to assembly to ensure all these
perforations are aligned in the same direction of airflow as much as possible, as
illustrated in Figure 3.6. These wires were removed before testing.
 - 54 -

Countersunk
Fibre based Pin Fins Ø≈6mm

Figure 3.4: Inserting pin fins through holes of base plate with countersunk at
the bottom of the heat sink

Pin Fin

Base plate of
heat sink

Countersunk soldering area

Ø=6mm

Figure 3.5: Schematic drawing of soldering area at the base plate of heat sink

Perforated Copper wires

Pin Fins Ø ≈0.8mm

Figure 3.6: Preparing aligned perforations of perforated pins in flow direction

 - 55 -

The result of this work was two types of heat sink; solid and perforated pin fins
heat sinks each pin having 2mm diameter and 10mm height with 64 pins in-line
array (8x8) with a constant spacing between the streamwise and spanwise directions
of 6.5mm, as shown in Figure 3.7. The new perforated pin fins have 3 circular
perforations of 1mm diameter, distributed along each pin. This allows the effect of 0
and 3 perforations to be studied. To assess the quality of the brazing process, a cross
section was taken and imaged with a camera, as shown in Figure 3.8. In general, the
brazing produced a strong joint, although some occlusions were seen as indicated on
the Figure 3.8.

Solid pins (0P) (A) Three perforations per (B)

pin (3P)

Figure 3.7: Final design of (A) solid pin fins and (B) perforated pin fins heat
sinks

Pin Fins Air gaps & Soldering Defects

Heat Sink Base

Figure 3.8: Detection of pin fin soldering zones at the base of heat sinks
 - 56 -

3.4 Rig Description

The test rig is designed and manufactured to fulfil the requirements of the pin heat
sink test system as summarised below. The experimental apparatus is shown in
Figure 3.9 and consists of:

1. Airflow channel (channel section).

2. Heat sinks and test section descriptions.
3. Heating and control sections.
4. Measuring devices and traversing system.
These parts are designed and manufactured with care and fastened using
adhesive and some screws between composite parts of the test rig to prevent any air
leakage between the connected sections during operation.

3.4.1 Airflow Channel

An experimental rig that is designed and fabricated consists of a closed

rectangular channel with removable test section (heat sink). The heat sink sits tightly
within the channel ensuring no flow over the top of the pins or around the side of the
heat sink. This channel is constructed of clear Perspex of 8mm thickness and has a
rectangular internal cross-section of 50mm width, 10mm height, and 370mm total
length, as shown in Figure 3.10. The test section (heat sink) is located at the centre of
the straight airflow channel, a distance of 110mm from the upstream entrance to the
channel. This heat sink section is heated using an electrical thin film heater that is
attached immediately below the heat sink. The important elements of the
experimental approach include a miniature fan, a power supply, an anemometer with
a hot wire, a digital manometer, digital thermometers and several thermocouples as
explained below.

The ambient air is driven over the heat sink at different velocities by an axial-
flow fan. The dimensions of the miniature fan (model San Ace 36: 9GV3612P3J03)
are 36x36x28mm with the rate voltage at 12VDC and the turbulent airflow can be
obtained easily by rotating this fan with maximum volumetric airflow 0.00708m3/s.
The fan curve is shown in Figure 3.11. The fan is located at the inlet of the test
section and the air motion created by the fan flows into the converging test section.
The channel is equipped with tappings allowing the pressure drop across the heat
sink to be measured using a digital manometer and insertion points allowing the
 - 57 -

change in temperature of the air to be recorded via a digital thermometer. Metal

meshes are positioned at a distance of 50mm on either side of the heat sink to
minimise flow maldistribution and create uniform airflow profile over the heat sink.
Air is discharged by the miniature fan into the mini airflow channel and passes
through a flow straightener (metal meshes), test section and then discharged to the
atmosphere. Figure 3.12 shows the final assembly rig design test with three views.

1: Heat Sink 2: Mini Channel 3: Film Heater Resistance 4: Teflon Insulation

5: Miniature Fan 6: Thermocouples 7: Digital Thermometers 8: Hot Wire
9: Anemometer 10: Power Supplied 11: Pressure Taps 12: Digital Manometer

Figure 3.9: Overall rig design and experimental measurements system

 - 58 -

Figure 3.10: Schematic Drawing of Overall Experimental System

Figure 3.11: Typical performance fan curve (model San Ace 36:
9GV3612P3J03)
 - 59 -

Figure 3.12: Final assembly of rig design with three views

 - 60 -

3.4.2 Heating and Control Sections

The heat sink is heated using an electrical heater (50x50x0.2mm) uniformly

along at the lower surface of the heat sink to provide a uniform heat flux, Figure
3.13. The electrical heater mimics the heat generation a CPU of a personal computer.
A maximum allowed heat flux in this sort of CPU is 24000W/m2, Yuan et al. (2012)
via the electrical power supplied (Aim-TTi EX354RD, EX-R Series).

This electrical heater has been fabricated from two lengths of wire Nickel-
Chrome of 0.2mm that has been coiled around a mica sheet for obtaining uniform
constant heat flux along the heater. The heater dimensions have the same base heat
sink dimensions of 50mmx50mm with 0.2mm thickness to give a uniform heat flux.
Thermally conductive Epoxy was used between the heat sink and the thin heater to
avoid any electrical contact with thin heater resistance. The bottom and side surfaces
of the heater are insulated with Fibreglass and Teflon as isolator layers to minimise
the heat loss through these sides.

Heat Sink

Thermally Conductive
Epoxy

Thin Film Heater

Fibreglass
Insulation

Teflon Insulation
Container

Figure 3.13: Installation of the heat sink with film heater into insulation
container
 - 61 -

3.4.3 Measurement Devices

A Hot wire, thermocouples, and digital manometer are utilized in the present
experiments to measure the local (inlet and outlet) air temperatures; variation of the
upper and lower heat sink surfaces temperatures; ambient air temperature: inlet and
outlet local pressure differences (pressure drop); and inlet air velocities.

3.5 Experimental Measurements

3.5.1 Hot Wire Anemometer

The hot wire anemometer (HHF2005HW) is located at the inlet of the channel
to measure inlet air velocity, Figure 3.9. The head of this device consist of a very
thin wire that is connected between two supports for local air velocity (hot wire) and
a second sensor is for the local air temperature. The resolution of device is 0.1m/s for
0.2 to 20m/s inlet airflow velocity.

3.5.2 Thermocouples

Type K thermocouples of 0.2mm diameter are used to measure the top and
bottom surface of the heat sink. The operating range of this type of sensor is from
-75oC to 250oC with very fast thermal response measurements.

The thermocouple at the back surface of the heat sink is fixed by an adhesive
material and used to measure the temperature of the heat sink. In a real world
application that is equivalent to CPU temperature (Tcase). The thermal resistance (Rth)
of solid and perforated pin fin heat sinks is also calculated. The thermocouple at the
upper surface of the heat sink is used to measure the mean temperature of the upper
wall to determine the heat transfer coefficient, the heat transfer rate, and the Nusselt
number. At the same time, other thermocouples are placed at the inlet and outlet of
the mini channel to measure the local air inlet and outlet temperature to find the
average bulk mean temperature (Tm). At this temperature (Tm), the values of the
thermo-physical properties of the air are known from tabulated data of Cengel
(2006).
 - 62 -

3.1.1 Digital Manometer

A digital manometer (2083P Digitron) is used in the experiments to measure

pressure at a specific point or a differential pressure of airflow through the test
section, heat sinks (Figure 3.9). Fan power and pressure drag coefficient are based on
pressure drop that is measured via the digital manometer. Two pressure taps are
located in front of and behind the test section to measure the airflow pressure drop
(∆P) with 0.1% as full-scale accuracy reading.

3.6 Experimental Procedure and Measurements

Several experimental parameters are measured such as the temperature,

velocity, and pressure drop to study the heat transfer and flow characteristics of solid
and perforated pin fins heat sinks. For each heat sink, four ranges of inlet air velocity
flow (6.5, 8, 10, and 12) m/s and constant heat flux (20000W/m2) are used.
Furthermore, repeatability tests are conducted to detect the influence of any noise
sources on the heat transfer and pressure drop. Thus, each experiment is repeated
three times under the same conditions for both solid and perforated pin heat sinks.
Figure 3.14 shows the repeatability tests of pressure drop and the CPU temperature
with varying inlet air velocity. It is observed that the deviation of these measured
values is less than 2% for both heat sinks models. Generally, 24 experimental runs
(four different velocities for two types of heat sinks, each repeated three times) are
carried out to ensure repeatability.

120 85
3P Exp.1 3P Exp.1
110 3P Exp.2 3P Exp.2
3P Exp.3 80 3P Exp.3
100
0P Exp.1 0P Exp.1
90 0P Exp.2
0P Exp.2
75 0P Exp.3
0P Exp.3
Tcase,ave (oC)

80
∆p (Pa)

70 70

60
65
50

40
60
30

20 55
6 7 8 9 10 11 12 13 6 7 8 9 10 11 12 13
U (m/s) U (m/s)
Figure 3.14: Repeatability of pressure drop and CPU temperature with variation
inlet air velocity for solid (0P) and perforated (3P) pin models
 - 63 -

3.6.1 Experimental Procedure

For a specified type of heat sink, the following procedure is applied for
conducting the experiments,
1. Check digital Manometer for the two taps and hot-wire anemometer at
entrance test section have zero readings before an operation.
2. Switch on the fan to pump the air through the mini test section.
3. The power supplied (Voltage and Amp) is adjusted for the required input
power to the film heater resistance and fan.
4. To achieve a steady state condition, the temperature difference between the
previous and the new reading is approximately zero. Thus, the system is left
for 20mins, as shown in Figure 3.15.
5. Finally, record the pressure drop, upper and lower surfaces temperature of the
heat sink and supplied power after the test reaches a steady state condition.
To check the repeatability, a set of tests were represented three times to ensure
that the variation in the experimental measurements recorded for the same parameter
and under the same conditions is small.
During each experimental run, the following measurement readings are recorded:

1. The local upper surface temperatures of heat sinks (Ts) are recorded via the
outputs of thermocouples type K.
2. The local lower surface temperatures of heat sinks (Tcase) are recorded via the
outputs of thermocouples type K.
3. The inlet and outlet air bulk temperatures (Tin, Tout) are the readings of two
thermocouples at the entrance and the exit of the mini heat sink.
4. The surrounding air temperature (Tair).
5. The thermocouples readings are recorded after 20mins via the digital
electronic thermometer the final set of steady state readings are then
recorded.
6. The pressure drop of the test section (∆P) is recorded using the digital
manometer.
7. The inlet air velocity (U) through the mini test channel is measured using a
hot-wire anemometer.
8. The inlet air velocity is confirmed every 5mins to be sure that this is constant
during testing.
 - 64 -

70
65
60
55
50

Tcase (oC)
45
40
35 3P model

30 0P model
25
20
15
0 3 6 9 12 15 18 21 24 27 30 33 36
Time (mins)
Figure 3.15: Time evaluation of Tcase for 0P and 3P heat sinks models at
Re= 5393. Steady state is reached after 20mins
 - 65 -

3.7 Experimental Data Analysis and Calculations

The experimental data recorded for the temperature, pressure, current, and
voltage are used for the following heat and fluid flow analyses and the experimental
uncertainty analysis is considered, as shown in Appendix B.

3.8 Hydraulic Characteristics Analysis

An important quantity in the flow analysis of pin fins heat sinks is the pressure
drop (∆P) along the test heating section in the direction of flow. The pressure drop is
directly related to the power requirements of the pump to maintain the flow, (Cengel
2006; and Incropera 2011) and the pressure drag coefficient. The pressure drop is
measured to calculate the fan power, Pfan and pressure drag coefficient, Pd these
parameters define the consumed energy for solid and perforated pin fin heat sinks
and allow the assessment of designs from an energy consumption perspective, see
section 2.5.2. The mechanical fan power (Pfan) and pressure drag coefficient (Pd) are
defined in sections 2.5.3 and 2.5.4.

3.9 Heat Transfer Analyses

Heat transfer rate, Nusselt number, the average temperature of the base heat
sinks, and the thermal resistance of heat sink are measured experimentally. These are
defined below.

3.1.2 Heat Transfer Rate

The steady-state rate of heat transfer can be expressed as follows:

Q conv  Q elec  Q rad  Q losses (3.1)

where Q elec refers to the total heat applied on the base of the heat sink and is
calculated from the electrical potential (V) and electrical current (I):

Q elec  IV (3.2)

Q rad , Q losses are the heat transfer rate from the heat sink by radiation and thermal
losses, respectively.
 - 66 -

The total steady-state rate of radiative heat transfer loss ( Q rad ) from the test section
is evaluated from Naik et al. (1987):


Q rad   F AT Ts4  Ta4  (3.3)

For the typical condition of the view factor (F) that can be found for the effect of fins
array geometry and emissivities between the fin material and the bounding
environmental surfaces, the Stefan-Boltzmann constant (σ=5.67×10-8W/m2.k4), the
total wetted surface area of pinned heat sin (AT), the upper surface temperature of the
heat sink (Ts), and the surrounding air temperature (Ta) (Naik et al. 1987). The pin
fins and base plate of the heat sink are made of highly polished aluminium to reduce
their emissivities (ɛ=0.05) and the experimental data of the present work showed that

Q rad / Q elec  0.002. Therefore, Q rad is neglected in the results presented in the next
chapter.

The thermal losses ( Q losses ) include the conductive and convective heat losses
through the insulations and channel walls are given by:

Q losses U overall. A.(Tw  Ta ) (3.4)

where A is the heat sink base area, Uoverall is the heat transfer coefficient losses, ∆T is
the temperature difference between the bottom surface of heat sink temperature (Tw)
and the surrounding air temperature (Ta). These losses are minimised by ensuring
that all the outer walls of the heat sink are well-insulated and thermocouple readings
of the heat sink outer wall temperatures are close to the ambient temperatures that

caused the thermal losses, which are estimated to be Q losses / Q elec  0.02 and can

therefore be neglected.
Therefore, it can be assumed with some confidence that the last two terms of
Eq. (3.1) may be ignored.

The heat transfer rate from the heat sink by convection ( Q conv. ) can be deduced as,
Sara (2003):

 T T 
Q conv  hT . AT Ts   out in  (3.5)
  2 

Hence, the average convective heat-transfer coefficient (hT) based on the total wetted
surface area (AT) can also be expressed via:
 - 67 -

Q conv
hT  (3.6)
T T
AT [Ts  ( out in )]
2

where Ts is the upper surface of heat sink temperature, Tin and Tout are the average
inlet and outlet air temperatures, respectively, and AT is the total surface area of the
heat sink.

According to previous researchers, the average heat transfer rate (have) has
been calculated based on either the projected, AP, or total, AT, total wetted surface
area of the heat sink and these are related to one another via the relationship
hP=hT(AT/AP). Thus, these two areas can be related to each other by:
Total wetted area = Projected area + Total surface area contribution from the pin
fins

For solid pin fins:

AT  W .L  N .( .D.H ) (3.7)

For perforated pin fins

d
AT  W .L  N [( .D.H )  (2 .n.( ) 2 )  ( .n.D.d )]
2
(3.8)
1
AT  W .L   .N [( H .D)  ( n.d 2 )  (n.d .D)]
2

where (W, L) are the width length of the base plate heat sink, (N) the total number of
fins, (H) the height and (D) the diameter of the fins and (d) the diameter of the fin
holes, and (n) the number of perforations, respectively.

The Nusselt number (Nu) and thermal resistance (Rth) are determined as per
sections 2.5.5 and 2.5.6.

In all the experimental calculations, the values of the thermo-physical

properties of the air are specified from Cengel (2006) using the average bulk mean
temperature (Tm), which is:

Tm  (Tin  Tout ) / 2 (3.9)

 - 68 -

3.10 Summary

In this chapter, the design and fabrication of two types of aluminium heat
sinks, solid (0P) and perforated (3P) pinned heat sinks and the integration of these
heat sinks into a test section are described. The measurement devices and test
procedures to measure the significant characteristics for calculating the crucial
thermal and airflow characteristics for solid and perforated pin fins heat sinks such
as heat transfer rate, Nusselt number, CPU temperature, and thermal resistance are
also described. The experimental uncertainty analysis is considered, as shown in
Appendix B.
 - 69 -

4 Chapter Four: Experimental Results

4.1 Introduction

In this chapter, the main characteristics of using new perforated pin heat sinks
with multiple perforations for cooling electronic components system are considered.
Two experimental heat sinks were designed and fabricated, one with solid pins (0P)
without perforations and another one with triple perforated (3P) pin heat sinks
(Chapter 3), to appraise the effect of perforated pin fin design on the thermal airflow
characteristics of those heat sinks, such as pressure drop, fan power, pressure drag
coefficient, CPU temperature, thermal resistance, and the total and projected Nusselt
number to be determined. The inlet velocities from 6.5m/s to 12m/s for the range of
Reynolds numbers are 3500-6580 and the mini-duct hydraulic diameter with 8x8 in-
line pin array at constant longitudinal and transverse distance is 6.5mm.

4.2 Hydraulic Characteristics

The effect of the perforated pinned heat sink design (3P) on the airflow
characteristics are compared with the solid pin fins (0P) in this section. The main
characteristics of airflow are measured pressure drop (∆P), calculated fan power
(Pfan), and pressure drag coefficient (Pd).

Figures 4.1A and 4.1B show experimental measurements from the effect of
perforations on the pressure drop, ΔP, across pinned heat sinks (PHSs) and the
power required to overcome the pressure drop.

Data are presented for the two models, the solid pin fins and the 3P once with
three perforations. The pressure drop and fan power consumption data in Figures
4.1A and 4.1B show that the perforations reduce ΔP and Pfan throughout the velocity
range. The main reason for that is the dead thermal-flow regions created just behind
the solid pin fins. In other words, those regions mean a hotter area and lower air
movement relative to other regions for the same test section. This leads to the
pressure drop and the fan power of the solid pin fin heat sinks increasing due to flow
separation and air recirculation; evidence for this will be provided in Chapter 5,
 - 70 -

where the numerical prediction will be presented. The perforations reduce the
pressure drop and fan power of the heat sinks. This is because a part of the frontal
area of the pins is removed, which allows an amount of airflow to pass through these
perforations (Alam et al., 2014a).

In the experimental data, the pressure drop and fan power consumption seen
with three perforations is typically around 7% smaller than that of the solid pin fins.

0.5
113
(B)
3P Exp. (A) 0.45 3P Exp.
103
0P Exp. 0.4 0P Exp.
93
0.35
83 Fan Power (W)
∆P (Pa)

0.3
73
0.25

63
0.2

53 0.15

43 0.1

33 0.05
6 7 8 9 10 11 12 13 6 7 8 9 10 11 12 13
U (m/s) U (m/s)

Figure 4.1: Effect of pin perforations on (A) pressure drop and (B) fan power as
a function of airflow speed

Figure 4.2 shows the effect of the perforated pinned heat sink model (3P) on
the pressure drag coefficient, Pd, for a range of inlet velocities from 6.5m/s to 12m/s
at Re=3500-6580 and 8×8 in-line pins with longitudinal and transverse distance of
6.5mm.

Following previous authors, e.g. Ismail (2013) and Ismail et al. (2013), the
drag force on the air due to heat sinks can be expressed in terms of a pressure drag
coefficient. The pressure drag coefficient associated with the perforated pins is lower
than that of the sold pins. For example, the Pd of the solid PHS is 1.33 while it is
reduced to 1.27 when using the perforated PHS at 10m/s. Overall, the Pd of the
perforated PHS is 7% lower than that of the solid pin fins model. The major reason
for this is that the frontal area of the perforated pins (3P) is smaller than that of the
 - 71 -

solid pins (0P) and so some airflow can easily pass through these perforations.
Generally, these benefits increase with increasing air velocity.

As a result of airflow parameter studies in this section, the amount of energy

spent to achieve a certain flow is reduced due to perforations. Thus, the perforations
are a useful technique for reducing fan power consumption. The second
characteristic (fan power) that also must be met is the ability to remove heat; this is
studied in the next section.

1.6
3P Exp.

0P Exp.
Pressure Drag Coefficient

1.5

1.4

1.3

1.2
3000 3500 4000 4500 5000 5500 6000 6500 7000
Re

Figure 4.2: Effect of pin design and inlet air velocity on the pressure drag
coefficient
 - 72 -

4.3 Heat Transfer Characteristics

The heat transfer characteristics such as the total and projected Nusselt
number, NuT, NuP, the CPU temperature (Tcase), and thermal resistance (Rth) of the 3P
pinned heat sink design (3P) are described and compared with those of the solid pin
(0P) fins.

4.3.1 Average Nusselt Number

Since the overall design goal for PHSs is to achieve a high heat transfer rate at
the minimum energy cost, Figure 4.3 presents the corresponding experimental
measurements of the Nusselt number, based either on the total wetted surface area of
PHS (NuT) or on the projected surface area (NuP), the base surface area of HS. The
latter is perhaps a more effective measure of cooling capacity for a given PHS size.

The data show that both NuT and NuP increase approximately linearly with the
inlet air velocity and that the 3P pin fins design achieves a significant enhancement
in heat transfer, with NuT and NuP typically 5% and 11% larger than that of the solid
pin fins for experimental data, respectively.

380 1000
(A) (B)
3P Exp. 950 3P Exp.
360

0P Exp. 0P Exp.
340 900

320 850
NuP
NuT

300 800

280 750

260 700

240 650

220 600
3000 3500 4000 4500 5000 5500 6000 6500 7000 3000 3500 4000 4500 5000 5500 6000 6500 7000
Re Re

Figure 4.3: Effect of inlet velocity on Nusselt number based on (A) total and (B)
projected surface area
 - 73 -

4.3.2 Thermal Management of PHSs

A key issue in the thermal management of electronics packaging is to ensure

that the CPU temperature, Tcase, for typical desktop computers is kept below the
critical temperature of approximately 85oC (Gurrum et al., 2004; Yuan et al., 2012)
at the minimum energy cost. The major aim of thermal management is to illustrate
the benefits and thermal reliability of the perforated pinned heat sink design on the
thermal management of a typical CPU. Figures 4.4 and 4.5 show the following
experimental measurements: the average base plate temperature, Tcase, and thermal
resistance, Rth, with fan power for 6.5m/s≤U≤12m/s, through a system of 8x8 pins, a
pin pitch of 6.5mm.

These figures confirm that the improved heat transfer with perforated pins
leads to a desirable effect of reducing base plate temperatures and thermal resistance.
For example, Tcase of the 3P model with three perforations reduces from 72oC to
58oC while it only reduces from 77oC to 61oC for the solid pins (0P) with increasing
fan power. This improved heat transfer from the perforated pins (3P) leads to
significantly lower CPU temperatures for the same fan power input compared with
the solid pins (0P). In the experimental data, the Tcase with three perforations is
typically around 6% (nearly 5oC) smaller than for the solid pin fins. The potential
sources of experimental errors are attributed to some practical considerations. One of
the possible areas where errors could arise is around the additional thermal resistance
as a result of the brazing process, see section 3.3.1.

As a result of thermal and airflow parameter studies, the amount of energy that
is spent by a fan which is used to cool the perforated pin fin heat sink (3P) with three
perforations is less than that required for the solid pins model. Thus, the perforations
are a useful technique for reducing fan power consumption and CPU temperature.
 - 74 -

80

3P Exp.
75
0P Exp.

70

Tcase ( C)
o 65

60

55
0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Fan Power (W)
Figure 4.4: CPU temperature variation with fan power for 0P and 3P heat sinks

1.2

3P Exp.
1.1
0P Exp.

1
R th (K/W)

0.9

0.8

0.7
0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Fan Power (W)
Figure 4.5: Experimental results of influence of fan power on Rth

The pin fin design can be optimised by maximising the heat transfer rate for a
given fin weight or by minimising the weight for a specified heat transfer rate has
been considered by Shaeri & Yagoubi (2009). For example, each perforation reduces
the weight of the pin by 5%. Accordingly, the CPU temperature, heat transfer,
pressure drop and fan power benefits of the pin with three perforations are achieved
with the additional benefit of a 4% the total reduction in pinned heat sink weight.
 - 75 -

4.4 Conclusion

Heat transfer of the solid pinned heat sink (0P) is lower compared with that of
the perforated pins (3P) because hot or dead regions are created behind those solid
pin fins as a result of the flow separation and poor air recirculation at these hot
zones. Thus, to avoid this problem, perforations could be added to accelerate flow
and reduce the dead zones. These perforations substantially improve the heat transfer
rate at the hot zones while at the same time reducing the pressure drop through the
pinned heat sink and the fan power needed to pump the air through it as well, as
detailed in Table 4.1. The perforations allow some of the airflow to pass through
them and mix well with the primary flow to create a larger amount of mixing and
turbulence, in addition to reducing PHS weight considerably. Furthermore, the
enhanced heat transfer due to perforations leads to considerably reduced processor
temperatures, a key goal of the thermal management of electronics.

Table 4.1: The experimental enhancement of Nusselt number (Nu), fan power
(Pfan), and CPU temperature (Tcase) of the 3P heat sink compared to the
solid pinned heat sink

Parametric Studies Nusselt Number

↑ AT ↓ Pfan ↓ Tcase
Heat Sink Design (W) (oC)
↑ NuT ↑ NuP
Experimental Perforated Pins with
15% 5% 11% 7% 6%
Three Perforations (3P)
 - 76 -

5 Chapter Five: Numerical Methods

5.1 Introduction

In this chapter, the numerical methods for simulating thermal airflows through
pinned heat sinks (PHSs) are described. The conjugate heat transfer model with
turbulent airflow is used to simulate this kind of heat sinks via commercial ANSYS
FLUENT 14.5 CFD code. Furthermore, each component of the numerical solutions,
boundary conditions, assumptions, and airflow and thermal characteristics of pinned
heat sinks calculations such as pressure drop, fan power, Nusselt number, thermal
resistance, and temperature base of heat sinks are explained. Finally, the test
numerical approaches such as domain verification and code validation of pinned HSs
are investigated.

5.2 Numerical Modelling Overview

During recent decades, both in-house and commercial CFD codes have become
ever more powerful. In addition, complex heat transfer and fluid flow problems can
be solved using these method. CFD analyses consist of three important processes:

1. Pre-processing: this is the first step where the geometry and grid mesh are
generated, and the boundary conditions are set.
2. Processing or Solver: in this step, the governing equations are solved.
3. Post-processing: the final step includes a presentation the results, graphics,
animations, plots, analyses and full reports that are created.

5.3 Numerical Simulation

CFD is now used to study the effect of pin perforations on the enhancement of
heat transfer rate and reduction in pressure drop (Shaeri & Yaghoubi, 2009; Shaeri &
Jen, 2012) the latter having a direct benefit on the associated power required to drive
the cooling air through perforated plate heat sinks, which is given by the product of
the flow rate and the pressure drop. ANSYS FLUENT-CFD software program is
selected to investigate numerical analysis of the heat sink models.
 - 77 -

This program uses the finite volume method (FVM) to solve the governing
equations. The Navier-Stokes equations combined with the continuity equation and
the energy equation in three dimensions are solved by FVM to show the dynamic
airflow and heat transfer around the pinned heat sinks (PHSs). The continuity
equation is satisfied using the Semi-Implicit Method for Pressure Linked Equations
(SIMPLE). Second order upwind discrimination schemes are used in the calculations
to reduce the numerical errors for the Navier-Stokes equations and the energy
equation (Versteeg & Malalasekera, 2007).

As mentioned earlier, each model consists of three parts: the entrance section is
a first part as a smooth duct, which has enough length to provide a fully turbulent
flow condition. The pinned heat sink (test section) that has 8 symmetric Aluminium
pins follows the first region, as the second part. The final section is the exit one that
comes after the test section and is long enough to prevent any feedback of boundary
condition into the test section. Each those parts have the same cross-section at
(6.5x10)mm. The air passes through all these three regions for different Reynolds
number range.

In the current numerical study, many heat sinks configurations are investigated
and the optimum model giving the lowest pressure loss and the highest heat transfer
(lowest CPU temperature) can be determined. These configurations are: circular
perforated pin fins; slotted pin fins; notched pin fins heat sinks; as well as different
types of perforations shape such as square, and elliptic perforations, Figure 1.27.

5.4 Pre-processing (Mesh Generation)

The set mesh volume elements are Tetrahedron Hyper cells and the type is Hex
Core T-grid to generate grids for all the heat sink models, including the complex
geometry of pinned heat sinks and the entrance and exit regions set as a Hexahedral
mesh type due to a straight and simple shape of those regions (Seyf & Layeghi,
2010; Nabati, 2008), as show in Figure 5.1. Both those types of mesh generation are
suitable for pinned heat sinks to reduce the time to reach a converged solution, and
save the memory of a computer (Chaube et al., 2006). After that, refining meshing
step is important for some critical area such as no-slip walls condition, the spaces
between the pins, perforations, slots, and notches zones that are included in those
 - 78 -

pinned heat sinks to ensure appropriate convergent solution because of the high
velocity and temperature supposed to be for heat sinks. Besides, the change of the
temperature, the velocity, and the pressure drop through pin fins heat sink are very
important in this study. Therefore, a large number of nodes are focused around
curved pin surfaces, perforations, slots, notches that are created in the test section.
Thus, the y+, which is the distance from a wall to the cell centres of the first grid
layer nearest to the wall, has a value approximately equal to 1 or less than 1 for cells
adjacent to these surfaces for SST k-ω turbulent model, as shown in Figure 5.2.
Furthermore, this grid independence is always verified that will be discussed
hereafter.

Tetrahedron Hyper
Mesh

Hexahedral Mesh

Dense grid near the solid

faces

Figure 5.1: Mesh generation for pinned heat sink

 - 79 -

0P heat sink

y+ (dimensionless)

3P heat sink

10S heat sink

Figure 5.2: y+ contour values for solid (0P), perforated (3P) and slotted (10S)
pinned heat sinks
 - 80 -

5.5 Numerical Solution (Processing)

The thermal air flows are modelled as three-dimensional, steady state,

turbulent airflow, with constant heat flux at the bottom of heat sinks and a k-ω SST
model, following Zhou & Catton’s (2011) CFD study of solid pin fins, and is used to
investigate airflow, pressure drop, and heat transfer through all PHSs models.

5.5.1 Turbulent Airflow Model

Several previous studies have used the Reynolds-Averaged Navier-Stokes

(RANS) equations to model turbulent flow through heat sinks successfully (Anandan
& Ramaligam, 2008; Naphon & Klangchart, 2011). RANS models consider the
turbulence fluctuation by splitting the velocity into a mean value plus fluctuation,
then time averaging the terms of the Navier –Stokes equations. Thus, this method
can be solved for the turbulent flow in the CFD methods and it is the most
commonly used in practical application (Versteeg & Malalasekera, 2007). Time-
averaging the continuity, momentum and energy equations with variables
decomposed into mean and fluctuating components leads to the Reynolds-Averaged
Navier-Stokes (RANS) equations, namely:


 .U  0 (5.1)
t
 U 
t

 .U U  .   U 'U '  (5.2)


where    p I   U  U 
T
 and  U 'U '   U  U   2 3(k I ) are the
t
T

Newtonian and Reynolds Stress tensors respectively, μ is the air viscosity, ρ its
density, U and U ' the average and turbulent fluctuation velocity vectors
respectively, P is the pressure, k turbulent kinetic energy and I the unit tensor. The

RANS equations are solved with the energy equation for the temperature field, T,
with a power source 𝑄̇ Watts, as is illustrated previously, using the following
equation

C p T f  C p t  
  U .(C p T f )    k  T f  Q (5.3)
t  Prt 
where Cp is the specific heat capacity of the air, Pr and ν are the Prandtl number and
 - 81 -

kinematic viscosity of the air, respectively and the subscript t indicates their
turbulent counterparts.

Following Zhou & Catton (2011) and Leung & Probert (1989), the thermal
airflow through the PHS is modelled using the k-ω SST model with automatic wall
function treatment. The radiation heat transfer rate is neglected as explained
previously in the experimental method Chapter 3. This model combines the accurate
formulation of the k-ω model in the near-wall region with the free-stream
independence of the k-ε one in the far field, and has been shown to predict highly
separated flows accurately in a number of previous validation studies, see e.g. Zhou
& Catton (2011), Anandan & Ramaligam (2008), Ndao et al. (2009), Shaeri &
Yaghoubi (2009b), Chaube et al. (2006).

The equations for the SST model are:

( k )
 .( kU )  Pk   * k  . (    k  t ) k 
~
(5.4)
t

( )
 .( U )    S 2     2  .(      t )   2(1  F1 )   2 k.
1
t 
(5.5)

where the blending function F1 is defined by

   k 500  4   2 k  
4

  
F1  tanh  min max  * , 2 ,
 C D y 2   (5.6)
 
    y y     
 k  
 1 
in which C Dk  max  2   2 k .  ,10 10  (5.7)
  
the turbulent eddy viscosity is computed from

a1 k
t  (5.8)
max( a1 , S F2 )

where S is the invariant measure of the strain rate and F2 is a second blending
function defined by

 2

  k 500  
F2  tanh  max 2 * , 2   (5.9)
     y y   
 
 - 82 -

To limit the build-up of turbulence in stagnation regions, a production limiter is used

in the SST model.

ui  ui u j  ~
Pk  t
x j

 x



  Pk  min Pk ,10  *  k   (5.10)
 j xi 

The empirical constants turbulent model for this model are, Zhou & Catton (2011):

5 3
 *  0.09, 1  , 1  ,  k1  0.85,    0.5,  2  0.44,  k 2  1,   2  0.856
9 40 1

5.5.2 Conjugate Heat Transfer Model

Heat sinks are simulated using a conjugate heat transfer model. The rate of
heat conduction passes through solid material of pin fins heat sink is balanced with
convection heat transfer from material of heat sink into moving air stream through a
coupled boundary condition at the solid/fluid interface, (Kraus, 2002) as illustrated
in Figure 5.3.

The energy equations in the fluid and solid domains are given by:

 C p t 
U(C pT f )    k f  T f For the fluid domain (5.11)
 Prt 

(k s Ts )  0 For the solid domain (5.12)

where U is fluid (air) velocity; Tf and Ts are fluid and solid temperature, respectively;
μT, PrT, kf and ks are the turbulent viscosity, the turbulent Prandtl number, the
thermal conductivity of the fluid and solid, respectively.

Pin Fin Heat Sink

Cool Inlet Flow Hot Outlet Flow

Conjugate Heat Transfer

Constant Heat Flux

Figure 5.3: Conjugate heat transfer model of pin fin heat sink
 - 83 -

5.5.3 Solver Settings

A commercial finite volume method (FVM) based code is used which employs
the SIMPLE method for the continuity equation in which the velocity components
are first calculated from the Navier–Stokes equations using a guessed pressure field.
The fully coupled momentum and energy equations are solved, using second order
upwinding to reduce the numerical errors for the Navier-Stokes equations and the
energy equation. Computation is started first by solving the continuity, momentum, k
and ω equations to determine the airflow field and then the energy equation to find
the thermal field in the computational domain. Following previous studies such as
Zhou & Catton (2011) and Yuan et al (2012), the procedure continues until the sum
of the residuals of continuity and momentum equations is less than 10-4 and for
energy equation is taken smaller than 10-6 in each cell.

The numerical data is considered at constant and variable thermodynamic air

properties. For constant thermodynamic air properties, they are equal to those at the
inlet temperature of 25oC. However, for variable air properties such as viscosity,
density, thermal conductivity and specific heat capacity vary with temperature
through the test section, as shown in Table 5.1. Thus, the air temperature variation
inside the heat sink is significant to highlight the effect of air properties on thermal
and airflow characteristics of pinned heat sinks when comparing with experimental
results and it cannot be disregarded when temperature changes through heat sink. It
can be chosen among different methods to compute the corrected air properties. A
piecewise-linear interpolation method is selected to define the properties values
(Yuan et al., 2012) that are considered in this study at several air temperatures based
on the following function of temperature:

  
 (T )  m   m1 m T  Tm  (5.13)
 Tm1  Tm 

where 1≤ m≤ M and M is the number of segments. ANSYS FLUENT-CFD code will

calculate the property values by linearly interpolating among the values defined.
 - 84 -

Table 5.1: The variation of air properties with increasing air temperature,
Cengel (2006)
Dynamic Thermal
Air temperature Density Specific Heat
Viscosity Conductivity
(oC) (kg/m3) (J/kg.K)
(kg/m.s) (W/m.K)
15 1.802 × 105 1.225 0.02476 1007
25 1.849 × 105 1.184 0.02551 1007
45 1.941 × 105 1.109 0.02699 1007
60 2.008 × 105 1.059 0.02808 1007
80 2.096 × 105 0.9994 0.02953 1008
100 2.181 × 105 0.9458 0.03095 1009
120 2.264 × 105 0.8977 0.03235 1011

5.6 Boundary Conditions

Fluid flow and heat transfer for problems require suitable boundary conditions
(BCs). Therefore, in this study, the boundary conditions for the present problem are
assumed below, as shown in Table 5.2 and Figure 5.4.

5.6.1 On the Pins

The rejected heat conduction rate through the aluminium pins heat sink is
balanced with the gained heat transfer convection into the moving air stream through
a coupled boundary condition at the solid/fluid interface. In other words, each pin fin
has two BCs: the one is a fluid surface that represents fluid flow and another one is a
solid surface as a material of pin fin heat sink itself that is known as conjugate heat
transfer.

5.6.2 At the Bottom Wall of the Heat Sink

A constant heat flux is applied at the bottom wall of the heat sink. No slip
condition is applied so the velocity of fluid (air) is zero in all directions,
Ux=Uy=Uz=0 due to a rigidity wall heat sink.

5.6.3 At the Inlet Side

The inlet air velocity is set to a series of values as Ux=6.5, 8, 10, and 12m/s
and Uy=Uz=0, such as Yang & Peng (2009a), Yang & Peng (2009b), Kumar &
Bartaria (2013), Zhou & Catton (2011). In addition, the inlet fluid temperature (Tin)
is constant at 25oC. The turbulence intensity of the flow entering through the inlet
 - 85 -

boundary is set to 5% (Zhou & Catton, 2011). The range of Reynolds number for
heat sinks in the most industrial electronic applications cooling varies from 1300 to
50000 (Ventola et al., 2014). Thus, Re is varied from 3500 to 6580 as a turbulent
airflow in this study to reduce consumption fan power and the noise level to
desirable levels, particularly in the office or home.

5.6.4 At the Outlet Side

The outlet boundary condition is set to pressure outflow to avoid the backflow
and diverged solution. The gauge pressure is zero at this condition, Dewan et al.
(2010), Zhou & Catton (2011), Ramesha & Madhusudan (2012), and Yuan et al.
(2012). The turbulence intensity of the flow exiting through the outlet boundary is
set to 5% as well, Zhou & Catton (2011).

5.6.5 Right and Left Sides

The right and left sides of the channel are a symmetric boundary condition
result from the uniform airflow and symmetry in the fin arrays, Zhou & Catton
(2011). Computations, therefore, are applied just for eight pin fins instead of the total
array of pin fins to shrink the model domain and the number of nodes. This reduces
the time to reach a converged solution, and saves computer memory.

5.6.6 The Other Surface Walls

All the other surfaces walls of computation domain are imposed as adiabatic
surfaces with zero heat flux resulting in no heat transfer passed through those walls.
A no slip condition is applied due to a rigidity of those wall that leads to a zero fluid
velocity in all directions (Zhou & Catton, 2011): Ux=Uy=Uz=0 are set.
 - 86 -

Adiabatic other walls Outlet

Perforated Pin Fins

Symmetry right
side surface

Symmetry left
side surface

Pinned Heat Sink

(PHS)
Constant Heat Flux

Inlet

Figure 5.4: Schematic diagram of the flow domain used in the CFD analyses,
showing eight perforated pin fins.

Table 5.2: The boundary conditions of the conjugate heat transfer model
Fluid Thermal Fluid Thermal
Locations Locations
Conditions Conditions Conditions Conditions

U= (6.5-12) Bottom wall of

Inlet T=25oC U=0 Q=constant
m/s heat sink

Right and left du dT dT

sides 0 0 outlet Pgage=0 0
dy dy dx
(symmetry)

dTair dT
Top wall and dT kair .  kS . S
U=0 0 Pin heat sink U=0 dn dn
other walls dz

5.7 Numerical Data Analysis (Post Processing)

The main important characteristics of airflow and heat transfer are explained,
to evaluate the hydraulic and thermal parameters of pinned heat sinks designs, which
can be obtained from the ANSYS FLUENT post processing options. These factors
are defined in section 2.5.
 - 87 -

5.8 Methods of Validation

In order to validate the numerical results, mesh verification and other

validation with the previous literature must be carried out. Therefore, the verification
of the computational domain, grid independence test (GIT) and the previous
validation studies of solid pins and single perforated pin fins heat sinks are
investigated and explained in this section.

5.8.1 Domain Verification

The verification of the computational domain that is used in this study must
also consider the entrance and exit regions. These regions should be sufficiently far
from the pinned heat sink to ensure that the numerical results are independent of the
boundary positions. For this reason, some tests have been carried out to determine a
sufficient distances away from the test section.

In this study, the Nusselt number (NuT), pressure drop (ΔP), and the CPU
temperature (Tcase) are determined in a range of cases for inlet air velocities between
6.5m/s and 12m/s. The distances of the entrance and exit zones to the heat sinks are
as shown in Table 5.3 where L=50mm refers to the length of the heat sink (test
section) in the flow direction. It can be noticed that the numerical solution is
converged for those domains except in domain 1 since the backflow (reversed flow)
will clearly happen at the outlet boundary of the heat sink due to its zero the exit
length.

Table 5.3 indicates that increasing in the length of entrance and exit regions
beyond domain 3 (0.5L), the errors in the numerical data is less than 2% for each of
the NuT, ΔP, and Tcase for 0P and 3P models for different inlet air velocities values
(6.5m/s and 12m/s). Thus, the computational domains used from now on have 0.5L
entrance and exit length (Domain 3) as a standard domain to save computer memory
and computational time.
 - 88 -

Table 5.3: The entrance and exit regions length of pin fins heat sinks
Domain Domain Domain Domain Domain Domain
1 2 3 4 5 6
Entrance Length 0L 0L 0.5L 1L 1.5L 2L
Exit Length 0L 0.5L 0.5L 1L 1.5L 2L

Nu 279.95 276.28 277.28 277.69 277.39

U= 6.5m/s

ΔP (Pa) 38.59 36.36 38.66 38.77 38.55

Solid Pins (0P)

Tcase (oC) 88.69 89.58 89.16 89.07 89.14

Nu 384.34 380 382.2 380.38 381.66

U= 12m/s

Solution is not converged

ΔP (Pa) 106 106.59 108 108.7 109

Tcase (oC) 72.57 73.17 72.77 72.96 72.83

Nu 305.16 299.4 300.39 300.63 300.79

U= 6.5m/s
Perforated Pins (3P)

ΔP (Pa) 39.78 35.61 36 36.43 37.84

Tcase (oC) 79.72 80.62 80.43 80.4 80.37

Nu 423.3 415.63 416.46 416.65 416.93

U= 12m/s

ΔP (Pa) 111.85 97.68 98.45 100.12 101.81

Tcase (oC) 66.13 66.75 66.68 66.67 66.65

 - 89 -

The effect of turbulence intensity boundary conditions is now investigated, as

shown in Figure 5.5. Thus, the turbulence intensity for both inlet and outlet are set to
2.5%, 5%, and 7.5% (Almoli, 2013). The pressure drop and temperature of the solid
base with solid (0P) and perforated (3P) pinned heat sinks for different inlet air
velocity are obtained. It is shown that the turbulent intensity at the inlet and outlet do
not have any substantial effect on the results in these specific cases. Hence, the
turbulence intensity is used from now on has 5% as a standard value (Zhou &
Catton, 2011).

110 85
0P Tur. Int. 2.5
0P Tur. Int. 2.5
100 0P Tur. Int. 5
0P Tur. Int. 5
0P Tur. Int. 7.5 80 0P Tur. Int. 7.5
90 3P Tur. Int. 2.5 3P Tur. Int. 2.5
3P Tur. Int. 5 3P Tur. Int. 5
80
3P Tur. Int. 7.5 3P Tur. Int. 7.5
75
∆p (Pa)

Tcase, ave.

70

60
70
50

40 65
30

20 60
6 7 8 9 10 11 12 13 6 7 8 9 10 11 12 13
U (m/s) U (m/s)

Figure 5.5: Inlet air velocity versus the pressure drop and temperature case of
HSs for different turbulence intensities
 - 90 -

5.8.2 Grid Independent Tests (GIT) (Mesh Verification)

Tetrahedron Hyper cells (Hex Core T-grid) are utilized for several various grid
distributions to ensure that mesh independence is achieved and the numerical data is
reliable and independent of grid density. Consequently, the CFD methodology is
firstly verified by comparing predictions of Nusselt number, pressure drop, and the
CPU temperature for the present solid pin (0P), and perforated pin fins 1A, 2A, 3P,
and 5P heat sink models with the number of cells with air velocity at 6.5m/s and
12m/s. Cases studies should be refined near the solid faces and near perforations to
predict the accurately fluid flow and temperature distributions.

In the case of solid pin fins (0P), the number of cells is from 98,104 to 171,059
in various steps. It is determined that after 124,00 cells, increasing the number of
cells leads to less than 3% of the average Nusselt number, pressure drop, and the
CPU temperature as shown in Table 5.4. Thus, the number of cells 124,000 is taken
as a standard for mesh independence.

With respect to the perforated pin fins 1A, 2A, 3P, and 5P designs, the number
of cells is varied from 102,000 to 233,000 with different levels, Table 5.4. Increasing
the number of cells beyond 147,000 has typically a 3% change in all outlet
parameters. Therefore, all results presented in this study have been obtained from
147,000 cells.

For the present slotted pin 3S, 6S, and 10S, and notched pin 2.5N, 5N, and
7.5N fin heat sink models. The grid points should be densely distributed near the
solid faces, slotted, and notched surfaces to predict accurately the fluid flow and
temperature distribution.

According to three slotted 3S, 6S, and 10S designs and three notched pins
2.5N, 5N, and 7.5N models, the number of cells is from 93,000 to 180,000 in various
steps. It is indicated that increasing the number of cells beyond 115,000 results in
typically a 2% change in all outlet parameters. Thus, the number of grid points
115,000 is chosen as a standard for mesh independence for slotted pins and 115,000
is selected for notched pins as grid independence.
 - 91 -

Table 5.4: Mesh validation of Solid and Perforated pinned heat sink designs

Parametric Solid Pins (0P) Triple Perforated Pins (3P) Notched pins (5N)
Studies
No. Cells 6.5m/s 12m/s No. Cells 6.5m/s 12m/s No. Cells 6.5m/s 12m/s
98104 253.15 348.23 113000 273.98 373.59 95008 253.83 336.7
124092 262.1 360.1 123689 275.95 379.7 115100 262.21 348.71
Nu
134035 263.49 362.31 161916 282.62 395.17 134112 267.34 358.78
171059 268.13 367 202678 287.71 400 171112 271.15 365.72

98104 35.28 107.18 113000 32.93 92.72 95008 26.47 78.8

124092 35.22 104.09 123689 32.76 94 115100 26.15 77.4
∆P (Pa)
134035 35 103.8 161916 33.65 93.55 134112 26.03 77.72
171059 35.74 103.67 202678 34.79 95.16 171112 26.71 77.36

98104 82.66 67.43 113000 75.9 63 95008 80.47 67.4

124092 81.06 66.22 123689 75.58 62.39 115100 78.76 65.84
Tcase (oC)
134035 81.18 66.31 161916 74.97 61.34 134112 78.34 65.16
171059 80.24 65.6 202678 74.53 61.66 171112 77.55 64.2
 - 92 -

5.8.3 Validation with Previous Studies

In this study, to ensure the CFD approach is accurate and reliable, validations
against four previous experimental and numerical studies are carried out at constant
air properties because the most previous numerical works such as Zhou & Catton
(2011) and Yuan et al (2012) have assumed that air properties is constant.

Solid Pin Fins Heat Sinks

The first validation of the numerical solutions is for the predicted Nusselt
number and pressure drop across the solid pin fins heat sinks and compared with
those of the numerical study of Zhou & Catton (2011). Figure 5.6 compares
predictions of Nusselt number (NuT) and pressure drop (∆P) across the pin fins with
various inlet air velocities from 6.5m/s to 12.2m/s. These both agree well with the
prediction of Zhou & Catton (2011) with typical discrepancies in the predictions of
NuT and ∆P of 3% and 4%, respectively.

275 125

250 100

225 75
∆P (Pa)
NuT

200 50

175 25
Present CFD Data Present CFD Data
Solid Pin Fins of Zhou & Catton Model Solid Pin Fins of Zhou & Catton Model
150 0
6 7 8 9 10 11 12 13 6 7 8 9 10 11 12 13
U (m/s) U (m/s)
Figure 5.6: Validation of Nusselt number (NuT) and pressure drop (ΔP)
predictions with those of Zhou & Catton (2011)
 - 93 -

The comparison of thermal resistance, Rth of solid pin fins heat sink between
the present CFD study data with the experimental results of Jonsson & Moshfegh
(2001) and the numerical data of Zhou & Catton (2011) are shown in Figure 5.7 for
6.5m/s≤ Uin ≤10m/s. It found that the maximum deviation of thermal resistance of
predicted CFD was less than 3% for both previous studies.

1.3
Experimental Data of
Jonsson & Moshfeg
1.25 Model Zhou & Catto

Present CFD Data

1.2
Rth (K/W)

1.15

1.1

1.05

0.95
6 7 8 9 10
U (m/s)

Figure 5.7: Comparison of thermal resistance predictions with those CFD

results of Zhou & Catton (2011), and experimental data of Jonsson &
Moshfeg (2001)

A further validation case is the pressure drop (ΔP) over the solid pin fins heat
sink for experimental data of Yang et al (2007) and the current numerical results.
Figure 5.8 indicates that the error percentage between predicted numerical results
and the literature’s data with various inlet air velocities is less than 2%. It is clear
that pressure drop measurement from the previous experimental study is in good
agreement with those predicted by the CFD.

An alternative approach of comparing the present simulation data with

experimental results in terms of heat transfer is to compare the heat transfer
coefficient (hT). The variation of heat transfer coefficient with inlet airflow for the
present CFD model and experiment are given in Figure 5.8. The results of this figure
show that the agreement is acceptable, with a typical error percentage of 5%.
 - 94 -

125 18
Exp. Yang's Data
115 16
CFD Present Study
105
14
95
12
85
h (W/K.m2)

10

∆P (Pa)
75
8
65
6
55
4
45
Exp. Yang's Data
35 CFD Present Study 2

25 0
0 1 2 3 4 5 6 0 1 2 3 4 5 6
U (m/s) U (m/s)
Figure 5.8: Validation between the experimental data of Yang et al. (2007) and
CFD analysis of heat transfer coefficient and pressure drop

Perforated Pin Fin Heat Sinks

The predictions of the current CFD model are compared with the experimental
data of Sahin & Demir (2008) for flow past a heat sink where the pin fins have a
single perforation. Figure 5.9 compares CFD predictions of the ratio Nu/Nus with the
previous experimental data, where Nus=0.077Re0.716 Pr1/3 is Sahin & Demir’s
experimental correlation for heat transfer from a smooth surface without pins. Again,
the agreement with the experimental data is generally good, with a maximum
discrepancy of less than 7%.
 - 95 -

20
Nu/Nus Present CFD
18 Nu/Nus Sahin & Demir

16

14

Nu/Nus
12

10

6
10000 20000 30000 40000 50000
Re

Figure 5.9: Comparison between CFD predictions of Nu/Nus with experimental

data of Sahin & Demir (2008) for pin fins with a single perforation

Given the range of factors that affect experimental and numerical data for flow
over heat sinks, the above validation cases confirm that the numerical approach
agrees well with previous results. The errors between the predicted numerical study
and those previous works are acceptable because of boundary conditions variances,
numerical solutions (discretization error), the type of grid independence, and
uncertainties in the experimental tests. Hence, the conjugate heat transfer approach
in the present work can be used for analysis of this type of heat sink.

5.9 CFD Validation with Present Experimental Results

In this section, complementary experimental and numerical simulation

validation models are used to investigate the main benefits of using the novel
perforated pinned heat sink with multiple perforations. The numerical data is
considered at constant and variable physical air properties (i.e. as a function of
temperature as indicated previously) to highlight the effect of air properties on the
hydraulic and heat transfer characteristics of pinned heat sinks when comparing with
experimental results. The inlet velocities are varied from 6.5m/s to 12m/s for the
range of Reynolds number 3500-6580 based on the mini-duct hydraulic diameter,
with 8x8 in-line pins array at constant longitudinal and transverse distance 6.5mm.
 - 96 -

5.9.1 Validation of Hydraulic Characteristics

The main hydraulic characteristics of airflow are pressure drop (∆P), fan
power (Pfan), and pressure drag coefficient (Pd) of 0P and 3P pinned heat sink design,
Figure 3.1, that are validated with CFD commercial code as air properties are
constant (Num.) and variable (Num. Variable).

Figures 5.10 compares experimental measurements with numerical predictions

into the effect of perforations on the pressure drop, ΔP, across pinned heat sinks
(PHSs) and the power required to overcome the pressure drop.

In the experimental data, the pressure drop with three perforations is typically
around 7% smaller than that of solid pin fins, while for the numerical predictions this
reduction is approximately 9%. For the solid and perforated pins, the average error in
the pressure drop predicted using constant air properties are typically 9.2% and 10.5
% respectively, whereas for predictions using variable air properties the error has
been reduced by two thirds to around 2.9% and 3.8% for the solid and perforated
pins respectively. Part of this may be due to the practical difficulties of fabricating
PHSs with several perforations, when slight misalignment of the perforations with
the dominant airflow direction and finite roughness of perforation surface can
increase the pressure drop considerably. However, the numerical predictions at
variable air properties are closer to the experimental pressure drop and within 5%
error percentage. Since, in practical ways, the viscosity of air will increase with
increasing air temperature that required higher pressure drop to push the air through
the heat sink. It is indicated that the behaviour of fan power is the same of pressure
drop.
 - 97 -

0.5
113 3P Num. 3P Num.
3P Num. Variable 0.45 3P Num. Variable
103 3P Exp. 3P Exp.
0P Num. 0.4 0P Num.
93 0P Num. Variable 0P Num. Variable
0.35 0P Exp.
0P Exp.

Fan Power (W)

83
∆P (Pa)

0.3
73
0.25
63
0.2

53 0.15
(A) (B)
43 0.1

33 0.05
6 7 8 9 10 11 12 13 6 7 8 9 10 11 12 13
U (m/s) U (m/s)
Figure 5.10: Effect of pin perforations on (A) pressure drop and (B) fan power
as a function of airflow speed

Figure 5.11 shows the effect of the perforated pinned heat sinks model (3P) on
the pressure drag coefficient for a range of inlet velocities from 6.5m/s to 12m/s at
Re=3500-6580 and 8×8 in-line pins with longitudinal and transverse distance is
6.5mm. The numerical results indicated Num. is constant ρ, cp, k, and μ; and Num.
Variable is for ρ, cp, k, and μ as a function of temperature

In line with the comparison between the pressure drag coefficient and air
velocities, the pressure drag coefficient is larger within the experimental studies
when compared with the numerical solution at constant air properties. Again, the
numerical predictions at variable air properties are closer to the experimental
pressure drag coefficient.
 - 98 -

1.6
3P Num.
3P Num. Variable
1.5 3P Exp.
0P Num.
0P Num. Variable

Pressure Drag Coefficient

0P Exp.
1.4

1.3

1.2

1.1

1
6 7 8 9 10 11 12 13
U (m/s)
Figure 5.11: Effect of pin design and inlet air velocity on the pressure drag
coefficient

5.9.2 Validation of Heat Transfer Characteristics

The experimental heat transfer characteristics such as the total and projected
Nusselt number, NuT, NuP, respectively, the CPU temperature (Tcase), and thermal
resistance (Rth) of 0P and 3P pinned heat sink design are validated with numerical
data again at constant (Num.) and variable (Num. Variable) air properties.

Average Nusselt Number

Figure 5.12 presents the corresponding experimental measurements and

numerical predictions of Nusselt number, based on either the total PHS wetted
surface area (NuT) or on the projected surface area (NuP) equivalent to the base
surface area of HS.

The data shows that both NuT and NuP increase approximately linearly with the
inlet air velocity and that the 3P pin fin design achieves a significant enhancement in
heat transfer. The average error between the experimental and predicted values of Nu
with constant air properties is 8.9% and 12.1% for 0P and 3P respectively, whereas
for those with variable air properties, this discrepancy is reduced to 4.2% and 7.7%
for 0P and 3P respectively. Since the viscosity of air increases with increasing air
temperature this causes reducing heat transfer rate. In addition, the considerations
mentioned above.
 - 99 -

Thus, the NuT and NuP of numerical data at variable air properties are lower
and closer to the experimental findings than that at constant air properties.

420 1250
3P Num. 3P Num.
3P Num. Variable
(A) (B)
400 3P Num. Variable
3P Exp. 1150 3P Exp.
380 0P Num. 0P Num.
0P Num. Variable 0P Num. Variable
0P Exp. 1050 0P Exp.
360

340
950

NuP
NuT

320
850
300

280 750

260
650
240

220 550
3000 3500 4000 4500 5000 5500 6000 6500 7000 3000 3500 4000 4500 5000 5500 6000 6500 7000
Re Re

Figure 5.12: Effect of inlet velocity on Nusselt number based on (A) total and
(B) projected surface area

Thermal Management

Figures 5.13 and 5.14 compare experimental measurements and numerical

predictions from the conjugate heat transfer analysis for the average base plate
temperature, Tcase and thermal resistance, Rth with fan power for 6.5m/s≤U≤12m/s,
through a system of 8x8 pins a pin pitch of 6.5mm.

As expected, the Tcase and Rth of experimental results are the highest. The heat
transfer coefficient measured experimentally is lower than the predicted values from
computation. For instance, in the experimental data the Tcase with three perforations
is typically around 6% smaller than for solid pin fins, while for the numerical
predictions at constant air properties this reduction is approximately 8%. The
average error in the numerical predictions of Tcase with constant thermo-physical
properties is around 2.8% and 5.2% for 0P and 3P heat sink models respectively,
while with variable thermo-physical properties these average errors are 2.5% and
5.1% for the 0P and 3P heat sink models, respectively. A further source of error is
possibly around the additional thermal resistance as a result of the brazing process,
where the brazing material does not completely fill the gap between the pin and the
 - 100 -

base plate. Thus, some air gaps appear within soldering zones, as indicated
previously in Figure 3.8, which causes greater thermal resistance for the
experimental conditions. The predicted numerical data at variable air properties is
slightly higher and closer to experimental results than for the constant air properties
by approximately 1.5oC.

80
3P Num.
3P Num. Variable
75 3P Exp.
0P Num.
0P Num. Variable
70 0P Exp.
Tcase ( C)
o

65

60

55

50
0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Fan Power (W)
Figure 5.13: Comparison between experimental and numerical predictions of
influence of fan power on Tcase

1.2
3P Num.
3P Num. Variable
1.1 3P Exp.
0P Num.
0P Num. Variable
1 0P Exp.
R th (K/W)

0.9

0.8

0.7
0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Fan Power (W)
Figure 5.14: Comparison between experimental and numerical predictions of
influence of fan power on Rth
 - 101 -

This demonstrates the thermo-fluid benefits obtained from the perforated

pinned heat sinks, in comparison to the solid PHS, since the two objectives designs
of heat sinks are achieved. The heat transfer of perforated pin (3P) enhances at
constant fan power when compared with the solid pin (0P) due to elimination the
dead thermal-flow zones just downstream the solid pin fins. It means CPU
temperature reduces at the minimum energy cost pin perforations.

5.10 Summary

The numerical approach for solving airflow over heat sinks has been described
and validated against previous results. Computational Fluid Dynamics (CFD) has
been used to simulate the conjugate heat transfer and turbulent airflow through PHSs
designs using ANSYS FLUENT 14.5 as the commercial code. Furthermore, the key
characteristics for airflow over PHSs are also understood and the grid independence
test (GIT) and validations are described.

The numerical data of thermal and hydraulic characteristics is validated with

the experimental results with the likely source of errors explained, Table 5.5, due to
the practical difficulties of fabricating PHSs with several perforations, when slight
misalignment of the perforations with the dominant airflow direction, and the effects
of finite perforation surface roughness. A further source of error for the heat transfer
measurements may be due to the additional thermal resistance because of the brazing
process, where the brazing material did not completely fill the gap between the pins
and the base plate. Thus, it may be that, in order to maximize the benefits from the
perforations, care must be taken to ensure that they are aligned with the dominant
flow direction and manufactured with a good-quality surface finish. Furthermore, the
numerical data at variable air properties are closer to the experimental findings than
that for constant air properties, Table 5.6.

Since there is good agreement between the experimental measurements and

predicted numerical data with variable air properties, the CFD conjugate heat
transfer model is now used to report further a parametric study of the influence of the
number, positioning of circular perforations, and other perforations shapes in the
next chapters.
 - 102 -

Table 5.5: The experimental and numerical enhancement of Nusselt number

(Nu), fan power (Pfan), and CPU temperature (Tcase) of 3P heat sink design
compared to solid pins (0P)

Nusselt Number
Parametric Studies
↑AT ↓ Pfan ↓ Tcase
↑ NuT ↑ NuP (W) (oC)
Heat Sink Designs
Numerical Perforated Pins with
9% 24% 9% 8%
Three Perforations (3P)
15%
Experimental Perforated Pins with
5% 11% 7% 6%
Three Perforations (3P)

Table 5.6: The errors percentage between the experimental and numerical data
at constant and variable air properties

NuT Pfan (W) Tcase (oC)

Parametric Studies

0P 3P 0P 3P 0P 3P
Heat Sink Designs

Constant air properties 8.9% 12.1% 9.2% 10.5% 2.8% 5.2%

Variable air properties 4.2% 7.7% 2.9% 3.8% 2.5% 5.1%

 - 103 -

6 Chapter Six: Pinned Heat Sinks with Circular

Perforation

6.1 Introduction

As the maximum discrepancy between the present experimental and simulation

data is acceptable (Chapters 3 and 4), the validated CFD model procedure is utilised
to perform parametric studies on perforated pinned heat sinks’ (PPHSs) effect on the
cooling performance in relation to the number, and positioning of circular
perforations with the variable physical air properties.

In this chapter, solid pin fins (0P), and novel perforated pin fin HSs (1A, 1B,
1C, 2A, 2B, 2C, 3P, and 5P, Figure 6.1) have been simulated as a conjugate heat
transfer and turbulent airflow problem for electronic cooling systems. CFD solutions
are carried out to investigate the thermal airflow characteristics of these heat sinks to
ascertain how these pin fins can reduce the hot spots inside them and enhance
airflow through them. In addition, the effect of the pins in in-line and staggered
arrays and the effect of the shapes of the perforations are considered as well.

6.2 Description of PHS Models

Eight types of perforated pinned heat sinks (PPHSs) are compared with solid
pin fins (0P), as shown in Figure 6.1. These perforations are aligned in the direction
of flow and their location (upper, lower, and centre of the pin) and their number (0,
1, 2, 3, and 5 perforations) vary, whilst their diameter is kept constant at 1mm. All
these perforated pins have the same physical domain that consists of three parts:
entrance section, test section (PHSs), and exit section. The pin fin heat sink
symmetric section comprises eight rows in an in-line array perpendicular to the flow
direction (cross flow) and each row has 8 pin fins.
 - 104 -

D = 2mm d= 1mm
for each pin for each
perforation

0P-Solid Pin Fin 1A-One Bottom Hole 1B-One Centre Hole 1C-One Top Hole
without Holes

2A-Two Bottom 2B-Two Top 2C- Two 3P-Three Holes 5P-Five Holes
Holes Holes Separated Holes

Figure 6.1: Solid and perforated pinned heat sink models

A B

Figure 6.2: (A) Plan view and (B) Side view of the pin fin heat sink being
analysed
 - 105 -

The overall heat sink has a base of 50 mmx50mmx2mm with an 8x8 in-line
array of 2mm diameter (D) and 10mm height pins (H) on a 6.5mm pitch in both
directions (Sz, and Sx), Figure 6.2. The air flows past pin fins with 1mm diameter
perforations. Different values of porosity are considered (ϕ=Vhole/V) at 0, 0.05, 0.1,
0.15, and 0.25 for 0P, 1P, 2P, 3P, and 5P perforated pin heat sinks, where Vhole, and
V are the perforation volume and solid pin volume, respectively. The entrance
section is formed of a straight rectangular duct having 25mm (12.5D) as length,
10mm (5D) as height and 6.5mm (3.25D) as the width, where D is pin fin diameter.
This section is located in front of the test section to ensure a hydrodynamically, fully
developed turbulent flow.
The total surface area of these pinned heat sinks can be calculated as
mentioned earlier in Chapter 2. Thus, the percentage of increase in this surface area
regarding the solid pins (0P) is 5%, 10%, 15% and 25% for the perforated pins 1P,
2P, 3P and 5P models, respectively.
The thermal airflow through the perforated pinned heat sinks with thermal
conductivity k=202W/m.K is analysed using CFD. The inlet air temperature is set to
25oC and the inlet air velocity is varied between 6.5, 8, 10 and 12m/s, as per Yang &
Peng (2009a), Yang & Peng (2009b), Kumar & Bartaria (2013), and Zhou & Catton
(2011). This range of velocity leads to Reynolds numbers in the range 3500-6580
based on a length scale given by the hydraulic diameter of the duct
Dh=2H.W/(H+W), where H and W are the height and width of the duct in which the
heat sink is located.

6.3 Perforated Pins

The need to reduce our usage of the world’s resources, combined with their
actual reduction together with environmental considerations, makes it necessary to
investigate ways of saving these resources and materials. Thus, there is clearly a
need to develop heat sinks that use less energy, to achieve required rates of heat
transfer (Sara et al., 2001).

Recently, many methods have been suggested to enhance the thermal

characteristics of engineering devices. As mentioned in Chapter 1, one of those
methods is the active cooling technique using traditional fins that cause heat transfer
rate enhancement at the expense of increasing pressure drop (fan power). In other
 - 106 -

words, the energy consumed will increase due to the extra friction of the fins. In
addition to the frictional energy loss, the external fan power should be taken into
account and this consumption of power should be reduced (Sara et al., 2001).

With respect to the literature review, the main problem of those traditional
solid objects (fins, ribs, and blocks) is that dead thermal-flow zones (hot spot) will
appear and develop in their wake, as shown in Figures 6.3A and 6.4A. In other
words, airflow separation and low speed recirculating flow behind the solid objects
are the main sources of poor cooling. This means that the heat transfer rates from
their surfaces are not high enough, while the pressure drop is usually relatively high.
Therefore, the thermo-flow characteristics of these solid objects are undesirable.

Many attempts have been proposed to overcome these adverse effects,

depending on changing the pattern of fluid flow and geometric conditions. One of
these attempts to enhance heat transfer rates and reduce fan power is to allow the
airflow path to pass through these solid fins via perforations, as shown in Figures
6.3B, C and 6.4B, C. The perforated fins or the permeable fins will reduce the hot
regions that usually appear behind solid fins by means of improving the fluid flow
and demolishing vortexes zones, due to well-mixed fluid flow layers (Sara et al.,
2001).

As a result, the main target of this study is to design and select the perforated
pin fin heat sinks that will yield the maximum enhancement to the thermal
characteristics with the minimum energy consumption.
 - 107 -

Hotspot
(A) 0P heat sink (Dead thermal-flow zone)

(B) 3P heat sink

Reduction thermal zone effects

(C) 10S heat sink

Temp. (oC)

Figure 6.3: Plan views of hotspot zones through (A) solid 0P, (B) perforated 3P
and (C) slotted 10S pinned heat sinks at Re=5393
 - 108 -

Separation zone
0P heat sink (Dead thermal-flow zone)

Airflow
3P heat sink

Airflow
Reduce separation zone effects
10S heat sink
Airflow

Pathlines Velocity (m/s)

Figure 6.4: Plan views of airflow field through (A) solid 0P, (B) perforated 3P
and (C) slotted 10S pinned heat sinks at Re=5393
 - 109 -

6.4 Hydraulic Characteristics

Since the nature of the airflow passing through pin heat sinks is expected to
enhance the thermal-hydraulic characteristics of these heat sinks, the airflow
characteristics are explained first. The airflow behaviour, pressure drop (∆P), fan
power (Pfan), profit power factor (J), and pressure drag coefficient of perforated
pinned (PPHSs) are explained and discussed in this section and compared with the
solid PHS model.

6.4.1 Airflow Behaviour

The effects of heat sink models on airflow behaviour are presented in Figure
6.5 for the inlet air velocity 10m/s at Reynolds number = 5393 and 8x8 in-line array
pins with streamwise and spanwise distances of 6.5mm.

The recirculation zones (vortices) behind the perforated pin fins will shrink
compared with the solid pin fins due to effect of perforations. These vortices can be
obvious behind the solid pin, while they are trivial in the case of perforated pin fins
because the airflow passing through the perforations reduces the size of the vortices
and the airflow path resembles a jet fluid flow. In addition, the size of the vortices
will reduce more with increases in the number of perforations. Hence, the formed
recirculation zones (wakes) are reduced in size in the case of perforated pin fin heat
sinks. With regard to the solid pin fin heat sinks, however, the airflow separates from
the frontal surface area of this pin.
 - 110 -

Recirculation zones
(vortices)

0P

2A

Jet airflow through

perforations

2C

Velocity
(m/s)

Figure 6.5: Comparison between predicted flow field in PFHSs with solid pin
fins and for designs 2A and 2C with two perforations
 - 111 -

6.4.2 Pressure Drop, Fan Power, Profit Power Factor, and Pressure Drag
Coefficient

Figure 6.6 shows the effect of heat sink designs on the pressure drop (∆P), fan
power (Pfan), and profit power factor (J) for a range of Reynolds numbers from 3500
to 6580 relying on the inlet air velocities (6.5-12)m/s and 8x8 in-line array pins with
longitudinal and transverse distances of 6.5mm.

The pressure drop over the perforated pins is lower compared with the solid
pins (without perforations). The remarkable point here is that the solid pins’ narrow
airflow path is due to them being impermeable, which leads to more recirculation
zones and airflow separation behind them. However, in the new designs, the airflow
path will widen and will be a straighter flow leading to less separation behind the
pins due to pin permeability. Therefore, the pressure drop and flow resistance of the
perforated pins are less than for the solid pins, and that is in agreement with the
findings of Yang et al. (2010).

For each of the pin designs (0P, 1A, 2A, 3P, and 5P) given, as shown in Figure
6.6, it is clear that the pressure drop reduces for pins that have more perforations
since the amount of air passing through these perforations will be larger with
increasing numbers of perforations. The pressure drop reductions of the 3P model
with 3 perforations and 5P model with 5 perforations are approximately 9% and
14%, respectively, lower than that of the solid pin case.

The fan power pattern according to Figure 6.6 is similar to that for the pressure
drop. This means that the amount of energy spent on a fan which is used to cool new
heat sinks is lower than that for traditional solid pins at a given air velocity.
However, the behaviour of the profit power factor is opposite to the pressure drop
pattern, since this factor includes the amount of consumed fan power against the
amount of heat applied at the heat sink base. The profit factor of perforated pins is
the highest compared with the solid one. In addition, it increases as the number of
perforations increases.

Commonly, as air velocity (Reynolds number) increases, the pressure drop and
fan power increase as a result of the shear forces induced by increasing the Reynolds
number, while the profit factor decreases.
 - 112 -

110 0.45
1A
1A
100 2A 0.4
2A
3P
90 0.35 3P
5P
5P

Fan Power (W)

80 0P 0.3
0P
∆P (Pa)

70 0.25

60 0.2

50 0.15

40 0.1

30 0.05
6 7 8 9 10 11 12 13 6 7 8 9 10 11 12 13
U (m/s) U (m/s)

800
1A
2A
700
3P
5P
600
0P
The Profit Factor

500

400

300

200

100
3000 3500 4000 4500 5000 5500 6000 6500 7000
Re

Figure 6.6: Effect of pin perforations and inlet velocity on pressure drop, fan
power, and profit factor
 - 113 -

The contour plots predict the variations in the local pressure through solid
(0P), perforated (3P) and slotted (10S) pinned heat sinks within the airflow domain,
as shown in Figure 6.7. The maximum local pressure is at the leading edge of heat
sink and then it reduces gradually along the airflow direction in both cases to reach
the minimum value at the end of heat sink due to the presence of pins (obstructions).
The perforated 3P and slotted 10S pins show lower pressure penalty than the
baseline case (0P) along the airflow direction due to perforations. These perforations
allow a part of airflow to pass through them with less resistance to airflow compared
to solid pins (0P). In the 0P case, local pressure varies between approximately 211Pa
and –95.5Pa, whereas for the perforated pins 3P and 10S the corresponding local
pressure varies from approximately 174Pa to –91Pa, and from 103Pa to –69Pa,
respectively. The local pressure on the pins is also significantly lower, as indicated
by the greater preponderance of blue regions on the perforated pins. Thus, the
minimum local pressure is for slotted 10S pins due to its large perforations along
pins.

0P heat sink

Airflow
3P heat sink
Airflow

10S heat sink

Airflow

Pressure (Pa)

Figure 6.7: Plan views of pressure contour through solid 0P, perforated 3P and slotted
10S pinned heat sinks at Re=5393
 - 114 -

Figure 6.8 shows the effect of the perforated pinned heat sink models on the
pressure drag coefficient for a range of inlet velocities from 6.5m/s to 12m/s at
Re=3500-6580.

The pattern of Pd shows the same behaviour for all perforated pin models.
This coefficient is formed due to the resistance of pin fins to airflow path and is
associated with a particular frontal surface area. With respect to the perforated pins,
the pressure drag coefficient is the lowest and its value decreases with the addition of
more perforations. The main reason for this is that the frontal surface area of the
perforated pins is smaller than that of the solid pins (Ismail, 2013). In addition, the
airflow passing through these perforations will be easier as there will be less
resistance to airflow as the number of perforations increases. Accordingly, the
pressure drag coefficient decreases as frontal area reduces with the presence of more
perforations.

Overall, this factor decreases with increases in the inlet air velocity (Reynolds
number) because the kinetic energy increases more than the pressure drop does.

1.6
1A
2A
1.5 3P
5P
Pressure Drag Coefficent

0P
1.4

1.3

1.2

1.1

1
3000 3500 4000 4500 5000 5500 6000 6500 7000
Re

Figure 6.8: Variation of pressure drag coefficient with inlet air velocity for solid
and different perforated pinned heat sink designs
 - 115 -

6.4.3 Effect on Power Consumption

With regard to the fan power, energy that is consumed by the fan operation can
be saved by reducing the pressure drop via the perforations. The reductions in fan
power consumption are approximately 9% and 14% for the 3P model and 5P model
PHSs, respectively, which is lower than that for the solid pin case. Thus, the profit
factor of the 3P model and 5P model will increase by nearly 10% and 16%,
respectively, compared to that for the solid pins. It is clear that these two factors, fan
power and profit factor, have an opposite trend; in other words, as the fan power
increases, the profit factor decreases. The solid pins require higher fan power
consumption to overcome the pressure drop through the heat sinks compared with
the perforated pins. This is because of the perforations, which enable air to easily
pass through the perforated pin fins compared with the solid pin fins. In addition,
when the number of perforations is increased, the fan power diminishes while the
profit factor increases at a given air velocity.

Consequently, the first aim of this study, reducing the fan power (pressure
drop) is achieved by using the perforated pinned heat sinks.

6.5 Heat Transfer Characteristics

The most important thermal characteristics of pinned heat sinks are illuminated
and discussed in the following sections.

6.5.1 Average Nusselt Number

Figure 6.9 illustrates the effect of each of the given perforated pin designs on
the Nusselt number for a range of Reynolds numbers from 3500 to 6580 relying on
the inlet air velocities (6.5-12)m/s and 8×8 in-line pins with longitudinal distance of
6.5mm.

For the perforated pin fins, it is clear from Figure 6.9 that the highest
percentage increase of NuT compared to the benchmark solid pin case is 11% when
increasing the total surface area by 25% for pinned heat sink design 5P with 5
perforations.

Airflow separates from the surface of the solid pin heat sink and then dead-
flow zones are generated behind these solid pins. Hence, the temperature is higher in
 - 116 -

those zones and the NuT is lower for the solid pin fin compared with the perforated
pins. In order to overcome the thermal dead zones, the perforations reduce the size of
the high-temperature zones behind the solid pins. These perforations resemble a jet
fluid flow, mixing fluid layers at the rear of the pin, and flow separation from the
surface will be delayed because the airflow may not be strong enough to cause it.
The improved heat transfer with perforations is due to the combined effects of
increased surface area and localised enhancement near the perforations through the
formation of localised air jets, as shown in Figure 6.5, and that is consistent with the
finding of Sara et al. (2001), which attributed improved heat transfer with perforated
rectangular blocks. As the number of perforations increases, the fluid mixing through
the pin heat sink also increases, which leads to the pin temperature decreasing due to
the multi-jet air and the NuT increases.

The results of the CFD simulation show that the NuT number is enhanced for
higher air velocities (with increasing Reynolds number) for all pin fin heat sink
designs due to the increases in the convective heat transfer.

400
1A
380 2A
3P
360 5P
0P
340
NuT

320

300

280

260

240
3000 3500 4000 4500 5000 5500 6000 6500 7000
Re
Figure 6.9: Effect of inlet velocity on NuT for the nine pin designs shown in
Figure 6.1
 - 117 -

Figure 6.10 shows the effect of the number of perforations and the total surface
area (AT) on the NuT number at U=10m/s, and shows clearly that the heat transfer
rate increases monotonically with the number of perforations at a given air velocity.

350

AT =25%
AT =15%
330

AT =10%
NuT

AT =5%
310

290
0P 1A 2A 3P 5P
Pinned Heat Sinks Models

Figure 6.10: Effect of number of perforations on Nusselt number at 10m/s for

the five pin designs

6.5.2 Thermal Management of PHSs

Figure 6.11 shows a more detailed investigation into the effect of pin fin
perforations on the relationship between fan power and heat sink temperature (Tcase)
and the thermal resistance (Rth) through a system of 8×8 in-line pins separated
longitudinally by a distance of 6.5mm for all perforated pin fin heat sink models.

For each of the pin designs (0P, 1A, 2A, 3P, and 5P) given, Figure 6.11 shows
that the CPU temperature (Tcase) and the thermal resistance (Rth) of the perforated
pinned heat sinks are lower than those of the solid pin fins at a given fan power. In
addition, these benefits increase as the number of perforations increases. For
example, the enhancement in Tcase for the 5P model is nearly 10% compared with the
solid pins. In addition, the perforated pins exhibit more gradually reduced Tcase with
increasing inlet air velocity. It is from 73oC to 61oC for the 5P model with five
perforations while from 81oC to 66oC for the solid pins. This confirms that the
improved heat transfer rates of the perforated fins lead to the desirable effects of
reducing both CPU temperature and thermal resistance of the heat sink. More
generally, Tcase and Rth reduce as the number of pin perforations increases at a
constant pressure drop or fan power.
 - 118 -

82 1.15
U= (6.5 - 12)m/s U= (6.5 - 12)m/s
80 1.1
Sy= 6.5 mm Sy= 6.5 mm
78 1A 1A
1.05
76 2A 2A
3P 1 3P
74 5P 5P
Tcase ( C)

Rth (K/W)
72 0P 0.95 0P
o

70 0.9
68
0.85
66
0.8
64
0.75
62

60 0.7
0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45
Fan Power (W) Fan Power (W)

Figure 6.11: Effect of pin design and fan power on Tcase and Rth

Figure 6.12 compares the surface temperature distribution of the solid pin heat
sink (0P design) with those obtained on the pin fin with five perforations (5P) at
Re=5393 (10m/s). In the former case, temperatures on the base plate vary between
approximately 58.5oC and 71oC, whereas for the perforated pins the corresponding
temperatures vary between approximately 49.5oC and 65.5oC. The temperatures on
the pins are also significantly cooler, as indicated by the greater preponderance of
blue regions on the perforated pins. This is because inlet airflow has more capacity
to transfer heat along the heat sink due to its relative coolness, while the airflow
temperature increases as it passes through the heat sink. Thus, the minimum
temperature of the pins is at the tip of the first pin fins and the maximum temperature
is at the bottom of the last pin fins.

Subsequently, the second aim of this study, reducing the CPU temperature by
increasing the heat transfer rate, is achieved using the perforated pinned heat sinks
(PPHSs). Since in an actual system, the two aims of the minimum Tcase (maximum
heat transfer rate) at the minimum fan power (less energy cost) are achieved for the
5P heat sink model in this study.
 - 119 -

0P Tin= 25oC

3P

5P

Figure 6.12: Temperature distribution through pinned heat sinks: 0P, 3P, and
5P models at Re=5393

6.6 Effect of Perforation Position

The effect of the position of the perforations is now investigated to obtain the
optimum perforated pinned heat sink design based on pressure drop (ΔP), Nusselt
number (NuT), and the CPU temperature (Tcase).

For the cases with two perforations (2P) and three perforations (3P), the
positions of the perforations do not have more influence on the pressure drop of the
perforated pinned heat sink models. The 3P perforated pin models have the same
lowest value of pressure drop, virtually 9% lower than that of the solid pin model
(0P). Figure 6.13 shows the pressure drop variation over the pinned heat sinks when
varying the perforations position in the 3P model at different inlet airflow values
(6.5-12)m/s.
 - 120 -

110
3P Up
100 3P Cen
3P Low
90 3P Sep
0P
80

∆P (Pa)
70

60

50

40

30
6 7 8 9 10 11 12 13
U (m/s)
Figure 6.13: Effect of perforation positions on the pressure drop through heat
sinks

The position of the perforations is far less influential on the NuT enhancement.
The NuT of the perforated pin (2B) and (2C) models are slightly higher (typically up
to 2% larger) than those for the perforated pin (2A) design, Figure 6.14. The CFD
results indicate that this may be due to the larger air speeds through the perforations
in cases 2B and 2C compared with case 2A, Figure 6.5. In addition, the conductive
heat transfer of the 2A pin model may decreases, leading to reduction in the NuT due
to removing part of the pin material from the bottom of these pins.

400
0P
380 1A
1B
1C
360 2A
2B
340 2C
3P
5P
NuT

320

300

280

260

240
6 7 8 9 10 11 12 13
U (m/s)
Figure 6.14: Effect of different perforation positions with inlet velocity on NuT
for the nine pin designs shown in Figure 6.1
 - 121 -

The vertical position of the three perforations model (3P) as shown in Figure
6.15, however, can enhance the overall characteristics to some extent. Figure 6.16
explains the effect of the position of the three perforations model (3P) on the Nusselt
number with variation in the Reynolds number (3500-6580). The NuT of the
perforated pin 3P-SEP model is nearly 2% larger than that of the other perforated pin
designs. Since the distribution of perforations is uniform along the 3P-SEP pins
model, the formation of localised air jets through the perforations is uniform along
the pins, which enhances the convective heat transfer of the 3P-SEP pinned heat
sinks. In the perforated pin 3P-LOW model that has perforations at the lower part of
the pins, the NuT is lower compared to the other 3P models because of the decrease
in vertical conductive heat transfer due to removing part of the material at the bottom
of these pins.

0P 3P-UP 3P-CEN 3P-LOW 3P-SEP

Figure 6.15: Different vertical positions of the three perforations model (3P)

400
3P Up
380 3P Cen
3P Low
360 3P Sep
0P
340
NuT

320

300

280

260

240
3000 3500 4000 4500 5000 5500 6000 6500 7000
Re
Figure 6.16: Variation of NuT with different perforation positions and Re
 - 122 -

Figure 6.17 explains the effect of the position of the three perforations (3P)
model on the CPU temperature with variation in the fan power. It is indicated that all
3P models have the lowest CPU temperature, except the 3P-LOW model. This is
because, again, the conductive heat transfer is weak at the bottom of the 3P-LOW
pin model due to the perforations.

It can be concluded that the pinned heat sink with the optimum overall
performance is the perforated pin 3P-SEP (standard design), as shown in Figure
6.16, which was previously tested experimentally.

82
3P Up
80
3P Cen
78 3P Low
76 3P Sep
0P
74
Tcase ( C)

72
o

70
68

66

64
62

60
0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45
Fan Power (W)
Figure 6.17: Comparisons of CPU temperature with the three perforations in
different positions

From an existing heat sink, wire Electrical Discharge Machining can be used
to directly cut into the circular perforations. This would also retain the high thermal
conductivity between the pins and the base plate of a heat sink cast from a single
block. The effect of the horizontal position of the three perforations models (3P) on
the Nusselt number and pressure drop is considered in the current study. The
positions of these perforations are shifted from the centre of the pin (0% moving
percentage) to the outside of the pin (100% moving percentage) with respect to the
centre solid pin (0P), as shown in Figure 6.18.
 - 123 -

0% 5.5% 25% 50% 75% 100%

(3P) (0P)

Figure 6.18: Horizontal movement percentage of perforations from the centre

(0%) to the outside of the pins (100%)

Figures 6.19 and 6.20 show the variation of pressure drop and Nusselt number
with different horizontal positions of the three perforations and inlet airflow at
10m/s. It is pointed out that, when the perforations are moved from the centre to the
outside of the pin fin, the NuT diminishes while the pressure drop will increase. The
pressure drop of those perforated pins will increase as the perforations are moved to
the outside, owing to reducing the pins’ porosity and increasing the airflow blockage
passing over them. In addition, the maximum Nusselt number and minimum pressure
drop are for perforations positioned at the centre of the pins in the 3P model.
Although the moving percentage is 5.5%, 25%, 50%, and 75% caused an increase in
surface area of the pins, the NuT of the pinned heat sink models reduces due to
reduction of localised air jets near the perforations

This indicates that two important reasons resulted in enhancement of the

overall characteristics’ benefits. These benefits arise due to not only the increased
surface area but also heat transfer enhancement near perforations through the
formation of localised air jets.
 - 124 -

90

85

80

∆P (Pa)
75

70

65

60
0 25 50 75 100

Shifting Perforations %

Figure 6.19: Pressure drop trend with different perforation positions of the 3P
heat sink model

350

340
NuT

330

320

310
0 25 50 75 100
Shifting Perforations %

Figure 6.20: Comparisons of NuT with the three perforations in different

positions
 - 125 -

6.7 Effect of Pin Fins Arrangement

In this section, the effects of pin fins in in-line and staggered arrangement on
fan power (Pfan) and CPU temperature (Tcase) are described in detail for solid (0P)
and perforated (3P) pinned heat sink designs. A total of 64 pin fins (8x8) separated
longitudinally and transversely by a constant distance of 6.5mm in in-line and
staggered arrays are tested for both models, heat sinks (0P) and (3P) models, with
variation, whether to the inlet airflow (6.5-12)m/s or Reynolds number (3500-6580).

Figure 6.21 shows the pressure drop behaviour for both in-line and staggered
arrays of the solid (0P) and perforated (3P) pinned heat sink models. It is found that
the pressure drop of the staggered array is approximately 30% higher than the in-line
array for both models. The main reason for this is that the staggered arrangement
will increase the flow blockage in the airflow direction while the airflow relatively
smoothly passes over the in-line array pinned heat sink.

150 0P Staggered Array

0P In-line Array
3P Staggered Array
130
3P In-line Array

110
∆P (Pa)

90

70

50

30
6 7 8 9 10 11 12 13
U (m/s)

Figure 6.21: Effects of pin array on pressure drop with variation in Reynolds
number for solid (0P) and perforated (3P) pinned HS models
 - 126 -

With respect to thermal management, Figure 6.22 illustrates the effect of pin
fins alignment on the CPU temperature of heat sinks with fan power for both solid
and perforated pin fins. The staggered array for both solid (0P) and perforated (3P)
models shows the lowest CPU temperature. The CPU temperature of the staggered
array is approximately 10% and 12% lower with a high-fan power for both 0P and
3P heat sink designs, respectively, compared with the in-line pin array. This is
because the staggered arrangement breaks down the thermal boundary layer and
increases intermixing of airflow layers, with more surface heat transfer area in
contact with the cooling air.

85
0P Staggered Array
0P In-line Array
80
3P Staggered Array
3P In-line Array
75
Tcase ( C)
o

70

65

60

55
0.05 0.15 0.25 0.35 0.45 0.55 0.65
Fan Power (W)

Figure 6.22: Effects of pin array on Tcase and Pfan for solid (0P) and perforated
(3P) pinned heat sink models

CFD predicts that the staggered pinned heat sinks for both solid and perforated
pins provides lower Tcase with higher fan power consumption than that of the in-line
array under the same boundary conditions. These thermal and airflow characteristics
findings are consistent with the recent conclusions of Yang et al. (2007), which
considered improved heat transfer with different solid pin fin configurations at an in-
line and staggered arrangement.
 - 127 -

6.8 Effect of Square and Elliptic Perforation Shapes

Since perforated pin fins have been shown to enhance the thermofluid
characteristics of heat sinks, the effect of perforation shape is now considered. The
primary goal is to investigate the effect of square, elliptic and circular perforation
configurations, as shown in Figure 6.23, on the cooling performance in electronic
devices. Each pin has three perforations and the hydraulic diameter of each
perforation is nearly 1mm, aligned in the direction of flow. Thus, the porosity is
considered with different values (ϕ=Vhole/V) at 0.15, 0.19, and 0.22 for circular,
square, and elliptic perforations, respectively, where Vhole is the perforation volume
and V is the solid pin volume. Hence, the percentage of increasing the total wetted
surface area with respect to the solid pins (0P) is 15%, 18%, and 17% for the circular
perforated (3CP), square perforated (3SP), and elliptic perforated (3EP) pinned heat
sinks, respectively.

d= 1mm

h= 1mm, h= 1.5mm,
w= 1mm w= 1mm

3PC- Circular Holes 3PS- Square Holes 3PE- Elliptic Holes

Figure 6.23: Circular, square, and elliptic perforated pinned heat sink models

The effects of perforation shape in a given PHS on thermal airflow

characteristics as pressure drop (ΔP), Nusselt number (NuT), and CPU temperature
(Tcase) with various inlet air velocity (6.5-12)m/s are considered for 8×8 pins with a
constant pin spacing of 6.5mm in either direction.

With respect to ΔP of these heat sinks, Figure 6.24, the elliptic perforated pins
(3EP) have the lowest pressure drop and fan power, nearly 12%, compared with the
equivalent solid pinned heat sink (0P) model, while the pressure drop reduction for
square and circular perforations are 7% and 9%, respectively. This is because the
void volume of the elliptic perforations is larger compared with the other perforation
 - 128 -

configurations. This induces airflow to pass through the elliptic perforated pin fins,
as it can do so easily and with less obstruction compared with the other perforated
pin fins.

110
3CP
100
3SP
90 3EP
0P
80
∆P (Pa)

70

60

50

40

30
6 7 8 9 10 11 12 13
U (m/s)
Figure 6.24: Effect of perforation shape on the pressure drop with various inlet
air velocities

Figure 6.25 shows the effect of perforation shape on the Nusselt number (NuT)
with various Reynolds numbers (3500-6580) and 8×8 pins at the constant
longitudinal distance of 6.5mm.

The predicted data illustrates that the NuT of the perforated pin fins provides
the maximum value. The NuT for the pins with circular perforations (3CP) is
typically 9% superior to that of the other perforated pins. Furthermore, the square
and elliptic perforation shapes have the same NuT enhancement percentage,
approximately 4%, compared with the solid pins (0P) model. It may be that the
major cause for this is that the circular perforations have the maximum mean jet-
local air velocity through those perforations compared with other perforation shapes,
as shown in Figure 6.27.
 - 129 -

395
3CP
370 3SP
3EP
0P
345

NuT 320

295

270

245
3000 3500 4000 4500 5000 5500 6000 6500 7000
Re
Figure 6.25: Variation of total Nusselt number for solid and different
perforation shapes with various Re

Figure 6.26 shows that the Tcase of the perforated pin fins are smaller than those
of the solid pin fins at a given airflow. The data shows that the lowest Tcase is
typically 8% for the circular (3CP) model and 5% for both square (3SP) and elliptic
(3EP) perforated pinned heat sinks compared to the solid pins system.

The principal cause for this relates to the effects of two parameters on the
enhancement heat transfer rate: the mean jet-local air velocity through perforations
(Ux) and total heat transfer surface area (AT). Although the heat transfer surface area
of the perforated pins increases for all pinned heat sink designs, jet-local air velocity
through the perforations still plays an important role in enhancing the heat transfer
rate. The maximum mean jet-local air velocity through the perforations of the
perforated pins is for the circular perforations, as shown in Figure 6.27. In other
words, cool air goes through circular perforations faster than through the other
perforation shapes, so removing more heat created by CPU running. Thus, the
circular perforated pins, 3CP model, have the lowest values of Tcase.
 - 130 -

85
3CP
3SP
80
3EP
0P
75

Tcase (oC) 70

65

60
6 7 8 9 10 11 12 13
U (m/s)
Figure 6.26: Variation of temperature with perforation shapes and various inlet
air velocities
14

13.5 3CP
13
3SP
12.5
3EP
12
Ux (m/s)

11.5

11

10.5

10

9.5
9
1 2 3 4 5 6 7 8
Number of Pins

Figure 6.27: Variation in mean local air velocity through different perforation
shapes of each pin

Figure 6.28 shows the comparison between the surface temperature distribution
of the solid pin heat sink and those obtained on the circular (3CP), square (3SP), and
elliptic (3EP) with inlet airflow at 10m/s (Re= 5393).

In the first model, 0P model, the temperatures variation on the base plate vary
between approximately 58.5oC and 71oC, whereas for the perforated pins the
corresponding lower temperatures vary between approximately 52oC and 66.5oC for
 - 131 -

the circular perforations (3CP), 52.5oC to 67oC for the square perforations (3SP), and
53oC to 67oC for the elliptic perforations (3EP), as shown in Figure 6.28. This
indicates that the heat transfer rate of the circular perforated pin fins (3CP) is the
largest, as explained previously (Figure 6.27) that the maximum mean jet-local air
velocity through the perforations of the perforated pins is for circular perforations.
Thus, the temperatures on the pins are also significantly cooler: the lower
temperature is at the tip of the first pin fins and the highest temperature is at the
bottom of the last pin fins.

Consequently, the two aims of this study are achieved. The heat transfer rate is
enhanced with less power consumption to drive air through the pin fins and that
leads to the desirable benefits of reducing the CPU temperatures of the heat sink in
the case of a fixed heat sink size.

Commonly, a compromise needs to be made between choosing either the

elliptic perforated pins, 3EP, which provide the smallest pressure drop and fan
power, or the circular perforated pins, 3CP, which have lowest CPU temperature and
highest Nusselt number.

0P

3CP Tin= 25oC

3SP

3EP

Figure 6.28: Temperature distribution through perforated pinned heat sinks:

0P, 3CP, 3SP, and 3EP models at Re=5393
 - 132 -

6.9 Optimum Design of the Perforated Pinned Heat Sink (1P)

PHSs are designed to maintain the processors below critical temperatures for
minimal fan power consumption input into the system. Recently, there have been a
number of previous studies dealing with the optimum heat sink designs with solid
plates and pins. For example, the multi-objective Genetic Algorithms was used to
optimise plate fin geometries for total heat transfer and annual costs (Najafi et al.,
2011). The pin density, pin size and air flow direction in PHSs were optimised by
Shaukatullah et al. (1996), while Soodphakdee et al. (2001) optimised for the cross-
sectional shape of solid pins heat sinks. This part deals with the optimisation of
single perforated pins, 1P, as a function of perforation diameter, d, and perforation
location, y, for PHSs with an 8x8 array of pins and a constant pin spacing of 6.5mm
in either direction. The multi-objective optimisation problem studied here is to
minimise Tcase and Pfan for 0.5mm≤ d ≤1mm and 2mm≤ y ≤8mm for a constant air
inlet velocity, Uair= 8m/s, since the above results may indicate that minimising Tcase
and minimising Pfan is in conflict with one another. Hence, the optimisation problem
it can be defined as follows:

Objective function: minimise Tcase & Pfan

Subject to: 0.5mm ≤ d ≤ 1mm

2 mm ≤ y ≤ 8mm

Following a number of recent, successful optimisation studies, see e.g. Khatir

et al. (2015), the response surface functions are built using the Moving Least Squares
(MLS) method from a set of known values at specified Design of Experiments (DoE)
points. The latter are obtained using an Optimal Latin Hypercube approach, that uses
a permutation genetic algorithm to achieve a uniform points spread within the design
space (Narayanan et al., 2007). In the present study, it is found that 30 DoE points
are sufficient to provide accurate response surface functions for both Tcase and Pfan.
These 30 points are divided into 20 building points that are used to determine the
response surface and 10 validation points that are utilised to validate the response
surface, as shown in Figure 6.29. This approach distributes the two design variables
in the spacing design uniformly within the lower and upper limits of each variable.
 - 133 -

6
Building points

y(mm)
5 Validation Points

3
d
y
2
0.5 0.6 0.7 0.8 0.9 1
d (mm)

Figure 6.29: Distribution of design points in design variable space for the
perforation diameter, d (mm) and the position of single perforations, y (mm)

The multi-objective function of CPU temperature and fan power of the pinned
heat sink in terms of the design variables perforation diameter, d (mm) and the
position of single perforations, y (mm) of the (1P) heat sink model are illuminated in
Figures 6.30 and 6.31. The ten model validation points are used to optimise a
closeness of fit parameter and the optimised MLS method has given very good
agreement with merged DoE (R2 value of 0.982 for DoEm for Tcase and Pfan). The
optimum values of Tcase and Pfan are on the design variable boundaries. This means
that the design variables, perforation diameter (d) and the height of perforation (y)
have an insignificant effect on the objective functions, Tcase and Pfan; it is less than
1.5%. Therefore, a Pareto front does not required to find in this case, as will be
explained in the next chapter, as a constrained optimisation design for the design
variables of the single perforated pinned heat sink (1P) model. It is easy to find that a
perforation diameter of 1mm for any perforation position is the optimum design for
the single perforated pinned heat sink (1P) model to provide the lowest Tcase and Pfan
at 68.4oC and 0.2W, respectively, as inlet air velocity of 8m/s (Re=4315).
 - 134 -

Figure 6.30: Response surface function of CPU temperature (Tcase) of the single
perforated pinned heat sink (1P) model

Figure 6.31: Response surface function of fan power (Pfan) of the single
perforated pinned heat sink (1P) model
 - 135 -

6.10 Conclusions

According to the predicted CFD data, perforated PHSs enhance thermal

airflow characteristics compared to the equivalent solid PHSs. These benefits
increase as the number of perforations increase. Evidently, pressure drop decreases
monotonically and Nusselt number increases monotonically when increasing the
number of perforations. For a given Reynolds number, the 5P pin fin design provides
the peak heat transfer rate and the lowest pressure drop and fan power requirement.
Thus, this cooling technique, using the perforated pins, can be regarded as an
effective cooling method because it reduces processor temperatures and fan power,
which is a key goal of the thermal management of electronics, as detailed in Table
6.1. CFD analysis indicates that the improvement in heat transfer is due to the
combined effects of enhanced heat transfer near the perforations through the
formation of localised air jets and increased total surface area (AT).

Based on the pin arrangement, the staggered pinned heat sinks for both solid
and perforated pins provide a lower CPU temperature than that of the in-line array,
while more fan power is required to overcome the pressure drop through these pins
compared with the in-line arrangement under the same boundary conditions, as
shown in Table 6.2.

Regarding the perforation shape, it is shown that a compromise is needed

between the choice of either the elliptic perforated pins, 3EP, which provide the
smallest amount of pressure drop and fan power, or the circular perforated pins, 3CP,
which have the lowest CPU temperature and the highest Nusselt number, Table 6.3.

The optimum design of the single perforated PHSs (1P) was investigated for
two design variables: diameter of perforations (d, mm) and the locations of single
perforations (y, mm). It was found that these design variables do not have a
significant effect on the objective functions, Tcase and Pfan; it is less than 1.5%.
 - 136 -

Table 6.1: The enhancement of Nusselt number (Nu), and fan power (Pfan) of
each 3P and 5P design compared with solid (0P) pins HSs

Parametric Studies ↓ Pfan ↓ Tcase

↑ AT ↑ NuT
Heat Sink Designs (W) (oC)

Perforated Pins with Three Perforations (3P) 15% 9% 9% 8%

Perforated Pins with Five Perforations (5P) 25% 11% 14% 10%

Table 6.2: The reduction of CPU temperature (Tcase), and the increasing fan
power (Pfan) of staggered array compared with in-line array for solid (0P) and
perforated (3P) pins HSs

Parametric Studies ↑ Pfan ↓ Tcase

Heat Sink Designs (W) (oC)

Staggered array of solid Pins (0P) 30% 10%

Staggered array of perforated Pins (3P) 30% 12%

Table 6.3: Enhancement of Nusselt number (Nu), fan power (Pfan), and CPU
temperature (Tcase) of different perforations shapes

Parametric Studies ↓ Pfan ↓ Tcase

↑ AT ↑ NuT
Heat Sink Designs (W) (oC)

Circular Perforated Pins (3CP) 15% 9% 9% 8%

Square Perforated Pins (3SP) 18% 4% 7% 5%

Elliptic Perforated Pins (3EP) 17% 4% 12% 5%

 -137 -

7 Chapter Seven: The Benefits of Slotted and Notched

PHSs

7.1 Introduction

This chapter further investigates the effects of different configurations of

rectangular perforated pinned heat sinks on conjugate heat transfer and turbulent
airflow. The two designs tested are slotted PHS (3S, 6S, 10S) designs with
rectangular perforations removed from the centre of the pin (henceforth referred to as
slotted pins, SPHSs) and notched PHS (2.5N, 5N, 7.5N) designs with rectangular
notches removed from the top of the pin (notched pins, NPHSs), as shown in Figure
7.1. The CFD predictions of thermal airflows over those new heat sink designs are
examined in detail in relation to heat transfer and airflow characteristics.
The main goal is to understand the airflow and thermal characteristics of these
new heat sink designs to discover how these pin fin models can reduce the hot spots
through the heat sink and enhance airflow along it compared with solid pin fins (0P).
In addition, the optimum new PHSs design is considered to reduce the processor
temperature for minimal fan power consumption input into the system.

7.2 Description of PHS Models

Six types of pinned heat sinks are examined for conjugate heat transfer and
turbulent airflow, as shown in Figure 7.1. Three pin designs with rectangular
perforations removed from the centre of the pin as slotted pins, SPHSs, and three
with rectangular notches removed from the top of the pin as notched pins, NPHSs,
are compared with baseline cases with solid pins and pins with circular perforations
based on thermal airflows past PHSs as considered in previous chapters. Slotted and
notched PHSs with 8×8 in-line arrangement of these pins are analysed
comprehensively under the same computational domain and boundary conditions as
previously mentioned. The pinned heat sink section comprises eight rows in the in-
line array perpendicular to the flow direction (cross flow), as shown in Figure 7.2.
 -138 -

Generally, the heat sink layout has a base of 50mmx50mmx2mm with an 8x8
array of 2mm diameter (D) and 10mm height pins (H) on a 6.5mm pitch in both
directions (Sx, Sz), as seen in Figure 7.2. Air flows past through the slots and notches
of these pin fins. The slot height (h) is changed at 3mm (3S), 6mm (6S), and 10mm
(10S) but the slot width (w) is kept constant at 1mm. The porosity is considered with
different values (ϕ=Vhole/V) where Vhole is the slot and the notch volume and V is
solid pin volume, respectively. Hence, the porosity of these slotted pin fins is 0.185,
0.370, and 0.617 for the S3, S6, and S10 designs, respectively. With respect to the
notched pin fins, the height of the notch (h) is varied at 2.5mm (2.5N), 5mm (5N),
and 7.5mm (7.5N) whilst the notch width (w) is kept constant at 1mm. Thus, the
porosity of these notched pins is 0.154, 0.308, 0.562, for N2.5, N5, N7.5 models,
respectively.

Total wetted area (AT) = Projected area + Total surface area contribution from the
pin fins

For solid pin fins:

AT  WL  N (DH ) (7.1)

For slotted pin fins:

AT  WL  N [(DH )  (2hD)  (2wD)  (2hw)] (7.2)

For notched pin fins:

AT  WL  N [(DH )  (2Dh)  (2wh)] (7.3)

where (W, L) are the width and length of the base plate heat sink (50x50) mm, (N)
the total number of fins (64 pins), (H) the height and (D) the diameter of the pins,
which are 10mm and 2mm, respectively, (h) the height of the slot or notch, and (w)
the width of the slot or notch (1mm). Therefore, the percentage of increase in the
total surface area with respect to solid pins (0P) is 10%, 16%, and 20% for the
slotted pins 3S, 6S, and 10S, respectively, while, for the notched pins 2.5N, 5N, and
7.5N, it is 5%, 10%, 15%, respectively.
 -139 -

h= 3mm,
h= 6mm, h= 10mm,
w= 1mm
w= 1mm w= 1mm

3S 6S 10S
Slotted Pin Fins

h= 2.5mm, h= 5mm, h= 7.5mm,

w= 1mm w= 1mm w= 1mm

2.5N 5N 7.5N

Notched Pin Fins

Figure 7.1: Slotted and notched pinned heat sink designs

A B

Figure 7.2: (A) Plan view and Side view (B) 3D of the notched pinned heat
sink being analysed
 -140 -

7.3 Open Slotted and Notched Area

The behaviour of the airflow passing through the pin fin heat sinks is described
firstly. The effects of the new heat sink models on airflow are presented in Figure 7.3
for inlet air velocity 10m/s at Reynolds number =5393 and 8 pins with a longitudinal
distance of 6.5mm.

As mentioned earlier, in the perforated pins section (Chapter 6), the dead
thermal-flow zones will appear and develop just in the wake of solid objects such as
fins, ribs, and blocks. The airflow separates from the surface of these objects and the
speed of recirculating flow behind solid objects is low, (see section 6.3, as shown in
Figure 6.3A and Figure 6.4A). This causes the heat transfer rate from these zones to
reduce and the pressure drop through these solid objects will usually be high. Thus,
to avoid this adverse effect, many attempts have been proposed depending on
changing the fluid flow pattern and geometric conditions (Sara et al., 2001). One of
these attempts to enhance thermal and fluid flow characteristics is allowing the flow
to pass through the solid fins by replacing them with slotted or notched fins. The
slotted or notched pin fins will reduce the hot spots that typically occur behind solid
fins by means of improving the airflow and vanishing vortexes zones, resulting in a
well-mixed layer of fluid flow, (see section 6.3, as shown in Figure 6.3B, C and
Figure 7.4B, C). Hence, the thermal characteristics and pressure drop characteristics
are enhanced in this case (Sara et al., 2001).

Consequently, a detailed investigation of the thermal and hydraulic

characteristics of slotted and notched PHSs is now presented.
 -141 -

7.4 Hydraulic Characteristics

The air fluid flow behaviour, pressure drop (∆P), fan power (Pfan), profit power
factor (J), and pressure drag coefficient of the slotted and notched pin fins HSs are
discussed in this section.

7.4.1 Airflow Behaviour

Enhancement of thermal characteristics and reduction in the fan power of heat

sinks are affected by airflow behaviour across pin fin heat sinks. Thus, it is important
to discuss this parameter study in this work first (Sara et al., 2001). The effects of the
new heat sink models on airflow behaviour are shown in Figure7.3 for the air inlet
velocity 10m/s at Reynolds number (5393).

Similarly to the perforated pin fin heat sinks, the recirculation zones behind the
slotted and notched pin fins will gradually reduce in size with the expansion of the
open slotted and notched area (increase the height of the slot and notch), as shown in
Figure 7.3. These vortices can be seen behind the solid pin heat sink (0P) model
while they will be less significant in the slotted and notched pin fins cases. The main
reason for this is that the airflow passing through the open slotted and notched area is
straighter and so the vortex zones will be reduced. Hence, the recirculation zones
(wakes) are eliminated for the slotted and notched pin fin heat sinks, while the
airflow attacks and interacts with the frontal surface area of the solid pin and so air
separation will occur.
 -142 -

Recirculating flow Separation flow

Solid Pin
(0P)

Slotted Pin
(3S)

Jet flowing through perforations with vanishing vortex & separation flow

Slotted Pin
(10S)

Velocity
(m/s)

Figure 7.3 Comparison between predicted flow field in PFHSs with solid pin
fins 0P and for designs 3S and 10S
 -143 -

7.4.2 Pressure Drop, Fan Power, Profit Power Factor, and Pressure Drag
Coefficient

Figures 7.4, 7.5, and 7.6 illustrate the effects of the slotted and notched pin fin
heat sink designs on the pressure drop, fan power, and profit power factor for a range
of Reynolds numbers (3500-6580) with the inlet air velocities ranging from 6.5m/s
to 12m/s.

It can be seen from these figures that the pressure drop of the slotted and
notched pins is smaller than that of the benchmark PHS. The main cause of this is
that the airflow path across the solid pins is narrow and wavy, which results in more
recirculation zones and greater separation of airflow behind the solid pins, as
indicated previously. In the case of the new designs, however, these rectangular
perforations enhance the mixing of fluid at the rear of the pin, and flow separation
from the surface will be delayed. Thus, there is less pressure drop and flow
resistance for the slotted and notched pins than for the solid pins (Yang et al., 2010).

For slotted (3S, 6S, 10S) and notched (2.5N, 5N, 7.5N) pin heat sinks, Figures
7.4 and 7.5, the pressure drop and fan power reduction is monotonically higher when
increasing the height of the slot or notch due to these rectangular perforations. The
highest reduction is nearly 40% for the 10S slotted pin model and approximately
33% for the 7.5N notched pin in relation to the solid pin fin (0P) model.

Figure 7.5 shows that the reduction in fan power has the same pattern of
pressure drop and they increase as the Reynolds number increases. This indicates
that the slotted and notched pin fins will save more energy that is consumed via the
fan than will the solid fins.

As indicated previously, the profit power factor compares the amount of

consumed fan power against the applied amount of heat flux at the heat sink base.
The profit factor of the slotted and notched pins is highest compared with the solid
one, Figure 7.6.

For more information about local pressure drop along pinned heat sinks, see
section 6.4.2.
 -144 -

110 110
3S (A) 2.5N (B)
100 100
6S 5N
10S 90 7.5N
90
0P 0P
80 80

∆P (Pa)
∆P (Pa)

70 70

60 60

50 50

40 40

30 30

20 20
6 7 8 9 10 11 12 13 6 7 8 9 10 11 12 13
U (m/s) U (m/s)

Figure 7.4 Effect of (A) slotted and (B) notched pins on pressure drop with
variation in airflow speed

0.45 0.45
3S 2.5N
(A) (B)
0.4 6S 0.4 5N
10S 7.5N
0.35 0P 0.35 0P

0.3 0.3
Fan Power (W)

Fan Power (W)

0.25 0.25

0.2 0.2

0.15 0.15

0.1 0.1

0.05 0.05
6 7 8 9 10 11 12 13 6 7 8 9 10 11 12 13
U (m/s) U (m/s)

Figure 7.5: Effect of (A) slotted and (B) notched pins on fan power as a function
of airflow speed
 -145 -

1000 1000

(A) 3S (B) 2.5N

6S 5N
800 800
10S 7.5N
0P 0P
The Profit Factor

The Profit Factor

600 600

400 400

200 200

0 0
3000 3500 4000 4500 5000 5500 6000 6500 7000 3000 3500 4000 4500 5000 5500 6000 6500 7000
Re Re

Figure 7.6: Comparisons of the profit factors with different heat sinks (A) slotted
and (B) notched pins

The effects of the slotted and notched pin fin heat sink models on the pressure
drag coefficient are shown in Figure 7.7 for a range of inlet velocities between
6.5m/s and 12m/s at Re=3500-6580 and 8 pins with a longitudinal distance of
6.5mm.

The pressure drag coefficient of these six pinned heat sink models is smaller
than that of the solid pins as well as its value decreases as the open area expands (the
height of the slot or notch increases). As mentioned earlier, the frontal area of the
slotted and notched pins is smaller than that of the solid pins, which means that part
of the airflow passes through this open area easily, as the open area is larger and so
has less resistance to airflow, and that is in agreement with the findings of Ismail
(2013). Therefore, the pressure drag coefficient decreases as the open area expands
when the slot and notch height are increased.

Generally, the ratio of pressure drop and kinetic energy is defined as the
pressure drag coefficient. This factor decreases when the inlet air velocity (Reynolds
number) is increased due to increasing the kinetic energy more than increasing the
pressure drop due to the open slotted and notched area.
 -146 -

1.6 1.6
(A) 3S (B)
6S 2.5N
1.5 1.5
5N
10S
7.5N
1.4 0P 1.4 0P
Pressure Drag Coefficent

Pressure Drag Coefficent

1.3 1.3

1.2 1.2

1.1 1.1

1 1

0.9 0.9

0.8 0.8

0.7 0.7
3000 3500 4000 4500 5000 5500 6000 6500 7000 3000 3500 4000 4500 5000 5500 6000 6500 7000
Re
Re
Figure 7.7: Variation in pressure drag coefficient of slotted (A) and notched (B)
pins with different Re

7.4.3 Effect on Power Consumption

As mentioned previously, the fan power factor plays a vital role in minimising
the power consumption, which increases the profit factor of PHSs. The reduction in
power consumption of the slotted and notched pins is higher than that of the solid
pins (0P), as shown in Figure 7.5. Additionally, the fan power consumption reduces
with expansions in the slot and notch areas and leads to the profit factor increaseings
at a given air velocity. For example, the reduction in power consumption is
approximately 15.5%, 30% and 40% for slotted pins 3S, 6S, and 10S respectively,
and nearly 13.5%, 24.5% and 33% for notched pins 2.5N, 5N, and 7.5N respectively.
The profit factor increases by approximately 18.5%, 40.5% and 66.5% for slotted
pins 3S, 6S, and 10S respectively, and by nearly 16%, 33% and 49.5% for notched
pins 2.5N, 5N, and 7.5N respectively, as seen in Figure 7.6.

Subsequently, the first aim of the current study in reducing the fan power
consumption (pressure drop) is achieved by using the slotted and notched PHSs.
 -147 -

7.5 Heat Transfer Characteristics

Some important thermal characteristics such as the Nusselt number and the
base heat sink temperature (Tcase) are explained and discussed in the following sub-
sections.

7.5.1 Average Nusselt Number

Figures 7.8A and 7.8B indicate the effect of each of the given slotted and
notched pin designs on the total NuT and projected NuP for a range of inlet velocities
from 6.5m/s to 12m/s (Re = 3500-6580) and 8 pins with streamwise and spanwise
distances of 6.5mm.

For the slotted and notched pin fin heat sinks, it can be observed from Figure
7.8A that the solid pin fin has a slightly higher NuT than those of slotted and notched
pin fins. When the height of the slot or notch increases, increasing the open area, the
NuT number decreases. The maximum percentage increase in NuT of the solid pin
does not exceed 2% compared with the other pin fin designs. The main reason for
this is that some of the airflow passes inside the open area and the local mean
velocity through this open area decreases with increases to the height of the slot or
notch, as shown in Figure 7.9 (local mean velocity). This local mean air velocity
through the slots and notches may be not strong enough to accelerate the airflow
over the slot or notch areas, which results in weakening the flow turbulence and flow
mixing (Alam et al., 2014). Secondly, the NuT of the slotted and notched pinned heat
sinks have decreased slightly, which means that the increase in heat transfer is
proportionately slightly less than the increase in the total wetted surface area in the
heat sink due to the perforations. These findings are consistent with the recent
conclusions of Shaeri & Yaghoubi (2009a). In addition, for heat conduction along
pin fins, the reduction in the cross-sectional area along the pins when increasing the
height of the slot or notch results in reduction to the heat transfer conduction rate of
these pins and to the Nusselt number (NuT).

However, as shown in Figure 7.8B, the projected Nusselt number (NuP) of

each of the slotted and notched pinned heat sinks will increase compared with the
solid pin (0P) model. For instance, the Nup enhancement reaches approximately 8%,
14.5%, and 17% for the 3S, 6S, and 10S slotted pins, respectively, while it is nearly
5%, 8%, and 12% for the 2.5N, 5N and 7.5N notched pins, respectively. Thereby,
 -148 -

NuP may be a more effective measure of a heat sink’s cooling capacity for a given
PHS size compared with NuT. It can be observed that the enhancement in the
projected Nusselt number, NuP, of the slotted pinned heat sinks is twice that of the
notched pins, except for the 10S and 7.5N models. This means that the amount of
heat removed from the heat sinks increases with these new pin designs because NuP
is based on a constant projected surface area, which demonstrates that perforations
significantly improve the magnitude of the heat transfer.

Regarding to the above results, the Nusselt number might not represent the
actual heat transfer rate from heat sink. The main reason for this is that the
calculation of the Nusselt number depends on the heat transfer coefficient (h) and the
characteristic length (X) and each of these parameters are found in different
procedure. For example, the heat transfer coefficient (h) are found based on either
the total wetted surface area (AT) of heat sink or the projected surface area (AP). In
addition, the characteristic length (X) might represent either the length of heat sink in
direction of flow (L), the pin diameter (d), or the duct hydraulic diameter (Dh). Thus,
it is required another thermal parameter to evaluate the thermal performance of heat
sinks that might be the CPU temperature, which is discussed in the next section.

Collectively, Figures 7.4, 6.5 and 6.8B show that the pressure drop and fan
power decrease monotonically and NuP increases monotonically with increases to the
slotted and notched perforation area (the height of slot and notch).
 -149 -

360 360

3S (A) Slotted Pins 2.5N (A) Notched Pins

340 6S 340 5N
10S 7.5N
320 0P 320 0P
NuT

NuT
300 300

280 280

260 260

240 240
3000 3500 4000 4500 5000 5500 6000 6500 7000 3000 3500 4000 4500 5000 5500 6000 6500 7000
Re Re
1100 1100
3S (B) Slotted Pins 2.5N
(B) Notched Pins
6S 5N
1000 10S 1000
7.5N
0P
0P

900 900
NuP
NuP

800 800

700 700

600 600
3000 3500 4000 4500 5000 5500 6000 6500 7000 3000 3500 4000 4500 5000 5500 6000 6500 7000
Re
Re

Figure 7.8: Effect of slotted and notched pinned heat sinks on Nusselt number
based on (A) total (B) projected surface area
 -150 -

14
(A) Slotted Pins
13 3S 6S 10S

Ux (m/s) 12

11

10

8
1 2 3 4 5 6 7 8
Number of Pins

14
(B) Notched Pins
13 2.5N 5N 7.5N

12
Ux (m/s)

11

10

8
1 2 3 4 5 6 7 8
Number of Pins

Figure 7.9: Variation in the mean local air velocity through (A) slotted and (B)
notched pins

7.5.2 Thermal Management of PHSs

Figure 7.10 shows an example of a conjugate heat transfer analysis which

predicts the average base plate temperature Tcase with fan power as inlet air velocity
is varied from 6.5m/s to 12m/s through a system of 8 pins separated longitudinally
by a distance of 6.5mm for all new models – slotted (SPHSs) and notched (NPHSs)
pinned heat sinks.

Figure 7.10 illustrates that the slotted and notched pin fins have smaller Tcase
and fan power than that of the solid pin fins (0P), except that the Tcase of the 10S
slotted pin model is slightly hotter than that of 0P solid pin model. This may be
because the number of slotted pins (10S) has been doubled, from 64 to 128 pins, by
making them thinner by reducing their diameter to half the diameter of the solid pin
fins (0P), leading to reductions in the conductive heat transfer rate through them.
Thereby, the 10S model requires more airflow to help to lower the CPU temperature
 -151 -

than does the solid pin (0P) model. It can be noticed that the lowest Tcase are nearly
4oC for slotted the 6S pin fins with h=6mm and notched 7.5N pin fins with h=7.5mm
both with notch and slot width w=1mm at a given fan power.

82 82
(A) (B) 2.5N
80 3S 80
5N
6S
78 78 7.5N
10S 0P
76 0P 76
Tcase ( C)

Tcase ( C)
74 74
o

o
72 72

70 70

68 68

66 66

64 64
0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45
Fan Power (W) Fan Power (W)

Figure 7.10: Effect of (A) slotted and (B) notched pins on Tcase and fan power

Figure 7.11 compares the surface temperature distribution of the solid pin heat
sink (0P design) with those obtained on the slotted and notched pin fins. The
maximum temperature is at the fin base and it reduces to the fin tip. It can be
observed that the drop in temperature of these new pin fin designs is less significant
with changes to the height of the slot or notch. The maximum temperature drop from
the fin base to the fin top increases by increasing the height of the notch from 2.5mm
to 7.5mm and by increasing the slot height from 3mm to h=6mm.

The CPU temperatures of the solid pins vary between approximately 58.5oC
and 71oC. In terms of the new heat sink designs, however, in the slotted pin 3S, 6S,
and 10S models the corresponding temperatures change between roughly 57.5oC –
70oC, 54.5oC –70oC, and 54oC –72oC, respectively. In the notched pin 2.5N, 5N, and
7.5N designs the temperature distributions vary from nearly 58oC –70oC, 57.5oC –
70oC, and 55.5oC –70oC, respectively.
 -152 -

According to the predicted CFD data, the first and second aims of the current
study, that is, slightly enhancing the CPU temperature (by nearly 2%) and producing
valuable reductions in the fan power of the slotted and notched PHSs, are achieved.
This means that the heat transfer rate increases at a given fan power (pressure drop)
using these heat sinks, which is one of the usual active cooling techniques.

0P
Tin= 25oC

6S

10S

7.5N

Figure 7.11: Temperature distribution through pinned heat sinks: 0P, 6S, 10S,
and 7.5N models at Re=5393

7.6 Optimum Design of the Notched Pinned Heat Sink

As indicated previously, PHSs are designed to maintain the processors below

critical temperatures for minimal energy input into the system. This section focuses
on the optimisation of notched pins as a function of notch height, h, and width, w, for
PHSs with an 8x8 array of pins with a constant pin spacing of 6.5mm in either
direction. The multi-objective optimisation problem studied here is to minimise Tcase
and Pfan for 2.5mm≤ h ≤10mm and 0.5mm≤ w ≤1.5mm for a constant air inlet
velocity, Uair= 8m/s (Re=4315). Since the above results have shown that minimising
Tcase and minimising Pfan leads to conflict between them, the goal is to construct a
Pareto front of non-dominated solutions, from which an appropriate compromise
design can be chosen.
 -153 -

Thus, the optimisation problem can be defined as follows:

Objective function: minimise Tcase & Pfan

Subject to: 2.5 mm ≤ h ≤ 10mm

0.5 mm ≤ w ≤ 1.5mm

Again, an Optimal Latin Hypercube approach uses a permutation genetic

algorithm to achieve a uniform spread of points within the design space (Narayanan
et al., 2007). This approach distributes the two design variables in the spacing design
uniformly within the lower and upper limits of each variable, as shown in Figure
7.12.
1.5

1.4

1.3

1.2

1.1 Building points

w (mm)

Validation Points
1

0.9
w

0.8 h

0.7

0.6

0.5
2.5 5 7.5 10
h (mm)

Figure 7.12: Distribution of design points in the design variable space for the
height, h (mm) and the width, w (mm) of the notch

Figures 7.13 and 7.14 show the response surface function of CPU temperature
and fan power of the notched PHS regarding the design variables height (h) and
width (w) of the notch at inlet air velocity 8m/s. The optimised response surface
function demonstrates that the Tcase and Pfan minima occur on the domain boundaries.
Pfan is reduced by increasing the notch area through increases to both h and w,
whereas the Tcase response surface function further highlights the importance of
localised air jets through the perforation. Tcase is reduced by increasing h and
decreasing the notch width, w. The optimised MLS method has given very good
agreement with merged DoEm: R2 =0.938 for Tcase and Pfan.
 -154 -

Figure 7.13: Response surface function of CPU temperature (Tcase) of the

notched pinned heat sink model

Figure 7.14: Response surface function of fan power (Pfan) of the notched
pinned heat sink model
 -155 -

The Pareto front is obtained by using the Tcase response surface function to
determine the design points (h, w) at which Tcase is a specified value and then using
the Pfan response surface function to determine which of these design points has the
smallest fan power. The resultant Pareto front is shown in Figure 7.15, where the
brown triangles compare numerical predictions of Tcase and Pfan against the Pareto
front values obtained from the response surface function. These are generally in very
good agreement, with typical discrepancies of less than 2%.

The Pareto curve shows the compromise options that are available between a
low Tcase and a low Pfan. In the cases considered, the minimum Pfan that can be
experienced while ensuring Tcase is below the reference critical temperature of 85oC
is approximately 0.06W, and this has to be increased by 30% (to 0.078W) and 60%
(to 0.096W) to ensure Tcase remain below 75oC and 70oC, respectively.

87

85
Pareto Front
83
CFD Prediction
81
Tcase ( C)

79
o

77

75

73
U=8 m/s
71 8x8 pins array

69
0.05 0.06 0.07 0.08 0.09 0.1
Pfan (W)

Figure 7.15: Pareto curve of Tcase and Pfan for an 8x8 PHs with notched pins,
with an inlet air speed of 8m/s
 -156 -

Figure 7.16 shows plan views of the flow fields for the points on the Pareto
curve with Tcase=86.3oC and Pfan=0.0592W, with h=10mm and w=1.35mm as a wide
notch pin model, and Tcase=70oC and Pfan=0.0934W, with h=10mm and w=0.8mm as
a narrow notch pin model; airflow is from right to left in both cases. The former case
corresponds to the low pressure drop case where air flows rapidly through the notch
(with a maximum speed of approximately 12.0m/s compared to the inlet air speed of
8m/s) and with minimal separation around the pins. The latter case, with the smaller
notch width w=0.8mm, causes a larger increase in air speed through the notch (up to
a maximum of approximately 13.3m/s) which leads to more effective convective
heat transfer at the cost of greater levels of separation and pressure drop across the
pins.

Minimal separation level around

Wide Notch Pin Model: h=10mm, w=1.35mm the pins

Greater separation level

Narrow Notch Pin Model: h=10mm, w=0.8mm

Velocity
(m/s)

Figure 7.16 Plan views of flow field through notch perforations for a wide
notch with Tcase=86.3oC and Pfan=0.0592W and a narrow notch with
Tcase=70oC and Pfan=0.0934W
 -157 -

The surface temperature distribution for the wide and narrow notch pin models
are shown in Figure 7.17. It is clear that the maximum temperature is for the wide
notch pin model compared to the narrow notch pin model that has lowest
temperature distribution. It can be observed that the drop in temperature of the
notched PHS design is significant with changes to the width of notch. The CPU
temperatures of the wide notch pin model vary between approximately 58oC and
88oC with low fan power consumption while the narrow notch pin model the
corresponding temperatures change between roughly 54oC–71.5oC with high fan
power consumption required. Table 7.1 shows the comparing between the predicted
Tcase and Pfan from MLS with simulated Tcase and Pfan from CFD with very well
agreement.

Tin= 25oC Wide Notch Pins Model: h=10mm, w=1.35mm

Narrow Notch Pins Model: h=10mm, w=0.8mm

Figure 7.17 : The optimum temperature distribution of the wide and the
narrow notch pin models with an inlet air speed of 8m/s

Table 7.1: Compare between Tcase and Pfan of predicted MLS and simulated CFD
Design Variable Multi-Objective Function
Predicted Simulated Predicted Simulated
h w Error Error
MLS CFD MLS CFD
(mm) (mm) % %
Tcase (oC) Tcase (oC) Pfan (W) Pfan (W)
10 1.35
86.3 85 1.5 0.0596 0.0592 0.67
Wide Notch Pin
10 0.8
70 70 00.0 0.0934 0.0951 1.78
Narrow Notch Pin
 -158 -

7.7 Comparison between Circular Perforated Pins, Rectangular

Slotted, and Notched PHSs

Table 7.2 illustrates the comparison between the Nusselt number (NuT, NuP),
fan power (Pfan), and CPU temperature (Tcase) for the circular perforated, slotted, and
notched PHSs compared to the equivalent solid pin HSs.

Despite increasing surface area of the slotted and notched pin designs, heat
transfer rate (in terms of NuT and NuP) and CPU temperature of the multiple circular
perforated PHS models show the greatest enhancement. This means that the benefits
arise due to not only the increased surface area but also to the heat transfer
enhancement near the perforations through the formation of localised air jets.
However, the fan power consumption required for the slotted and notched pins is
smaller than that for the multiple circular perforated PHSs because the porosity of
the slotted and notched pins is larger compared with that of the circular perforated
pins, which enables air to flow easily across the pins.

It can be concluded that a compromise has to be struck between the choice of

perforations. Since the larger enhancements in heat transfer with multiple circular
perforations come at the price of both significantly increased power consumption
and, perhaps most importantly, a much more complex manufacturing process, while
the slotted and notched PHSs are more practical and bring about a greater reduction
in fan power consumption.
 -159 -

Table 7.2: Comparison of Nusselt number, fan power (Pfan), and CPU
Temperature (Tcase) between perforated, slotted, and notched PHSs

Nusselt Number
Parametric Studies
↑ AT ↓ Pfan ↓ Tcase
↑ NuT ↑ NuP (W) (oC)
Heat Sink Designs
Perforated Pins with One
5% 1.7% 5% 2% 2%
Perforation (1CP)
Circular PPHSs

Perforated Pins with Two 5%

10% 14.5% 6% 5%
Perforations (2CP)
Perforated Pins with Three
15% 9% 24% 9% 8%
Perforations (3CP)
Perforated Pins with Five
25% 11% 36% 14% 10%
Perforations (5P)
Slotted Pins (3S) 10% -1% 8% 15.5% 2%
SPHSs

Slotted Pins (6S) 16% 0% 14.5% 30% 2%

Slotted Pins (10S) 20% -1% 17% 40% 0%

Notched Pins (2.5N) 5% 0% 5% 13.5% 1%

NPHSs

Notched Pins (5N) 10% -1% 8% 24.5% 2%

Notched Pins (7.5N) 15% 0% 12% 33% 2%

7.8 Weight Reduction of Heat Sinks

Figure 7.18 illustrates the percentage weight reduction of all pinned heat sink
designs. The weight of these pins decreases with increases in the number of
perforations or the open slotted and notched area, which leads to saving material in
manufacturing the pin fins and lighter assembly as well. Furthermore, the cost and
energy of the force required to drive the air by fan power will reduce significantly.
According to Shaeri (2009b), the two optimal outcomes for pin fin design are to
maximise the heat transfer rate for any given fin weight or minimise the weight for a
required heat transfer rate. Another advantage of this weight reduction is associated
with heat transfer enhancement for the perforated pinned heat sink designs according
to the numerical data. However, the cost manufacturing process of perforated pinned
heat sinks is higher compared to that solid pined heat sink.
 -160 -

The total weight reduction of the pins considered here has been calculated
utilising the following equations and the values are shown in Figure 7.18:

𝑉𝑇 = 𝑉𝐵𝑎𝑠𝑒 + 𝑉𝑃𝑖𝑛𝑠 (6.4)

𝑊𝑇 = 𝜌𝐴𝑙 × 𝑉𝑇 (6.5)

where VT is the total volume of PHS, VBase is the volume of base PHS, VPins is the
total volume of pins, WT is the total weight of PHS, and the density of aluminium
𝜌𝐴𝑙 = 2700 Kg/m3.

In the case of the perforated, slotted, and notched pins, the highest percentage
of reduction in pin weight is seen in the 5P model with 5 perforations, 10S at 10mm
slot height, and 7.5N with 7.5mm notch height at 7%, 14%, and 18%, respectively.

In terms of different types of perforation shape, the percentage total weight

reduction is approximately 5% for both square perforated pin fins (3SP) and elliptic
perforated pin fins (3EP). Therefore, by using these types of pinned heat sink, both
aims of pin fin optimisation are achieved, particularly by increasing the number of
perforations.
 -161 -

20 20

16 16

Total Weight of PHSs (g)

Total Weight of PHSs (g)

W=1%

W =3%
12

W =5%
12

W =4%

W =9%
W =7%

W =14%
8 8

4 4

0 0
0P 1P 0P
2P 5N
3P
5P 2. 5N
5N
7.
Models of Perforated Pin Fins Models of Notched Pin Fins

20
20

16
Total Weight of PHSs (g)

16
Total Weight of PHSs (g)

12
W =5%

12 W =4%
W =11%

W =5%

W =6%
W =18%

8
8

4
4

0
0
0P
3S
6S S 0P P
10 3C P
Models of Slotted Pin Fins 3S P
3E
Models of Perforated Pin Fins

Figure 7.18: The percentage total weight reduction of PHSs

 -162 -

7.9 Conclusions

Airflow past a heat sink with arrays of slotted (SPHSs) and notched (NPHSs)
pins has been solved numerically, and the solution method has explored the thermal
and hydraulic characteristics of these heat sinks compared with the benchmark solid
pin fin (0P) model. Slotted and notched pins may offer a more practical means of
manufacturing perforated PHSs: either wire Electrical Discharge Machining could be
used to directly cut into the slots/notches, or a series of thin cutting discs mounted on
a common shaft could be used with support to the pins provided through a jig. This
would also retain the high thermal conductivity between the pin and the base plate of
a heat sink cast from a single block.

Generally, the CFD data shows that, in relation to the fan power (pressure
drop) of the heat sinks, the new pinned heat sink designs require a smaller amount of
fan power compared with the solid pins. The slotted (10S) pin model has the lowest
fan power of 40%. The solid PHS has a NuT slightly higher than those of slotted and
notched pins while the NuP of the new pinned heat sinks is the largest. The
maximum percentage increase in NuP is nearly 17% for 10S model compared with
the other pin designs. The Tcase of the slotted and notched pins is slightly (2%) lower
than that of the solid pin model, as detailed in Table 7.3. The perforations etched into
the top of the pins, notched pins, may offer a more practical means of manufacturing
perforated PHSs, as indicated previously.

The optimum design of the notched PHS has been investigated for two design
variables: the height (h, mm) and width (w, mm) of the notch. The main goal of this
study was to reduce both CPU temperature and fan power of the pinned heat sinks.
The formal optimisation study has demonstrated the practical compromise that has to
be struck between low processor temperatures (modelled in terms of the variable,
Tcase) and the fan power needed to achieve the required rate of cooling. Thus, the
minimum Pfan that can be experienced while ensuring Tcase is below the reference
critical temperature of 85oC is approximately 0.06W, and this has to be increased by
30% (to 0.078W) and 60% (to 0.096W) to ensure Tcase remains below 75oC and
70oC, respectively.
 -163 -

The new pinned heat sink SPHS and NPHS models are superior to the solid
PHS because they require less fan power to push air over the pin heat sinks and there
is an acceptable reduction in thermal resistance while, as discussed earlier, they
require more preparation in their manufacture.

Table 7.3: Enhancement of Nusselt number (Nu), fan power (Pfan), and CPU
temperature (Tcase) of slotted and notched pinned heat sinks

Nusselt Number
Parametric Studies
↑ AT ↓ Pfan ↓ Tcase
↑ NuT ↑ NuP (W) (oC)
Heat Sink Designs

Slotted Pins (3S) 10% 10% -1% 8% 15.5%

SPHSs

Slotted Pins (6S) 16% 16% 0% 14.5% 30%

Slotted Pins (10S) 20% 20% -1% 17% 40%
Notched Pins (2.5N) 5% 5% 0% 5% 13.5%
NPHSs

Notched Pins (5N) 10% 10% -1% 8% 24.5%

Notched Pins (7.5N) 15% 15% 0% 12% 33%
 - 164 -

8 Chapter Eight: Effect of Pin Density and Applied Heat

Flux

8.1 Introduction

After an indication that the new pinned heat sinks, perforated and notched
PHSs, have a lower CPU temperature and fan power for active air-cooling of
electronic systems, the reliable performance of high-power density electronics for
PHSs is another important consideration for efficient cooling design strategies.
Essentially, the thermal effects cause some failure of the mechanisms in devices
containing electronic components, such as void formation, metal migration, and
inter-metallic growth. For each 10oC increase above the operating temperature of
high-power electronics, the rate of these failures almost doubles (Gurrum et al.,
2004). Thus, thermal management of electronics is of crucial significance to the
industry market.

This chapter considers two key parameters for the performance of pinned heat
sinks: density distribution of the pin fins and heating power applied at the sink base.
This consideration specifically relates to the CPU temperature value in addition to
the Nusselt number, NuT, NuP, and pressure drop (∆P). The main purpose for this is
to investigate the application reliability (capability) of these pinned heat sink designs
in the desktop PC UPS for waste heat dissipation. In addition, the study also wishes
to estimate the allowable level of applied heating power on these new pinned heat
sink designs.

8.2 Effect of Pin Density Distribution

The effects of the distance between pins (Sx, pin columns) on the pressure drop
(∆P), heat transfer rate (NuT, NuP), and CPU temperature (Tcase) are explained in
detail in this section for the in-line array solid (0P), perforated (3P), and notched
(7.5N) pinned heat sinks to obtain the optimum distribution of pin density on pinned
heat sinks.
 - 165 -

According to previous researchers such as Sahin & Demir (2008), the flow
blockage increases as the distance between pins (Sy, pins rows) decreases, leading to
increases in the pressure drop (fan power) along the heat sink as well. Thus, the pin
spacing (Sx, pin columns) is only considered at 15mm, 9mm, 6.5mm, and 4.5mm
while the pin spacing (Sy, pin rows) is not reported in this study and its value is
constant at 6.5mm, Figure 8.1. In other words, there will be models with 4, 6, 8 and
11 pin columns in the stream flow direction and each transverse column that is
perpendicular to the airflow direction has 8 pin fins only for solid (0P), perforated
(3P), and notched (7.5N) pin heat sink models.
Columns

Rows
Flow
Direction

A: 4x8 Arrays B: 6x8 Arrays

Flow
Direction

C: 8x8 Arrays D: 11x8 Arrays

Figure 8.1: Schematic of different heat sink geometries in in-line arrangement for
top and side views
 - 166 -

The variations in pressure drop with the number of columns and different
Reynolds numbers for solid (0P, left), perforated (3P, right), and notched (7.5N)
pinned heat sink models are illustrated in Figure 8.2.

As expected, the pressure drop of the heat sink (ΔP) increases with increasing
numbers of pins and Reynolds number as well. In all cases, halving the number of
columns from 8 to 4 would reduce the pressure drop by approximately 35%.
Commonly, the lowest pressure drop value is for the notched pins (7.5N) and then
the perforated pins (3P), compared with that of solid pins (0P), due to the
perforations. When increasing the Reynolds number from 3500 to 4315, the pressure
drop gradually increases while, when the Reynolds number increases up to 6580, the
pressure drop sharply increases. The pressure drop of the solid pins sharply increases
when the columns are increased in number from 8 to 11 compared with the 3P and
7.5N pin models. This is because the presence of more solid pins (decreasing pin
spacing) in addition to increasing air viscosity due to increasing air temperature
through the heat sink, leads to increasing the blockage of the airflow passing over the
solid pins.
 - 167 -

140 140
Each
Each Row has
column 8 Solid
has Pins
8 solid (0P)(0P)
pins Each
Each column has8 8Perforated
Row has perforatedPins (3P)(3P)
pins
Re=3500
120 Re=4315 120 Re=3500
Re=5393 Re=4315
Re=6580 Re=5393
100 100 Re=6580

80 80
∆P (Pa)

∆P (Pa)
60 60

40 40

20 20

0 0
4 5 6 7 8 9 10 11 4 5 6 7 8 9 10 11
Number of Columns Number of Columns

140
Eachcolumn
Each Row has 8 Notched
has Pins
8 notched (7.5N)
pins (7.5P)
120 Re=3500
Re=4315
Re=5393
100 Re=6580

80
∆P (Pa)

60

40

20

0
4 5 6 7 8 9 10 11
Number of Columns

Figure 8.2: Variation of pressure drop with the number of columns and
different Reynolds numbers for solid (0P), perforated (3P), and notched
(7.5N) PHS designs
 - 168 -

The dependence of total (NuT) and projected Nusselt number (NuP) on the
number of columns and Reynolds number for both solid (0P), perforated (3P), and
notched (7.5N) pinned heat sink models is shown in Figures 8.3 and 8.4.

The CFD data of the solid pinned heat sink (0P) indicates that the total Nusselt
number (NuT) gradually increases when increasing the number of columns from 4 to
8 (nearly 11% larger), as shown in Figure 8.3. For additional pin columns from more
than 8 columns up to 11 columns, however, the NuT increase remains almost
constant because the total surface area will increase with the presence of more pin
columns, leading to decreases the heat transfer coefficient as indicated previously. In
terms of the notched pins (7.5N), the pattern of NuT with a different number of
columns is similar to that of the solid pins (0P) and the NuT reaches a maximum
value for the 8 pin columns nearly 10% higher than that of the 4 pin columns.
However, the optimum total Nusselt number value of the 3P model is for the 6 pin
columns, typically 4% higher than for the 4 pin columns. Conversely, it seems that
the Nusselt number remarkably decreases when increasing the pin columns up to 11,
as seen in Figure 8.3. This is because, with more perforated pin or notched pin
columns, the total surface area will increase to higher than that of the solid pins,
resulting in a remarkable decrease in the heat transfer coefficient.

On the other hand, the variations of projected Nusselt number (NuP) with the
different number of columns and Reynolds number for solid (0P, left), perforated
(3P, right), and notched (7.5N) pinned heat sink designs gave different results, as
presented in Figure 8.4.

The projected Nusselt number, NuP, of the solid, perforated, and notched
pinned heat sinks will enhance as the number of pin columns increases. The
enhancement reaches approximately 50% as pin density doubles from 4 to 8 columns
for all cases. It means that the amount of heat removed from the heat sinks will
increase with the presence of more pin material due to moving the amount of heat
through the base of the heat sink to the pins and then into the surrounding air.

Generally, the total and projected Nusselt number of the perforated pins (3P) is
superior compared with the solid (0P) and notched (7.5N) pins, as well as this value
increases when increasing the Reynolds number for the pinned heat sink designs.
 - 169 -

500 500
Each
Eachcolumn has
Row has 8 solid
8 Solid pins
Pins (0P)
(0P) Each column
Each has88Perforated
Row has perforated pins
Pins (3P)
(3P)

450 450 Re=3500

Re=3500 Re=4315
Re=4315 Re=5393
400 Re=5393 400 Re=6580
Re=6580
NuT

NuT
350 350

300 300

250 250

200 200
4 5 6 7 8 9 10 11 4 5 6 7 8 9 10 11
Number of Columns Number of Columns

500
Each
Each Row has
column has8 8Notched
notchedPins
pins(7.5N)
(7.5P)

450
Re=3500
Re=4315
400 Re=5393
Re=6580
NuT

350

300

250

200
4 5 6 7 8 9 10 11
Number of Columns

Figure 8.3: Effect of the number of columns on the Nusselt number and the
Reynolds number for solid (0P), perforated (3P), and notched (7.5N) PHSs
 - 170 -

1400 1400
EachRow
column Each column
hashas 8 perforated
Pins pins
(3P) (3P)
Each has 8has 8 solid
Solid pins (0P)
Pins (0P) Each Row 8 Perforated
1300 1300

1200 1200

1100 1100

1000 1000
NuP

NuP
900 900

800 800

700 700 Re=3500

Re=3500 Re=4315
600 Re=4315 600 Re=5393
Re=5393 Re=6580
500 Re=6580 500

400 400
4 5 6 7 8 9 10 11 4 5 6 7 8 9 10 11
Number of Columns Number of Columns

1400
Each
Each column
Row hashas 8 notched
8 Notched pins
Pins (7.5P)
(7.5N)
1300

1200

1100

1000
NuP

900

800

700
Re=3500
600 Re=4315
Re=5393
500
Re=6580
400
4 5 6 7 8 9 10 11
Number of Columns
Figure 8.4: Variation in pressure drop with the number of columns and
different Reynolds number for solid (0P), perforated (3P), and notched
(7.5N) PHS designs
 - 171 -

Figure 8.5 shows the effect of the number of pin columns on the CPU
temperature with variations in the Reynolds number for solid (0P, left), perforated
(3P, right), and notched (7.5N) pinned heat sink models. It is indicated that the CPU
temperature of the perforated pins is lower than those of the other pin designs due to
the perforations.

The reliability of these pin fin heat sink designs in a desktop PC CPU should
be considered in relation to the minimum number of pin columns in order to obtain
the cheapest cost and simplify fabrication of the heat sinks. Hence, the most
important thermal parameter in practical applications of heat sinks is to keep the
CPU temperature at less than the critical temperature (~85oC). Figure 8.5 indicates
that the maximum allowed temperature of a PC CPU is as a red line at 85oC with
different pin density (Yuan et al., 2012; Yu et al., 2005).

This temperature value drops as the Reynolds number increases and with the
presence of more pin material resulting from the increased convection and
conduction heat transfer via the amount of heat moving through the heat sink base to
the pins and then being transferred to airflow passing over the pins, causing a drop in
CPU temperature. At the lowest given Reynolds number (3500), it is recommended
that the number of pin columns should be no lower than 8 columns for the solid (0P)
and notched (7.5N) pins, while 6 pin columns is enough for the perforated pins (3P)
to cool the PC CPU. With the highest given Reynolds number (6580), however, it is
recommended to use the 4 pin columns for PC CPU cooling for the perforated
pinned heat sink model (3P) while no fewer than 5 columns are required for both the
solid (0P) and the notched (7.5N) pins to keep the CPU temperature lower than
85oC.
 - 172 -

110 110
Each
Eachcolumn has
Row has 8 solid
8 Solid pins
Pins (0P)
(0P) Each column
Each has88Perforated
Row has perforated pins
Pins (3P)
(3P)
105 105

100 Re=3500 100 Re=3500

Re=4315 Re=4315
95 Re=5393 95 Re=5393
Re=6580 Re=6580
90 90

Tcase ( C)
Limit for desktop PC CPU Limit for desktop PC
Tcase ( C)

85 85

o
o

CPU
80 80

75 75

70 70

65 65

60 60

55 55
4 5 6 7 8 9 10 11 4 5 6 7 8 9 10 11
Number of Columns Number of Columns

110
Each
Eachcolumn
Row hashas 8 notched
8 Notched pins
Pins (7.5P)
(7.5N)
105
Re=3500
100
Re=4315
95 Re=5393
Re=6580
90
Tcase (oC)

Limit for desktop PC

85
CPU
80

75

70

65

60

55
4 5 6 7 8 9 10 11
Number of Columns

Figure 8.5: Effect of the number of columns on the CPU temperature and the
Reynolds number for solid (0P), perforated (3P), and notched (7.5N)
pinned heat sink models
 - 173 -

Focussing on the practical outcomes of the cooling, reducing the heat sink
temperature for a given fan power input with pin density is shown in Figure 8.6.
Results are plotted with respect to a critical reference temperature of 85oC as a red
line. The results show that, as heat transfer rate from the CPU increases, convection
and conduction heat transfer increases, resulting from the higher pin densities. It
means that the CPU can be cooled below the critical temperature for a significantly
lower fan power input with greater pin density. For example, the Tcase reduces by
approximately 30~35% as the number of pins increases from 4 to 11 pin columns.

At a given fan power, the lowest base plate temperature Tcase is for the 11 pin
columns compared with the other heat sinks. This is because the column with the
smallest number of pins requires more airflow passing over the pins to remove a
certain amount of heat, while less airflow is required to cool columns with a denser
number of pins due to the increased conduction and convection heat transfer
(presence of more pin material) for the CPU to be significantly cooler. The
perforated pins (3P) exhibit smaller Tcase than the solid and notched pins, while the
notched pin (7.5N) model consumes less fan power than the solid and perforated
pinned heat sinks due to the large notched area.

For the solid and notched pins, a fan power of 0.1W enables the CPU
temperature to be maintained below 73oC when 11 columns of pins are used
whereas, for 4 columns, the CPU temperature of 100oC is well above the critical
CPU temperature. Using columns of the 3P perforated pin model reduces the CPU
temperature yet further, for a given fan power input, and even makes the adoption of
4 columns of perforated pins viable for fan power inputs above 0.15W.

Generally, the CPU temperature reduces and the heat transfer rate enhances
as pin density increases, while the pressure drop increases.
 - 174 -

110 110
Solid Pins (0P) Perforated Pins (3P)
105 105
11×8 Arrays
100 100 11×8 Arrays
8×8 Arrays
95 6×8 Arrays 8×8 Arrays
95
4×8 Arrays 6×8 Arrays
90 90 4×8 Arrays
Tcase ( C)

Tcase ( C)
85 85
o

o
Limit for desktop PC CPU Limit for desktop PC CPU
80 80

75 75

70 70

65 65

60 60

55 55
0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Pfan (W) Pfan (W)

110
Notched Pins (7.5N)
105
11×8 Arays
100
8×8 Arays
95 6×8 Arays
4×8 Arays
90
Tcase ( C)

85
o

Limit for desktop PC CPU

80

75

70

65

60

55
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Pfan (W)

Figure 8.6: Effect of the number of columns on the CPU temperature and fan
power of solid (0P), perforated (3P), and notched (7.5N) pinned heat sink
models
 - 175 -

8.3 Effect of Applied Heat Flux

Since modern CPUs have dynamically changing voltages, leading to variations

in heating power 𝑄̇, at the base of a PHS. This section of the numerical investigation
considers the supplied heating power that is selected based on the real working
conditions of the PC CPU (Yuan et al., 2012), to estimate the allowable level of
applied heating power on these new pinned heat sink models. Thus, the heating
power applied at the base of the pin fin heat sinks is considered 10, 20, 40, 60, 70,
80, and 90W typical of heating generated by PCs (Yuan et al., 2012). In other words,
the heat flux employed on the solid (0P), notched (7.5N) and perforated (3P) pin heat
sink models is 0.4, 0.8, 2.4, 2.8, 3.2, 3.6W/cm2, respectively. Figures 8.7, 8.8, 8.9
and 7.10 illustrate the variation of pressure drop (ΔP) and CPU temperature (Tcase)
with different applied heat flux on the pinned heat sink bases.

According to the heating power at 10W, the effect of air temperature inside the
flow passage on the variation in air properties is small and can be ignored. The air
properties, however, will be affected by this temperature inside a test section as the
heat flux increases above 20W. Thermodynamic properties of air such as density,
thermal conductivity and other properties vary with temperature through the heat
sink. Thus, the air temperature variation inside the heat sink is significant to the
analysis and it cannot be disregarded when increasing the applied heat flux (Yuan et
al., 2012). It can be chosen among different methods to compute the corrected air
properties. As indicated previously, ANSYS FLUENT-CFD code will calculate the
property values by piecewise-linear interpolation method among the values defined
at several air temperatures.

The variation of the pressure drop along heat sinks with different applied heat
flux and inlet air velocities from 6.5 to 12 m/s is illustrated for the solid (0P), Figure
8.7, perforated (3P), Figure 8.8, and notched (7.5N), Figure 8.9, PHSs with (A)
constant air properties and (B) variable air properties. Generally, the pressure drop of
these heat sinks will increase as the supplied heating power increases from 10W to
90W, considering the variable air properties, while the change of pressure drop is
unremarkable when the air properties are constant. The main reason for this is that
the air viscosity will increase due to the increase in air temperature that results from
increasing the supplied heating by 800% with variable air properties. Therefore,
 - 176 -

higher air viscosity results in more fan power being required to push the air through
the heat sink (test section). It can be seen that this pressure drop increases slightly –
by nearly 4% for the solid (0P) design while it is approximately 6% and 8% for
notched (7.5N) and perforated (3P) heat sinks, respectively – when the applied heat
flux increases from 10W to 90W. This indicates that the heat transfer rate from the
3P model is higher than that of the 7.5N and solid (0P) designs, meaning that the
temperature of the airflow passing through the 3P and 7.5N models is higher
compared with that of the solid (0P) design. These findings are consistent with the
recent conclusions of Yuan et al. (2012), which attributed improved heat transfer to
plate-pin heat sinks to illustrate the effect of increasing applied heat flux on the
pressure drop through a compact heat sink.

125 125
Q=10W (A) Q=10W (B)
115 Q=20W 115 Q=20W
Q=40W Q=40W
Q=60W Q=60W
105 Q=70W 105 Q=70W
Q=80W Q=80W
95 Q=90W 95 Q=90W

85 85
∆P (Pa)

∆P (Pa)

75 75

65 65

55 55

45 45

35 35

25 25
6 7 8 9 10 11 12 6 7 8 9 10 11 12
U (m/s) U (m/s)

Figure 8.7: Variation in pressure drop through perforated pins (3P) with
different applied heat flux and inlet air velocities (A) constant and (B)
variable air properties
 - 177 -

115 115
Q=10W Q=10W
Q=20W (A) Q=20W (B)
105 Q=40W 105 Q=40W
Q=60W Q=60W
95 Q=70W 95 Q=70W
Q=80W Q=80W
Q=90W Q=90W
85 85

∆P (Pa)
75 75
∆P (Pa)

65 65

55 55

45 45

35 35

25 25
6 7 8 9 10 11 12 6 7 8 9 10 11 12
U (m/s) U (m/s)
∆p (Pa)

Figure 8.8: Variation in pressure drop through perforated pins (3P) with
48
different applied heat flux and inlet air velocities (A) constant and (B)
7.5 8.5
variableU air
(m/s)properties
 - 178 -

115 115
Q=10W (A) Q=10W (B)
105 Q=20W 105 Q=20W
Q=40W Q=40W
Q=60W Q=60W
95 Q=70W 95 Q=70W
Q=80W Q=80W
85 Q=90W 85 Q=90W
∆P (Pa)

∆P (Pa)
75 75

65 65

55 55

45 45

35 35

25 25
6 7 45 8 9 10 11 12 6 7 8 9 10 11 12
U (m/s) U (m/s)
∆p (Pa)

Figure 8.9: Variation in pressure drop through notched pins (7.5P) with
different applied heat flux and inlet air velocities (A) constant and (B)
variable air properties

35
Figure 8.10
7.5 indicates that the maximum allowed temperature 8.5 of a PC CPU is
U (m/s)
as a red line at 85oC for solid (0P), perforated (3P), and notched (7.5N) PHSs with
variable air properties. The CPU temperature increases as more heat flux is applied
on the base of the heat sinks while it decreases as air velocity increases from 6.5m/s
to 12m/s. At heat flux 70W, the critical temperature is exceeded for air speeds below
8m/s. However, the air speed must be above 10m/s for the perforated pin (3P) model
and it must be above 12m/s for the solid pins (0P) and notched pins (7.5N) if the
power is greater than 90W. Thus, the perforated (3P) model has Tcase lower than the
other pinned heat sink (PHS) models.
 - 179 -

Commonly, an applied heat flux of 60W is recommended since the peak CPU
temperature is still under the required maximum temperature at the lowest inlet air
velocity for all pinned heat sink cases, as shown in Figure 8.10 and that is in
agreement with the findings of Yaun et al. (2012).

115
Q=10W
Q=20W
105 Q=40W
Q=60W
Q=70W
95
Q=80W
Q=90W
Limit for desktop
PC CPU 85
Tcase ( C)

75
o

65

55

45

35

25
6 7 8 9 10 11 12
U (m/s)

115 115
Q=10W Q=10W
Q=20W Q=20W
105 Q=40W 105 Q=40W
Q=60W Q=60W
Q=70W Q=70W
95 95 Q=80W
Q=80W Q=90W
Q=90W
85 85
Tcase( C)
Tcase( C)

75 75
o
o

65 65

55 55

45 45

35 35

25 25
6 7 8 9 10 11 12 6 7 8 9 10 11 12
U (m/s) U (m/s)

Figure 8.10: Variation in CPU temperature of 0P (top), perforated (3P, Left), and
notched (7.5N, Right) pins with different applied heat flux and inlet air
velocities
 - 180 -

8.4 Conclusion

Results indicate that, with higher pin density, the CPU temperature of the
pinned heat sinks reduces while the fan power (pressure drop) increases through the
heat sinks. In all cases (0P, 7.5N, and 3P models), halving the pin density from 8 to 4
pins reduces the pressure drop by roughly 35%. The projected Nusselt number (NuP)
increases up to 50% as the pin density doubles from 4 to 8 columns. However, the
total Nusselt number (NuT) is slightly enhanced with greater pin density, from 4 to 8
columns for solid and notched pins and from 4 to 6 columns for perforated pins,
whereas no further enhancement is seen when increasing the number of pins up to
11.

In terms of the possibility of heating power to the desktop PC CPU for waste
heat dissipation, the CPU temperature and the fan power increase when increasing
the supplied heating power from 10W to 90W. For example, the pressure drop of the
solid (0P) increases by nearly 4% while it is almost 6% and 8% for the 7.5N and 3P
pin models, respectively, when increasing supplied heat flux.

Generally, under the same conditions, the heat dissipation performance will be
enhanced with more pin columns while the pressure drop will increase. Furthermore,
the perforated PHS (3P) has the lowest CPU temperature and largest NuT, NuP while
the notched PHS (7.5) has the lowest pressure drop to satisfy the electronic cooling
applications at these conditions of pin density and applied heating power.
 - 181 -

9 Chapter Nine: Conclusions and Recommendations

9.1 Main Conclusions

The main conclusions of this study can be divided into three parts: perforated
pinned HSs, slotted and notched pinned HSs, and the practical limitations with
optimised pinned heat sink design. Collectively, the PHSs with perforations provide
an effective cooling technique to enhance the thermal hydraulic characteristics of
heat sinks by improved airflow mixing and increasing of the surface heat transfer
area with less fan power required.

9.1.1 Perforated PHSs

The following major conclusions for the perforated pinned HSs have been
determined from the present study:

1. The thermal airflow characteristics experimental data of the perforated (3P)

PHS model are improved compared with the solid (0P) PHS. The Nusselt
number of 3P model is higher while the pressure drop, fan power and CPU
temperature are lower than that of 0P model.
2. The maximum deviation between the experimental and numerical results
with constant air properties is acceptable within 10-15% for solid (0P) and
perforated (3P) models, given the practical difficulties of fabricating PHSs
with several perforations, when slight misalignment of the perforations with
the dominant airflow direction and finite perforation surface roughness may
occur. A further source of error for the heat transfer measurements may be
due to the additional thermal resistance because of the brazing process, where
the brazing material did not completely fill the gap between the pins and the
base plate.
3. Numerical results with variable air properties are closer to the experimental
results, within 5-10% for the solid (0P) and perforated (3P) models. Since the
air viscosity will increase with increasing air temperatures, more pressure
drop is required to push the air through the heat sink.
 - 182 -

4. The Nusselt number of the perforated PHSs increases with the presence of
more perforations, up to the maximum NuT and NuP values for the 3P model
with 3 perforations and the 5P model with 5 perforations, respectively,
compared with the solid (0P) PHS.
5. The pressure drop and pressure drag coefficient reduce with increasing
numbers of perforations. Thus, the fan power consumption is reduced for the
perforated PHSs compared with the solid PHS design.
6. The average CPU temperature (Tcase) of the perforated PHSs is lower than
that of the solid PHS (0P) design.
7. To maximise the benefits from the perforations, care must be taken to ensure
that they are aligned with the dominant flow direction and manufactured with
a good-quality surface finish.
8. The change of perforations vertically for the 2P and 3P PHS models only has
minor influence on the heat transfer enhancement. Since the perforations are
uniformly distributed along the pins, the formation of localised air jets
through perforations is also uniform along the pins. In addition, the
conductive heat transfer for the perforations at the bottom of the pins may be
not enough to augment the Nusselt number due to removing a part of the pin
material at the bottom of these pins.
9. When the perforations are moved from the centre to the outside of the pin fin
(horizontal perforations movement), the Nusselt number reduces while the
pressure drop increases. This may be due to vanishing the localised air jets
near the perforations and reducing the porosity of the pins and increasing the
blockage to the airflow passing over them.
10. Staggered arrangements for both the solid and perforated PHSs have the
lowest CPU temperature compared to the in-line arrangement under the same
boundary conditions, while the staggered pin array has the largest pressure
drop.
11. The different configurations of perforations shapes show a compromise
between the choices of either the elliptic perforated pins, 3EP, which provide
the smallest amount of pressure drop and fan power, or the circular
perforated pins, 3CP, which have the lowest CPU temperature and highest
Nusselt number.
 - 183 -

12. The optimum design of the singular perforated PHS (1P), the perforation
diameter (d) and the height of perforation (y) have an insignificant effect on
the objective functions, Tcase and Pfan.

9.1.2 Slotted and Notched PHSs

In the case of the rectangular perforations, slotted, SPHSs, and notched,

NPHSs, the following conclusions can be drawn from this study:

1. The perforations etched into the top of the pins, slotted pins, may offer a
more practical means of manufacturing perforated PHSs. For example, either
wire Electrical Discharge Machining could be used to directly cut into the
notches, or a series of thin cutting discs mounted on a common shaft could be
used with support to the pins provided through a jig. This would also retain
the high thermal conductivity between the pin and the plate of a heat sink cast
from a single block.
2. The Nusselt number might not represent the actual heat transfer rate from
heat sink. Because the calculation of the Nusselt number depends on the heat
transfer coefficient (h) and the characteristic length (X) and each of these
parameters are found in different procedure. Hence, it is required another
thermal parameter to evaluate the thermal performance of heat sinks that
might be the CPU temperature.
3. The solid PHS (0P) design has NuT slightly higher than those of the slotted
and notched pins, while the NuP of the new SPHSs and NPHSs is the largest.
The maximum percentage of increase is seen in NuP for the slotted (10S)
model compared with the other pin fin designs.
4. Nusselt number based on the projected surface area of a PHS, NuP, may be a
more effective measure of a heat sink’s cooling capacity for a given PHS size
compared with Nusselt number based on the total wetted surface area of a
PHS, NuT.
5. The average CPU temperature (Tcase) of the slotted and notched pins is
slightly lower than for the solid pin model.
6. With respect to the fan power or pressure drop, the SPHS and NPHS designs
use a smaller amount of fan power compared with the solid pins. The slotted
(10S) pin model uses the lowest fan power. This results in the fan power
 - 184 -

consumption of the SPHSs and NPHSs being smaller than that of the solid
(0P) PHS model.
7. The optimum design of the notched perforations has demonstrated the
practical compromise that has to be struck between a low processor
temperature (Tcase) and the fan power needed to achieve the required rate of
cooling.
8. The Pareto curve shows the minimum Pfan that can be experienced while
ensuring that Tcase should be below the reference critical temperature of 85oC.

9.1.3 Pin Density and Applied Heat Flux

General conclusions regarding the application limitations of PHSs have been

discovered from the present study:

1. In terms of pin density, the projected Nusselt number (NuP) increases up to

50% as pin density doubles from 4 to 8 columns for all models. However,
halving the pin number from 8 to 4 pins would reduce pressure drop by
roughly 35%.
2. The CPU temperature reduces and the NuP enhances as pin density increases
while the fan power increases.
3. With respect to the possibility of heating power applied on the desktop PC
CPU for waste heat dissipation, the CPU temperature and the fan power
increase when increasing the supplied heating power from 10W to 90W.
4. The comparison between the circular perforated pins, rectangular slotted and
notched pins highlights that a compromise needs to be struck between the
choice of perforations since the larger enhancements in heat transfer with
multiple circular perforations come at the price of both a significantly
increased power consumption and, perhaps most importantly, a much more
complex manufacturing process.
5. The total weight of these pins decreases when increasing the number of
perforations or the open slotted and notched area; this results in saving
material when manufacturing the pin fins and lighter assembly as well.
Furthermore, the cost and energy of the force required to drive the air fan
(fan power) will reduce remarkably.
 - 185 -

Generally, at the same conditions of pin density and applied heating power, the
perforated pinned heat sink (3P, 5P) models have the largest NuT, NuP and lowest
Tcase. If the fan power and pressure drop are considered, however, the notched PHSs
are superior to those of the perforated PHSs. That is because the porosity of the
notched pins is larger when compared with the perforated pins, leading to increasing
the airflow passing across the pins. In addition, the notched pins are much more
practical.
Finally, this study provides a mechanism for designing the optimal
perforations for specific heat transfer, fan power consumption and heat sink weight
requirements.
 - 186 -

9.2 Recommendations for Future Works

The following points are suggested for future studies:

1. The investigation of unsteady flow effects (e.g. vortex shedding) could be

proposed as a future consideration.
2. Perforated heat sink models such as perforated pinned HS, perforated strip
fins HS, perforated plate fin HS, perforated folded fin HS and on lateral
perforation plate fins HS can be experimentally and numerically investigated
using water, Nanofluids, and polymers liquid as a coolant for forced and
natural convection heat transfer and fluid flow.
3. The thermal and airflow characteristics of perforated strip fins heat sink can
be experimentally and numerically conducted for forced and natural
convection heat transfer and fluid flow.
4. It is recommended that the experimental and numerical investigation of
natural convection heat transfer and fluid flow should be studied for
perforated pinned heat sink models.
5. The perforations can be employed for other types of fins, such as square pins,
elliptic pins, and compact plate-pin heat sinks to study the thermo-fluid
characteristics using air, water, Nanofluids, and polymer liquid as a coolant
for forced and natural convection heat transfer and fluid flow.
6. The perforations might be employed for other applications that require
remove amount of heat such as solar collectors, PV panels, turbine blades etc.
7. Investigate the effect of noise and vibration of high level of inlet fluid on
thermal and hydraulic characteristics of solid and perforated heat sinks.
 - 187 -

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 - 194 -

Appendix A: Drawing of Experimental Rig Design

The parts of experimental rig design such duct and test sections are illustrated
as drawing figures in this appendix. All dimensions in mm.

Figure A 1: Insulation Teflon plate views

 - 195 -

Figure A 2: Other plate of duct views

 - 196 -

Figure A 3: Top Plate of duct views

 - 197 -

Figure A 4: Side plate of duct views

 - 198 -

Figure A 5: Solid pinned heat sinks (0P) model views

 - 199 -

Figure A 6: Perforated pinned heat sinks (3P) model views

 - 200 -

Figure A 7: Final rig design assembly with three views

 - 201 -

Appendix B: Experimental Uncertainty Analysis

By following Holman J. P. (2011) and McClinctock, (1988), errors in

experimental testing can be generally classified into two groups: precision errors
(random errors) and bias errors. Precision errors are discovered via a lack of
repeatability in the experimental measurement output and can be reduced by
generating multiple results and averaging them. Main sources of the bias errors are
calibration errors, an accuracy of measurements devices. Thus, it is often difficult to
detect these errors to the experimenter and reduce them. The experimental errors can
be given within a certain range of uncertainty. The uncertainty range of experimental
test (Un) that is associated with experimental parameters results (ψ) as a function of
other measured variables (A, B, C,….., Z) are found in this section with utilised
accepted errors analysis,

  f ( A n , B m , C p ,..., Z i )

Un
2 2 2 2
 UnA   UnB   UnC   UnZ 
 n    m   p   .........   i   (B.1)
  A   B   C   Z 

The uncertainties of each of the sensors and instruments in the experiment are
evaluated. The effect of these uncertainties on the values of convective heat transfer
coefficient, Nusselt number, thermal resistance, pressure drop, fan power, and
pressure drag coefficient is then.

Therefore, the uncertainty of heat transfer characteristics can be expressed as:

Heat transfer rate;

Qconv
have 
As [Ts  Tm ]

2 2 2
 UnQconv   UnAs   UnTs   UnTm 
2
Unhave
            (B.2)
have  Q   As   Ts   m T

Qconv  Qelectrical  V .I

2 2
UnQconv  UnV   UnI 
     (B.3)
Qconv  V   I 
 - 202 -

As  Abase  A fins

2
 UnAbase   UnA fins 
2
UnAs
      (B.4)
 A 
As  base   fins 
A

Abase  W .L

2 2
UnAbase  UnW   UnL 
     (B.5)
Abase  W   L 

For solid pin fins

A fins  N .( .D.H )

2 2
UnA fin  UnD   UnH 
     (B.6)
A fin  D   H 

For perforated pin fins

1
A fins   .N [( H .D)  ( n.d )  (n.d .D)]
2

2 2 2
UnA fin  UnD   UnH   Und 
       (B.7)
A fin  D   H   d 

Tin  Tout 
Tm 
2

2 2
1  1 
UnTm    0.5     0.5   0.353 o C
 2   2 

Where, the uncertainty of thermocouples (UnT), voltage (UnV) and current (UnI) of
power supplied (Aim-TTi EX354RD, EX-R Series) are ±0.5oC, ±0.003V, and
±0.006Amps, respectively. The number of pin fins (N) is 64.

The uncertainty of Nusselt number;

h.L
Nu 
k air

2
 Unh   UnL   Unk air 
2 2
UnNu
      (B.8)
Nu  h   L   k air 
 - 203 -

Unk air
0
k air

UnL
 0.0002
L

Thermal resistance uncertainty;

T Tcase  Tin
Rth  
Qelectrical Qelectrical

2
 UnT   UnQelectrical 
2
UnRth
    (B.9)
Rth  T   Qelectrical 

UnT  0.52  0.52  0.707 o C

The uncertainty of airflow characteristics such as; pressure drop, fan power, and
pressure drag coefficient can be expressed as:

Pressure drop;

P  Poutlet  Pinlet

2 2
UnP  UnPout   UnPin 
      (B.10)
P  out   Pin
P 

The uncertainty of fan power;

Pfan = U.A c .P

2
 UnU   UnAc   UnP 
2 2
UnP
        (B.11)
P  U   Ac   P 

Ac  H.S z .(n  1)

where, (n) is number of pins rows and the uncertainty of air velocity (UnU) is ±0.1

2
 UnH   UnS z 
2
UnAc
      (B.12)
Ac  H   Sz 

The uncertainty of pressure drag coefficient

Pd= ∆P/0.5ρ.U2
 - 204 -

2
 UnP   Un   UnU 
2 2
UnPd
        2   (B.13)
Pd  P      U 

As a result of that, the minimum and maximum uncertainties of the thermal and the
airflow relevant parameters such: heat transfer coefficient, Nusselt number, thermal
resistance, fan power, and pressure drop coefficient are illustrated in Table B.1.

Table B.0.1: Uncertainties of Experimental Parameters Studies

Parameters Uncertainty Parameters Uncertainty Parameters Uncertainty

have ± 2.5% Rth ± 2% Pd ± 2%

Nu ± 2.5% ∆P ± 2% T ± 0.5oC