Excerpt from the Proceedings of the 2011 COMSOL Conference in Boston

Design of Cooling System for Electronic Devices Using Impinging

Jets
Po Ting Lin1*, Ching-Jui Chang2, Huan Huang3, and Bin Zheng4
1
Rutgers, The State University of New Jersey, Mechanical and Aerospace Engineering, 2FTR
Systems (Shanghai) Inc., 3PolarOnyx, Inc., 4University of Electronic Science and Technology of
China, School of Mechatronics Engineering.
*Corresponding author: 98 Brett Road, Piscataway, New Jersey 08854, USA, potinglin223@gmail.com

Abstract: The heat sink designs using impinging Earlier in the end of last century, forced
liquid jets, which form stagnation flows, feature convection cooling systems replaced natural
uniform heat transfer coefficients, and provide convection systems on computer chips to
thin thermal boundary layers, are studied to improve the low efficiency in the latter one.
reduce the heat from GPUs. Three different Furthermore, the literature review [1] and
designs using central, micro, and uniform-cross- experiments [2-3] showed the forced convection
section (UCS) central jets are studied and cooling systems, including air and liquid cooling
simulated in COMSOL. The efficiency factors, technologies, provide higher power dissipation
defined as the ratio of total removed energy over capabilities. There are three major techniques to
inlet pumping energy, are measured to improve the efficiency of dissipating the heat
quantitatively represent the heat transfer from the computer components utilizing the air
performances. The central and micro jet designs cooling systems: changing the geometry of the
consume smaller amounts of pumping powers conducting material to increase convection
but form vortexes and thicker thermal boundary surface area, changing the conducting material to
layers near the outlets. The UCS central jet increase the surface temperature and achieve
design not only avoids the vortex formations but higher convection coefficient, and, lastly,
also maintains the thermal boundary layer increasing the flow rate of the external fluid to
thickness; therefore, higher efficiency has been reduce the thermal and hydraulic boundary
achieved. layers.
However, increasing the surface area
Keywords: impinging jet, CPU/GPU cooling, increases the cost in terms of using more
stagnation flow, computational fluid dynamics, materials for more complicated manufacturing
thin thermal boundary layer. processes for the conductive fins. Changing the
more conductive material such as copper often
1. Introduction increases the costs and the difficulties of
fabrication processes. Increasing the flow rate
System cooling has become a major problem usually requires larger fans which occupy
in designing and operating equipment used in a valuable spaces and generate annoying noises.
variety of industries, such as aerospace, nuclear, Furthermore, frequent maintenance was usually
and electronics. Recently, in the electronic required for air cooling systems, such as
industry, the need for rapid cooling on the lubricating the bearing of the fans and cleaning
integrated circuits (ICs) keeps increasing due to the dust accumulated over time. Therefore, we
the increasing number of transistors in the ICs mainly focus on the development of the liquid
which generate considerable amount of heat. cooling systems in this paper and intend to
Furthermore, while the refinement of design the next-generation cooling system for
manufacturing techniques, the sizes of the electronic devices.
computer ICs are dramatically reduced. Thus, Facing the increasing need for faster and
the heat flux on the chips is keeping climbing in larger computations in the recent engineering
a startling rate. Moreover, the sizes of the technologies, the frequency of the processing
electronic devices are reduced to meet the unit has become higher but its size has become
market’s needs. As a result, the available space smaller, that is, extensively increasing heat per
for cooling system is very limited and the area. Furthermore, the latest designs of the
convectional cooling techniques cannot satisfy personal computers (PCs) or the servers tend to
the increasing needs. decrease their sizes resulting in limited working
spaces for the computer components, such as heat via conduction heat transfer. The material
central and graphics processing units (CPUs and property of the heat sink is greatly related to the
GPUs), and the cooling apparatuses for them. performance of the conduction. The liquid
The conventional cooling systems such as heat coolant flows through the top surface of the heat
sink and fans cannot satisfy the needs for high sink and carries the heat away via convection
performances and efficiency, especially for the heat transfer. The geometry of the heat sink,
GPU in PC which only has very restricted area which not only varies the flow behavior but also
for cooling devices. To this end, the liquid affects the thermal efficiency of cooling, is
cooling system provides an efficient and another significant factor in the design of liquid
compact solution in terms of higher conductivity, cooling systems.
lower requirement of flow rate, and less noise. The chip size of the GPU is considered as 14
In the liquid cooling, the stagnation flows × 14 mm2 while the working area for the heat
provide higher heat efficiency [4-5] due to the spreader is considered as 39 × 39 × 18 mm3 due
characteristics of thin thermal and hydraulic to the common limited spaces in computers.
boundary layers. Therefore, three different Figure 1 illustrates the model of the liquid
cooling systems using liquid impinging jets are cooling system for a GPU chip. In the figure, the
designed and studied in this paper. The first kind black rectangular plate represents the GPU chip
utilizes single impinging jet at the center of the and the brown case is the design of the heat
heat sink while the second one uses multiple jets. spreader, which has the inner dimension of 35 ×
In the first two designs, the vortexes are formed 35 × 13 mm3. Some circular holes are drilled on
decreasing the thermal efficiency of cooling. the top of the heat spreader as the inlets and
The last design considers a uniform cross-section outlets of liquid coolant as the flow directions
channel for the single impinging flow in order to are illustrated by the blue arrows. Due to the
avoid the vortex formations and improve the geometrical symmetry of the design, only a part
thermal efficiency. The COMSOL multiphysics of the design space, illustrated by the dashed
software is utilized to numerically analyze and pentahedron, is modeled and studied in
simulate the three liquid cooling systems while COMSOL with appropriate boundary conditions.
multiple physics domains including conduction
heat transfer, convection heat transfer, and fluid
dynamics are involved.

2. Design of Liquid Cooling Systems

In this section, the design considerations of

the liquid cooling systems are presented. The
first subsection defines the cooling problems of
CPU or GPU using the designs of liquid cooling
systems. Furthermore, the numerical methods as
well as the boundary conditions for the cooling
systems are defined. To simplify the problem,
the conduction is decoupled from the multiple Figure 1. A drawing of the liquid cooling system.
physics domains and the detailed information is
further discussed. 2.2 Numerical Methods

2.1 Cooling Problems of Electronic Devices Multiple physics phases are considered in the
pentahedral design domain, including the solid
In this paper, the liquid heat sinks are conductive area at the bottom and the liquid
designed for the cooling of GPUs and they are convective region for the rest. There are 11
also applicable for other heat-generating different surface regions in the model of the
electronic devices such as CPUs. The cooling cooling system, illustrated in Figure 2. The
apparatus is directly attached on top of the GPUs surface regions A and D represent the interfaces
which is the main source of the heat generation between the coolant and the cold wall; the
while the bottom of the heat sink spreads the
surfaces E and K are the boundaries between 2.3 Further Simplifications
symmetric fluid domains; the circular regions C
and G respectively indicates the outlet and inlet Three physics domains are coupled in the
of coolant; lastly, the rest of the surfaces are the pentahedral design model. Although only a part
conductive boundaries in the heat spreader while of the whole model is selected for analysis, it is
the surface I is constantly heated by the GPU still costly to calculate the numerical results.
chip. Further simplifications on the boundary
Furthermore, the boundary conditions are conditions need to be made to reasonably
reconstructed and listed in Table 1. Note that the decouple the problem. The first attempt is to
boundary A is considered as insulation to neglect decouple the heat conduction in the solid part
the end effect. The actual temperature of the from the physics acting in the fluid if some
fluid out of the model should be expected to be evidences can be found to justify this idea. That
slightly higher. In CPU or GPU, the power is, if constant temperature on the fluid-heat
consumption is usually a constant value so that a spreader interface can be assumed, the
steady working state of the heat generated by the conduction domain can be decoupled form the
chips is assumed to be a constant. The heat flux problem.
q0 of GPU is defined as a constant value of The numerical result in Figure 3 shows that
25 W/cm2 to simplify the problem. The flow is the conductivity of copper is sufficiently high
driven by the pressure difference between the such that only slight temperature difference
inlet and the outlet and the pressure drop is (around 1.5 K) can be found at the interface
defined as 20 Pa. Copper is used as the spreader between the water and the copper heat spreader.
material because of the characteristic of high Furthermore, the finite element analysis tends to
conductivity. over-estimate the temperature at the sharp
corners with higher temperature gradients due to
C D E F G the computational singularities of interpolations
from near points. Therefore, the temperature
A difference can be considered as less than 1.5 K,
B Back Surface which supports the idea of treating the bottom
copper heat spreader as constant temperature. It
saves a lot more computational powers by
reducing the three-physics domain into a two-
physics design problem and considering
constantly heated wall at the bottom surface of
H I J K the heat sink. In the further simulation, the heat
Bottom Surface
spreader temperature is fixed at 350 K.
Figure 2. Illustrations and IDs of the surface regions
in the pentahedral design domain.

Table 1. Boundary conditions in Figure 2.

ID Fluidic Convection Conduction

A No slip Insulation –
B – – Insulation
C Outflow Convective flux –
D No slip Insulation –
E Slip Insulation –
F – – Insulation
G Inflow T0 = 300 K –
H – – Insulation
I – – Constant heat flux
J – – Insulation Figure 3. Nearly constant temperature is found at the
K Slip Insulation – water-copper interface as P0 = 0 Pa, Pin = 20 Pa, T0 =
300 K, and q0 = 25 W/cm2.
3. Detailed Information and Numerical the total exhausted power of the pump. The
Results utilized power of pump to maintain the constant
volume flow rate in the control volume is
In the paper, three different geometries are calculated by the product of the total pressure
studied. They are the central impinging jet, the difference between inflow and outflow.
micro impinging jet and the alternative central jet Therefore, the heat transfer efficiency E is given
designs. The design variables and results are by:
∫ q dAbase
''
presented and discussed in this section. An
efficiency factor is defined to quantitatively e= (1)
∆p ⋅ Ain ⋅ Vin
represent the heat transfer performances.
The results of different designs are listed in
3.1 Design I: Central Impinging Jet Table 2. When the inlet radius decreases,
stronger vortexes are formed to help the heat
In the central impinging jet design shown in transfer from the spreader to the fluid; however,
Figure 1, different dimensions of inlets and larger pumping power is required to maintain the
outlets have been examined. In order to maintain total volume flow rate. As a result, central jet
constant pressure drop from inlet to outlet, the design with smaller inlet radius is capable of
dimensions are subjected to the constant total releasing more energy from the heat spreader but
volume flow rate, 10 liter per hour. The inlet less efficient than the design with larger radius.
radius rin is chosen as the design variable and the
Table 2. The design parameters and results for central
outlet dimension is calculated accordingly. A jet design.
typical numerical result is shown in Figure 4.
The top subfigure shows the streamline and the
∫ q dA ∆p ⋅ Ain
''
rin Vin b e
formation of vortex inside the while the bottom
( mm ) ( mm / s ) ( w) (N )
subfigure shows the temperature distribution.
The thermal boundary layer at the bottom is 6 24.56 10.746 3.291e-6 1.329e5
fairly thin at the beginning when the flow comes 8 13.82 9.473 1.740e-6 3.941e5
in and grows thicker as the liquid flows out. 10 8.84 7.848 1.582e-6 5.613e5

3.2 Design II: Micro Impinging Jets

Another geometry design of the conducting

media is an array of micro-jets, vertically
flushing the bottom copper heat spreader and
acting as stagnation flows. The objective of the
micro-jet design is to take advantage of the
specific characteristic of constant heat transfer
rate at the stagnation point and expect to find
optimal heat transfer efficiency. Similarly, the
design variable is the inlet radius. Since the
numbers of inlets and outlets remain the same,
the inlet radius equals the outlet radius in order
to maintain the constant volume flow rate,
10 liter per hour.
On the top of the fluid domain, a number of
micro jets are designed as shown in Figure 5
Figure 4. Streamline and temperature distribution in with a pitch of 5 mm. Eighteen inlets and
the central jet design. eighteen outlets are arranged in an interlaced
arrangement. Therefore, the inflows act
To investigate the performances of heat sink consistently with each other, as well as the
designs with different inlet dimensions, a heat outflows. The flow motions are found
transfer efficiency factor is defined as the ratio of symmetric so that only a pentahedron shown in
the total heat flux at the fluid-solid interface and Figure 5 is needed to analyze the fluid dynamics
and thermal behavior for the entire fluid domain. Several different radiuses of inlets and
Due to the symmetry, the boundary conditions of outlets are designed and modeled. A typical
the side walls are slipping / symmetric. The top result of this design is shown in Figure 6. The
and bottom surfaces are no-slipping. The left subfigure shows the vortex in the design
boundary condition at the inlet is considered as domain while the right subfigure shows the
zero-normal-pressure. The copper heat spreader boundary temperature profile. The thermal
is considered as a constant temperature wall of boundary layer is fairly thin throughout the
350 K as described previously. The variations at cooling device. Due to the manufacturing
the sides of the fluid domain are neglected. Due limitation, the radius is limited in a bound
to the symmetry, the side walls of the between 0.2 and 2.3 mm (i.e. the holes of inlets
pentahedron are considered as heat insulated (i.e. and outlets cannot be less than 0.2 mm; the gaps
no heat exchange between two pentahedron of between the holes cannot be less that 0.2 mm).
fluid). The top surface is set as constant In Table 3, the resultant total heat fluxes at
temperature of 300 K, as well as the thermal the fluid-solid interface are found in different
boundary condition at the inlet. The outlet is set radiuses. As the size of the inlet increases, the
as convective flux. relative inlet velocity increases, as well as the
pressure difference. As a result, the exhausted
power of the pump increases gradually.
Although the total heat flux increases due to the
higher stream velocity, a huge amount of the
energy is exhausted by the shear forces from the
vortexes. In general, the increment of the inlet
size will enhance the heat transfer efficiency.
However, too large inlet size slows down the
stream velocity resulting in a great drop of the
total heat flux. The radius of 2 mm is found to
be the most efficient design for the micro-jet
cooling system.

Table 3. The results of micro-jet designs with

Figure 5. A drawing of the micro-jet design. (The
different radius.
pentahedron, the red-hatched region, is chosen to be
the design domain.
∫ q dA ∆p ⋅ Ain
''
rin Vin b e
( mm ) ( mm / s ) ( w) (N )
0.2 1.228 1.165 1.397e-5 6.791e4
1 4.912e-2 2.759e-1 6.167e-7 9.108e6
1.5 2.183e-2 1.550e-1 2.789e-7 2.546e7
2 1.228e-2 7.865e-2 1.300e-7 4.928e7
2.3 9.286e-3 4.160e-2 1.530e-7 2.929e7

3.3 Uniform-Cross-Section (UCS) Central Jet

From the previous two designs, the fluid

forms vortexes in the control volume which
dissipate unnecessary lost of energy on shear
stresses and decrease the efficiency of heat
transfer. Furthermore, the thickness of the
thermal boundary layers is not uniform
especially at the outlet positions where the heat
transfer rates are low.
The third design is to use an uniform cross
Figure 6. A typical result of streamlines and boundary section of the flow channel to decrease and
temperature profiles in the micro jet design. maintain the thickness of the thermal boundary
layer throughout the bottom surface such that the design is shown in Figure 8. The thermal
temperature gradient is increased near the boundary layer is uniformly thin throughout the
boundary. With increased temperature gradient, entire heat exchange surface. The total heat
the heat flux is therefore increased. Furthermore, transferred by this design is extremely high
by the design of the geometry, the vortex is because the thermal boundary is extremely thin
reduced so that all the pump work is mainly used and the temperature gradient is considerable high.
to propel the fluid against the wall shear only. In
order to minimize the frustrations of the fluid
generated by the geometry, the device is
designed to have uniform cross section area
along the fluid flowing path. The thickness of
the opening on the control volume is indicated in
Figure 7. The height on the curve is governed by
the flowing equation:
Ainlet π r2
h= = inlet (2)
Aflow _ band 2π rx
where rx is the distance of the position away
from center.

Figure 8. A typical result of streamlines and

temperature profiles in the UCS central jet design.

Five different designs of varying the radius

of the inlet from 3mm to 7mm are carried out
and the results are shown in Table 4. The pump
efficiency is calculated using the equation
aforementioned. It is worth notice that this
design has the fluid in it behavior as laminar
Figure 7. A drawing of the uniform-cross-section while the other two designs have turbulent.
central jet design that has fluid coming in the central From the results shown above, it can be noticed
opening and flow out toward the side with uniform that the efficiency varies with the inlet radii.
flow intersection. Under the same amount of flow rate, the optimal
efficiency is expected larger than 7mm of the
A control volume base on a slice of the fluid inlet radius. However, the heat transfer rate is
domain of 10 degree out of a full revolution is dropping to a level that can not be well utilized.
selected since this design is axisymmetric. For Although it requires more pressure difference to
thermal analysis, the upper surfaces are drive the fluid because of the extra contacting
considered to be the same temperature as the
inflow stream (300K), the bottom surface is set
Table 4. The results of UCS central jet design with
to be a constant temperature (350K), the outlet is different radius.
set to be convective flux, and both sides are
configure d to be insulated. For hydrodynamic
analysis, the inlet pressure is set to be a constant,
the outlet is configure d to have a constant flow
velocity calculated base on the given system
flow rate and the inlet radius, the both sides
adjoint to fluid are set to slip/symmetric and the
surfaces adjoint to solid parts are specified to be
the wall against the fluid. A typical result of this
surface area comparing to the first two designs in Heat and Mass Transfer, 26, page 689-699
this paper, this design is very thermally efficient (1983)
considering the total releasing heat. Better 4. Cengel, Y.A., Heat Transfer: A Practical
results can be expected with higher flow rate. Approach. McGraw Hill, New York, NY, USA
(1998)
4. Conclusion 5. Incropera, F.P., Liquid Cooling of Electronic
Devices by Single-Phase Convection. John Wiley
Liquid based cooling devices using & Son, Danvers, MA, USA (1999)
impinging jets are designed and studied in this
paper because a jet against a wall forms a thin
hydrodynamic boundary layer as well as a thin
thermal boundary layer which improves heat
dissipation tremendously. Three different
designs of geometries are carried out in this
paper and their cooling efficiency against pump
power consumption is studied. The first two
designs consumes smaller amount of pump
power because they have fewer liquid/solid
interface area. Vortexes are found in these two
designs due to the geometry and the turbulent
models are used to obtain the result. The thermal
and hydrodynamic boundary layers distort much (a)
in the design control volume. The third design
tries to confine the fluid in a uniform-cross-
section channel to minimize the boundary layers
and avoid the appearance of the vortexes. This
design can use fewer amount of flow rate to
achieve high thermal efficiency. Lastly, the
detailed comparisons of the numerical results of
three different heat sink designs are given in the
Figure 9. In general, smaller inlet dimensions
provide higher total removed energy but require
larger pumping energy at the inlet. In the
subfigure (c), the UCS central jet design has
higher thermal efficiency while the central jet (b)
design has the lowest.

5. References

1. Incropera, F.P., Convection Heat-Transfer in

Electronic Equipment Cooling, Journal of Heat
Transfer-Transactions of the Asme, 110, page
1097-1111 (1988)
2. Sparrow, E.M., J.E. Niethammer, and A.
Chaboki, Heat transfer and pressure drop
characteristics of arrays of rectangular modules
encountered in electronic equipment,
International Journal of Heat and Mass Transfer, (c)
25, page 961-973 (1982)
3. Sparrow, E.M., S.B. Vemuri, and D.S. Kadle, Figure 9. Comparisons of three different heat sink
Enhanced and local heat transfer, pressure drop, designs: (a) total removed energy; (b) inlet pumping
energy; (c) efficiency factor.
and flow visualization for arrays of block-like
electronic components, International Journal of