Effect of Using External Vertical Fins in Phase Change Material Modules

for Domestic Hot Water Tanks.

Albert Castell1, Cristian Solé1, Marc Medrano1, Joan Roca1, Daniel García2, Luisa F. Cabeza1
1
Dept. d’Informàtica i Eng. Industrial, Universitat de Lleida
Pere de Cabrera s/n, 25001 Lleida, Spain
Tel. +34 973003576, Fax. +34 973003575, e-mail: acastell@diei.udl.es, csole@diei.udl.es,
mmedrano@diei.udl.es, jroca@diei.udl.es, lcabeza@diei.udl.es
2
Engineering Projects Dept., Polytechnic University of Catalonia
Colom 11, 08222 Terrassa, Spain
Tel. +34 937398921, e-mail: daniel.garcia@upc.edu

Abstract 1 Introduction
When using renewable energies, the difference
The effect of using external vertical fins in Phase
between hot water availability and consumption
Change Materials (PCM) modules to improve the
increases the importance of thermal energy storage
natural convection coefficient in water is studied in
systems. Latent heat thermal storage has become a
this paper.
promising technology.
The use of PCM in a water tank working with a solar
Latent heat thermal storage uses Phase Change
system is able to store a lot of energy, but it is
Materials (PCM) to provide a higher energy density
necessary to transfer this energy to the water during
to thermal systems. Their use in Domestic Hot
demand.
Water (DHW) tanks would supply hot water for a
longer time.
Optimization of the natural convection to the water
is of great importance for the heat transfer. External
The use of PCM in a water tank working with a solar
fins increase the heat transfer surface and the heat
system has been studied in previous works [1,2].
transfer coefficient changes.
This technology is able to store a lot of energy, but it
is necessary to transfer this energy to the water
Experimental work was carried out to determine
during demand, therefore heat transfer within the
natural convection heat transfer coefficients for
PCM and to the water is of high interest.
PCM modules with two different external vertical fin
geometries. Results were presented as a
PCM composites and modules have been optimized
temperature variation over time of the PCM and the
to enhance the heat transfer [3,4], but natural
water, and the heat transfer coefficient as a function
convection from the PCM to the water have not.
of the temperature difference for different fins.
External fins increase the heat transfer surface and
the heat transfer coefficient changes.
These results were used to validate a simulation
code to determine the behaviour of the system
Fins geometry is very important to enhance the heat
using finned PCM modules. The results prove the
transfer coefficient. Two different geometries have
technical potential of external fins for heat storage
been studied: horizontal and vertical fins. There is
systems using PCM.
much more literature about horizontal fins [5-23] but
this geometry interferes natural convection in the
The experimental results were used to determine
water. No literature is available for vertical fins
different correlations for Nusselt number as a
around circular vertical cylinders, but this geometry
function of different dimensionless numbers.
improves the natural convection of the system.
Therefore, in this work external vertical fins have
Key Words been attached to the PCM module.
Phase Change Material (PCM), Fins, Natural
convection, Solar Energy, Nusselt Number, Previous work has been done introducing PCM
Experimental correlations. modules in DHW solar systems [1,2]. Four PCM
modules were introduced in a 146 L tank connected
to two solar collectors and the performance of the
systems was tested.

https://doi.org/10.24084/repqj04.253 118 RE&PQJ, Vol. 1, No.4, April 2006

The objective of this work is to study the effect of Each module had eight external fins, providing a
adding external vertical fins in the PCM modules. 28,45% and 44,28% transfer surface increase
Since there is no correlation in the literature to respectively compared to the reference module
evaluate the natural convection heat transfer without fins.
coefficient for the specific geometry studied,
experimental set-up has been designed and B. Experimental work
performed.
Experimental work consisted in simulating a storage
2 Analytical solution tank with PCM modules inside. Temperature of the
PCM and the water were registered for three
A. PCM modules without fins different experiments: first one used modules
without fins, another one used modules with 20 mm
To study the behavior of the storage system, an fins, and the last one used modules with 40 mm
energy balance of the water was done. This balance fins.
considers the following parameters:
Tank used was 440 mm of diameter and 450 mm of
• Heat transfer rate from the PCM to the height. Five K type thermocouples and a data-
water logger instrumented the experimental set-up. Two
• Heat transfer rate from the upper to the thermocouples were located inside the PCM module
lower layer of water (one in the centre and another one at half distance
• Heat losses from the water to the ambient between the first one and the metal container). The
air other ones were situated inside the water, outside
• Increase of the water temperature the PCM module, one of them in contact with the
external surface of it. The distance between the
To evaluate each term of the balance, experimental inside water thermocouples was 50 mm, and all
thermocouples were at 135 mm distance of the top
correlations found in the literature were used.
of the tank. Fig. 2 illustrates the instrumentation of
the experiments.
B. PCM modules with external vertical fins

The procedure to study the behavior of the PCM

modules with external vertical fins is the same used
for PCM modules without fins.

3 Experimental work
A. Geometry

To determinate the natural convection heat transfer

coefficient additional experiments were necessary.
The geometry of the PCM modules is the same
used in other experimental work done by the
authors [24,25]. These modules are cylindrical, with
a diameter of 88 mm and 315 mm high.
Fig. 2. Instrumentation of the experimental work.
Two different fins profiles have been analyzed to
determine the influence of the heat transfer surface The modules, containing melted PCM at 70ºC, were
to the water. The first one with 20 mm fins, the introduced into the cold water tank to evaluate the
second one with 40 mm fins, and both 310 mm heat transfer phenomena. The experiment was
high. Fig. 1 shows the PCM modules geometry. stopped when PCM and water temperatures were
the same.

The PCM-graphite composite used was sodium

acetate trihydrate with graphite (90:10 vol.%). This
product has a melting point of 58ºC, melting
enthalpy between 180 and 200 kJ/kg, density
between 1,35 and 1,4 kg/L, heat capacity of 2,5
kJ/kg·K, and thermal conductivity between 2 and 5
W/m·K.

Fig. 1. Module with external vertical fins.

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4 Results and discussion 70
WATER CLOSE
SURFACE MODULE
65
PCM 1/4

The experimental results show an increase in the 60

PCM 1/2
WATER FAR

heat transfer rate when using PCM modules with 55

vertical fins. This effect is a result of the increase of

Temperature (ºC)
50

the heat transfer area and the heat transfer 45

coefficient for natural convection. 40

35

The heat transfer coefficient for natural convection 30

for each PCM module geometry is determined and 25

compared in Fig. 3. The use of fins increased 20

significantly that coefficient, achieving heat transfer 0 200 400 600 800 1000 1200 1400 1600 1800
Time (s)
coefficients up to 3 times larger than the ones
without fins.
Fig. 5. Water and PCM temperature over time of
experimental work using a PCM module with vertical
1600
Big Fins
external fins of 20 mm length.
Natural convection heat transfer

1400

1200 Small Fins

coefficient (W/m2·K)

1000 No Fins
70
800
65 WATER CLOSE
600 SURFACE MODULE
60 PCM 1/4
400
PCM 1/2
200 55 WATER FAR

Temperature (ºC)
0 50
0 0,5 1 1,5 2 2,5 3 3,5 4
45
Temperature difference (K)

40

Fig. 3. Comparison of the natural convection heat transfer 35

coefficient for different PCM modules. 30

25

20
An important characteristic in a storage tank 0 200 400 600 800 1000 1200 1400 1600 1800 2000
Time (s)
connected to a solar system is the time needed to
heat the water to a useful temperature. This time is
Fig. 6. Water and PCM temperature over time of
reduced by using external vertical fins in the PCM experimental work using a PCM module with vertical
module. external fins of 40 mm length.

Fig. 4 shows the time needed to cool down a PCM Table I. Reduction of the time necessary to solidify the
module without fins from 60ºC to 45ºC, while Fig. 5 PCM.
shows the same results for a PCM module with 20
mm fins. Finally, the results of the experiments Without 20 mm 40 mm
Parameter
using a PCM module with 40 mm fins are presented Fins Fins Fins
in Fig. 6. Initial Temp (ºC) 60 59 60,1
Final Temp (ºC) 46,3 45,5 45,5
∆T (ºC) 13,7 13,5 14,6
70 WATER CLOSE
SURFACE MODULE Initial Time 12:43 12:41 12:41
65 PCM 1/4
PCM 1/2 Final Time 13:00 12:54 12:48
60 WATER FAR
∆t (minutes) 17 13 7
55
Temperature (ºC)

50

45 Using bigger fins allows achieving the highest heat

40 transfer coefficient value with a lower temperature
35 difference in comparison with the smaller ones.
30 Analyzing the obtained results, experimental
25 correlations can be determined for each specific
20
0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600
geometry. These equations (1 and 2) provide the
Time (s) heat transfer coefficient for natural convection as a
function of the temperature difference of the system.
Fig. 4. Water and PCM temperature over time of
experimental work using a PCM module without fins. For 20 mm fins, the experimental correlation is
shown in Equation 1, and for 40 mm fins, the
The time necessary for the cooling down process is experimental correlation is presented in Equation 2.
presented in Table I. When adding 20 mm fins, the Using these correlations for the simulation of the
time reduction was about 23,53%, while when using solar system, the results obtained showed a faster
40 mm fins, this reduction reaches 58,82%. heat transfer rate from the PCM to the water when
using finned PCM modules. Fig. 7 presents the
comparison of the temperature of the water in the

https://doi.org/10.24084/repqj04.253 120 RE&PQJ, Vol. 1, No.4, April 2006

experimental work (without fins) and the ones Grashof) and several combinations of them were
obtained simulating PCM modules with vertical fins. used.

60,0 First analysis consisted in plotting Nusselt number

PCM Temperature - Experimental data (No Fins)

59,5
Water Temperature - Fins simulation (20 mm Fins) as a function of Rayleigh number for each
Water Temperature - Fin simulation (40 mm Fins)
Water Temperature - Experimental Data (No Fins) geometry, as showed in Fig 8 and Fig 9. The
59,0 obtained correlations are Equation 3 for 20 mm fins,
Temperature (ºC)

58,5
and Equation 4 for 40 mm fins.
58,0 180
First region (20 mm fin)
160
57,5 Second region (20 mm fin)

140 Third region (20 mm fin)

57,0 Polynomic (Third region)

120
0 500 1000 1500 2000 2500 3000
Polynomic (Second region)
Time (s) 100

Nusselt
Polynomic (First region)
80

Fig. 7. Comparison between experimental and simulated 60

results from the solar system using PCM modules with 40

and without fins. 20

5 Numerical solution
0,00E+00 1,00E+11 2,00E+11 3,00E+11 4,00E+11 5,00E+11 6,00E+11 7,00E+11 8,00E+11 9,00E+11

Rayleigh

To compare the behaviour of the system using Fig. 8. Experimental correlation of Nusselt number over
finned PCM modules with another one without fins, Rayleigh for a PCM module with 20 mm fins.
two numerical codes were implemented.
180
First region (40 mm fin)

The first one simulated the storage system with 160

Second region (40 mm fin)

PCM modules without fins. This code consisted in 140 Third region (40 mm fin)

Polynomic (Third region)

the energy balance presented before simulating a

120
Polynomic (Second region)

long time working conditions.

100
Nusselt

Logaritmic (First region)

80

60

The results obtained from the simulation were 40

compared with the experimental ones to validate the 20

numerical code. 0
0,00E+00 1,00E+11 2,00E+11 3,00E+11 4,00E+11 5,00E+11 6,00E+11 7,00E+11
Rayleigh

The second code was used to simulate the storage

tank with finned PCM modules. To simulate the
Fig. 9. Experimental correlation of Nusselt number over
energy balance of the system, the natural Rayleigh for a PCM module with 40 mm fins.
convection heat transfer coefficient obtained from
the experimental set-up was used. As in the first Nusselt over powered Rayleigh was studied. In Fig.
case, the code was validated comparing the 10 and Fig. 11 Nusselt as a function of Rayleigh
numerical results with the experimental ones. powered to ¼ is represented. The experimental
correlations are Equation 5 for 20 mm fins, and
Once both numerical codes were validated, the Equation 6 for 40 mm fins.
heating of the water was studied in order to
determine the improvement achieved by attaching 160

external vertical fins in the PCM modules. 140

120

6 Experimental correlations 100

Nusselt

80

Experimental correlations to evaluate Nusselt

number have been obtained as a function of
60

Rayleigh number for each geometry.

40

20

The geometry studied in this paper consists in a 0

0 100 200 300 400 500 600 700 800 900 1000

cylindrical module of 88 mm of diameter and 315

Rayleigh 1/4

mm height with external vertical fins of 310 mm

height and 20 and 40 mm length situated in the Fig. 10. Experimental correlation of Nusselt number over
Rayleigh powered to ¼ for a PCM module with 20 mm
middle upper part of a cylindrical plastic water tank
fins.
of 440 mm of diameter and 450 mm height.

Different correlations were analysed to find which

one fits better to the experimental data. Three
dimensionless numbers (Rayleigh, Prandtl,

https://doi.org/10.24084/repqj04.253 121 RE&PQJ, Vol. 1, No.4, April 2006

 hPCM = −5.281,3 ⋅ ∆T 3 + 12.000 ⋅ ∆T 2 − 5.602,9 ⋅ ∆T 0 ≤ ∆T < 1,3
 (1)
hPCM = 368,48 ⋅ ∆T − 3.171,3 ⋅ ∆T + 9.828,9 ⋅ ∆T − 13.688 ⋅ ∆T + 8.438 1,3 ≤ ∆T < 2,9
4 3 2


hPCM = 0,1659 ⋅ ∆T − 6,0142 ⋅ ∆T + 82,712 ⋅ ∆T − 548,72 ⋅ ∆T + 1.790,5 ⋅ ∆T − 2.285,7 2,9 ≤ ∆T < 13
5 4 3 2

hPCM = 21.601 ⋅ ∆T 4 − 46.632 ⋅ ∆T 3 + 31.600 ⋅ ∆T 2 − 4.871,8 ⋅ ∆T 0 ≤ ∆T ≤ 0,9


hPCM = 155,74 ⋅ ∆T − 1.199,2 ⋅ ∆T + 2.313,2 0,9 < ∆T ≤ 3,3
2
(2)

hPCM = −2,138 ⋅ ∆T + 71,468 ⋅ ∆T − 979,88 ⋅ ∆T + 7.051,2 ⋅ ∆T − 28.085 ⋅ ∆T + 58.722 ⋅ ∆T − 50.309
6 5 4 3 2

 3,3 < ∆T ≤ 8


Nu = −1 ⋅10 −20 ⋅ Ra 2 + 5 ⋅10 −9 ⋅ Ra − 257,96 6,65 ⋅1010 ≤ Ra < 1,05 ⋅1011

Nu = −1 ⋅10 − 21 ⋅ Ra 2 − 2 ⋅10 −10 ⋅ Ra + 190,81 1,05 ⋅1011 ≤ Ra ≤ 2,93 ⋅1011 (3)
Nu = −2 ⋅10 − 45 ⋅ Ra 4 + 4 ⋅10 −33 ⋅ Ra 3 − 3 ⋅10 − 21 ⋅ Ra 2 + 1 ⋅10 −9 ⋅ Ra − 158,96 3,49 ⋅1011 ≤ Ra ≤ 7,9 ⋅1011

Nu = 115,16 ⋅ Ln(Ra ) − 2731,9 1,87 ⋅1010 ≤ Ra < 7,53 ⋅1010

Nu = −4 ⋅10 − 44 ⋅ Ra 4 + 3 ⋅10 −32 ⋅ Ra 3 − 5 ⋅10 − 21 ⋅ Ra 2 − 6 ⋅10 −10 ⋅ Ra + 212,28 7,53 ⋅1010 ≤ Ra < 3,05 ⋅1011
(4)
Nu = −1 ⋅10 −66 ⋅ Ra 6 + 3 ⋅10 −54 ⋅ Ra 5 − 3 ⋅10 − 42 ⋅ Ra 4 + 2 ⋅10 −30 ⋅ Ra 3 −
− 7 ⋅10 −19 ⋅ Ra 2 + 1 ⋅10 − 7 ⋅ Ra − 10273 3,05 ⋅1011 ≤ Ra ≤ 6,63 ⋅1011

6 5 4 3 2
 1   1   1   1   1 
Nu = 1 ⋅10 −12 ⋅  Ra 4  − 5 ⋅10 −9 ⋅  Ra 4  + 9 ⋅10 − 6 ⋅  Ra 4  − 0,0084 ⋅  Ra 4  + 4,1867 ⋅  Ra 4  −
          (5)
1 1 1
− 1070,6 ⋅ Ra 4 + 109128 510 ≤ Ra 4 ≤ 770 and 830 ≤ Ra 4 ≤ 945

6 5 4 3 2
 1   1   1   1   1 
Nu = 5 ⋅10 −13 ⋅  Ra 4  − 2 ⋅10 −9 ⋅  Ra 4  + 4 ⋅10 − 6 ⋅  Ra 4  − 0,0034 ⋅  Ra 4  + 1,6085 ⋅  Ra 4  −
          (6)
1 1
− 395,89 ⋅ Ra 4 + 39113 370 ≤ Ra 4 ≤ 900

180 process and the higher was the heat transfer

160 coefficient.
140

120 With this modification, the storage systems with

100 PCM would have a faster availability of the stored
Nusselt

80 energy and would be more flexible to match the hot

60 water availability and demand. This would be a
40 good advantage for the applications of Thermal
20 Energy Storage (TES) in solar systems.
0
0 100 200 300 400 500 600 700 800 900 1000
Rayleigh 1/4 Using experimental results, useful Nusselt
correlations in function of Rayleigh number were
Fig. 11. Experimental correlation of Nusselt number over found to be able to evaluate the natural convection
Rayleigh powered to ¼ for a PCM module with 40 mm heat transfer coefficient for that specific geometry.
fins. These tools would be very useful for numerical
simulations to predict the behaviour of a solar
Other correlations were also studied. system with PCM modules in the storage tank, as in
this paper and for other applications with similar
7 Conclusions geometries.

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