Renewable Energy 163 (2021) 698e719
Contents lists available at ScienceDirect
Renewable Energy
journal homepage: www.elsevier.com/locate/renene
Evaluation of heat sink performance using PCM and vapor chamber/
heat pipe
A. Ghanbarpour a, M.J. Hosseini b, *, A.A. Ranjbar a, M. Rahimi b, R. Bahrampoury c,
M. Ghanbarpour d
a
School of Mechanical Engineering, Babol University of Technology, Babol, Iran
Department of Mechanical Engineering, Faculty of Engineering, Golestan University, Gorgan, Iran
Department of Mechanical Engineering, K. N. Toosi University of Technology, Tehran, Iran
d
Department of Energy Technology, KTH-Royal Institute of Technology, Stockholm, Sweden
b
c
a r t i c l e i n f o
a b s t r a c t
Article history:
Received 24 February 2020
Received in revised form
22 August 2020
Accepted 29 August 2020
Available online 31 August 2020
This paper presents a numerical study on heat sink thermal performance using phase change materials
(PCM) and a vapor chamber for heat source cooling. Heat sink performance in both natural and forced
convection heat transfer modes is investigated. The influence of various geometrical parameters such as
number, height and thickness of fins for three different modes of conventional heat sink, PCM-based heat
sink and heat sink integrated with vapor chamber is studied. Numerical results showed that the number
of fins and fin height were more effective than the fin thickness in reducing heat source temperature.
Furthermore, in natural convection, the addition of PCM and vapor chamber to the heat sink reduces the
heat source temperature by a maximum of 33.1% and 9.5%, respectively, compared to a conventional heat
sink. But in forced convection, the use of vapor chamber reduces the heat source temperature by 7.9%
while the addition of PCM to the heat sink affects its performance adversely. In fact when fresh air is
blown to the heat sink, it provides a higher temperature potential at all the surfaces.
© 2020 Elsevier Ltd. All rights reserved.
Keywords:
Heat sink
PCM
Heat pipe
Natural convection
1. Introduction
Thermal management is an important factor in various applications. The use of thermal energy storage (TES) systems for thermal applications, such as heating and cooling, has recently received
much attention. Among the various applications, TES systems may
play a role in solar systems [1e4], building thermal energy system
[5,6], cooling of electronic equipment and etc. Another facilities
that affects thermal systems are heat pipes. Heat pipes are used in
solar application [7,8], electronic cooling, waste heat recovery [9]
and other applications.
As mentioned, one of the applications in which thermal management plays a very important role is electronic technology. Due
to the rapid development of electronics packaging technology, an
increase in power and a decline in size of electronic components are
observed. So, by producing a lot of heat, system performance and
efficiency are affected. Therefore, different techniques should be
employed to reduce heat source temperature and increase its
* Corresponding author.
E-mail address: Mj.hosseini@gu.ac.ir (M.J. Hosseini).
https://doi.org/10.1016/j.renene.2020.08.154
0960-1481/© 2020 Elsevier Ltd. All rights reserved.
efficiency and longevity.
Techniques including use of phase change materials and vapor
chamber/heat pipe have been utilized in recent years to control the
generation of high rate of heat fluxes. The advantages of using
phase change materials whose valuable characteristics are chemical stability, high value of latent heat and heat absorption at constant temperature make them applicable in various industries. The
disadvantage of these materials is their low thermal conductivity.
Generally, phase change materials are suitable heat capacitors and
are not suitable heat conductors. The high effective thermal conductivity of vapor chamber/heat pipe coupled with the heat absorption capacity of the PCMs can make a valuable match for
cooling electronic equipment about which many researches have
been conducted.
Regarding heat sink and parameters affecting its performance,
Feng et al. [10] studied two different configurations of fins and
compared conventional plate fin heat sink with the cross fin one.
Yang et al. [11] evaluated the effects of fin shape with non-uniform
heights on the heat sink thermal performance. Thermal performance of a heat sink enhanced with plate fins cooled by air and by
water was optimized based on different fin thicknesses is studied
A. Ghanbarpour et al. / Renewable Energy 163 (2021) 698e719
by Kim et al. [12,13]. It was shown that as the fin thickness increases, the thermal resistance of the air case decreases by 10% and
that of the water case decreases by 15%. Moradikazerouni et al. [14]
investigated the thermal performance of a flat plate heat sink
cooled by air under forced convection. They showed that increasing
the number and the height of fins decreases the plate surface
temperature by 25% and 20%, respectively. Sufian et al. [15]
experimentally and numerically studied heat transfer increment in
high power LEDs by using an integration of piezoelectric fans and a
heat sink. Their results showed that the vertically positioned dual
fans and quad fans increases heat transfer performance about 3.2
times and 3.5 times, respectively compared to the case of natural
convection.
Considering studies about PCM-based heat sink, Sahoo et al. [16]
presented a variety of methods studied by researchers to enhance
the performance of PCM application in electronic component
cooling. In this research, various parameters such as number of fins,
fins thickness and fins height in PCM-based heat sinks were studied. Saha et al. [17] investigated the effect of fin distribution on a
given volume fraction as a thermal conductivity enhancer. They
used 36 pin fins with sectional dimension of 2 2 mm2 and 9 pin
fins of 4 4 mm2 dimensions. Their results showed that in the 36
fins case, due to the higher contact surface area between the fins
and the PCM, the heat transfer from the fins increases and consequently the heater’s temperature decreases. Fok et al. [18] experimentally investigated the effects of several parameters such as
PCM, number of fins, power level and inclination angle of the device in a PCM-based plate fin heat sink for electronic cooling applications. They observed that as the number of fins increases, due
to better distribution of heat transfer to the PCM and its release to
the environment, the heat transfer rate increases. Adding the
number of fins also increases the size of the heat sink, which
doesn’t lead to fixed values for the two components of available
space and weight. Hosseinizadeh et al. [19] experimentally and
numerically studied the effects of different parameters in PCMbased heat sinks. It was shown that increasing the number and
height of fins leads to a significant improvement in the thermal
performance. But, the increase in fin thickness causes only a slight
improvement. It is also observed that there is an optimal value for
fin thickness, more than which the performance of heat sink falls.
Baby and Balaji [20] optimized the configuration of PCM-based pin
fin heat sink. Their results showed that there is a sufficient domain
to optimize the heat sink design. They experimentally observed
that heat sink configuration with 72 pin fins gives the best thermal
performance compared to the 33 and 120 pin fins heat sinks. It is
also shown that their experimental results and the results of optimization, by using Artificial Neural Network-Genetic Algorithm
technique, were in an acceptable agreement. Levin et al. [21] proposed a method of optimizing for latent heat thermal management
system for cooling application of electronic components. Their results showed that the parameters including the characteristics of
the fins, the heat flux at the interface and the temperature difference between critical point and PCM melting point determine the
optimum percentage of the PCM. Mahmoud et al. [22] experimentally studied the influence of different PCM-based heat sink
configurations. The results showed that the use of honeycomb
insert is the best method compared to the application of other
configurations in the cooling phase. Furthermore, the use of PCM
while with an increase in the number of fins results in a reduction
of the peak temperature of the heat sink. Pakrouh et al. [23] optimized the geometry of PCM-based heat sink based in which the
decision parameters are number of fins, fin height, fin thickness and
base thickness for various crucial temperatures. Arshad et al. [24]
conducted an experiment to study cooling performance of PCMbased heat sinks used for electronic components. The research is
699
carried out for different thicknesses, different volume fractions of
PCM and different heat fluxes. The results showed that the heat
sink with a 2 mm thickness has the best thermal performance
compared to the heat sinks having 1 mm and 3 mm thicknesses. Ali
and Arshad [25] investigated four different PCM-based pin-fin heat
sink configurations with fin thicknesses of 2, 3, 4 mm and no-fin
case. The volume fraction of PCM was also considered as a variable to find the best value of PCM volume. It was found that the
configuration with 3 mm thickness had the best thermal performance compared to the other cases. The reason for the lower performance of the heat sink having 2 mm thickness is the higher
number of fins and for the heat sink with 4 mm thickness it is the
larger gap which in turn increases the temperature of the base plate
and the local melting of the PCM instead of distributing the heat
transferred from fins to the PCM. Kalbasi et al. [26] presented a
correlation in order to estimate the optimal volume fraction of PCM
and the optimal fins number in a PCM-based heat sink. Their results
revealed that increasing the fin thickness reduces the optimal
number of fins and boosting the height of the heat sink leads to an
increase in the optimal spacing of the fins, which in turn reduces
the optimal number of fins. For the fixed-width heat sink, a greater
number of fins is required to avoid interference with thermal performance due to the increased heat flux. Yazici et al. [27] experimentally demonstrated that the fin number and inclination angle
play a crucial role in the heat transfer performance by affecting the
formation of the convective cells in the liquid PCM domain. Hence,
it leaves some influence on the heat transfer trend and the time of
operation in the PCM-based heat sinks.
Various studies have been conducted on the use of heat pipes/
vapor chambers in electronic cooling applications. Li et al. [28]
compared the thermal performance of a vapor chamber heat sink
with a conventional aluminum heat sink using infrared thermography. It was found that using the vapor chamber results in a more
uniform transfer of the heat generated at the base plate, thereby
reducing the maximum temperature. In addition, it was shown that
the effect of the fin dimension is dependent on the Reynolds
number. Naphon et al. [29] studied the thermal performance of a
vapor chamber for the application of hard disk drive cooling in
personal computers. Experimental results showed that using the
vapor chamber can reduce the hard disk drive temperature by up to
15.21% compared to the no vapor chamber mode. Furthermore,
Naphon et al. [30] showed the significant impact of heat sink
configuration, working fluids, components operation, type and direction of coolants on the thermal performance of the plate fin
vapor chamber. Tang et al. [31] developed a heat sink integrated
with a vapor chamber for thermal management of high power
LEDs. It is observed that the junction temperature, when the vapor
chamber is added to the heat sink, is lower than the conventional
heat sink by 13.04 C. Han et al. [32] developed a new configuration
including a heat sink merged with four flat heat pipes and
compared them with conventional heat sinks. Experimental results
showed that by increasing multiply heat sources, the total heat
resistance decreases and the maximum heat transfer capacity rises.
Chang et al. [33] studied the effective thermal conductivity for a
thin vapor chamber. Tests were performed at two different orientations and three thicknesses. The results showed that the thickness of the vapor chamber has a significant influence on its thermal
performance, but, the orientation of the vapor chamber affects its
thermal resistance and effective thermal conductivity of the
evaporator less significantly. Velardo et al. [34] studied the thermal
conductivity of a vapor chamber both numerically and experimentally. They developed a numerical model to estimate the
effective thermal conductivity of the vapor region by replacing the
different components of the vapor chamber with solid regions. The
range of effective thermal conductivity obtained in their
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A. Ghanbarpour et al. / Renewable Energy 163 (2021) 698e719
W to 2400 W .
investigation was 1900 mK
mK
In a review article, Ali [35] studied researches on the simultaneous use of heat pipe and PCM in cooling system applications. Yin
et al. [36] investigated the thermal performance of the heat pipebased heat sink coupled with a highly thermal conductive composite PCM. It was observed that the addition of PCM to the system
increases the heat transfer coefficient by 1.36e2.98 times. Weng
et al. [37] studied the use of a heat pipe with PCM for cooling of
electronic devices. It was found that the fan power consumption at
PCM cooling module decreases by 46% compared to the conventional heat pipe. Behi et al. [38] introduced a hybrid system of heat
pipe and PCM for cooling application of electronic components.
Experimental and numerical results showed that this hybrid system provides more than 86.7% of the required cooling load in the
range of 50e80 Watt.
The intention of this study is to provide a comprehensive evaluation of cooling of electronic devices using a heat sink improved
by PCM and a vapor chamber under different geometrical and
operating conditions. For this purpose, the main and common
geometric parameters of the heat sink, such as the height, thickness
and number of fins are taken into account. In addition, the impact of
the parameters on the same volume of materials and different
operating conditions were specifically compared, which is not
endeavored in pervious works. In addition to the geometric parameters, the performance of a convectional heat sink and the
improved ones with PCM and a vapor chamber, under different
conditions are studied and compared. The novelty in this study
includes both the consideration of natural convection conditions as
well as its evaluation and comparison of the performance of the
simple heat sink and the improved ones with PCM and a vapor
chamber in the forced convection condition. In this study it is
shown that whether the use of different techniques separately or
simultaneously in different operation conditions can improve the
performance of a heat sink or not.
which are kept fixed in all cases. A 10 mm 10 mm heat source
with a constant input power, 20 W, is located at the center of the
bottom surface of the heat sink. Except for the bottom surface, all of
the heat sink walls are in contact with the surrounding air. Table 1
presents the geometric variation of the number of fins, the fin
height and the fin thickness.
In order to reduce the simulation time and since there is a
symmetry in the model, a quarter of the heat sink volume is
considered as the computational domain (Fig. 2). In addition, the
position of the PCM and the vapor chamber with respect to the heat
sink is shown in Fig. 2.
The PCM used in this study is paraffin RT42 the latent heat of
which is high. The melting temperature of this material is lower
than many electronic components critical temperatures. The vapor
chamber which applies phase transition in transferring heat is
made of copper. In this study, the effective thermal conductivity of
the components is used by replacing vapor chamber components
by a solid region. The properties of materials used in the simulation
are shown in Table 2. The criterion for investigating the heat sink
performance is the temperature of the heat source. The cooling
process period is 60 min, while the heat source temperature is
recorded every minute.
In this study, the simulation is performed by using Ansys Fluent
software. It is assumed that the flow is laminar, unsteady and
incompressible. The enthalpy-porosity method is used to simulate
PCM melting process.
2.1. Governing equations
For the heat sink section, which includes the heat sink base and
fins, only conduction heat transfer process is considered:
v
v
vT
ðrs hÞ ¼
ks
vt
vxi
vxi
The equations governing the PCM system are as follows:
Continuity equation:
2. Numerical models
In Fig. 1 the configuration of heat sink considered in this study is
showed. All heat sinks are made of aluminum. The dimensions of
the base section of heat sinks are assumed to be 90 40 8 mm3
(1)
Dan
¼0
Dt
(2)
Momentum equation:
r
D!
v
! !
¼ VP þ mV2 !
v þ r g þ Sm
Dt
(3)
Energy equation:
r
DH
¼ kV2 T
Dt
(4)
The Boussinesq approximation is used to consider the effect of
buoyancy on the PCM, using the following equation.
r¼
rl
(5)
½bðT Tl Þ þ 1
In the above equation, rl is the PCM density at the melting
temperature and b is the PCM thermal expansion coefficient, which
is set at 0.001 for RT42.
Table 1
Studied parameters and their values at different cases.
Fig. 1. Isometric view of heat sink configuration.
Parameters
Levels
Number of fins
Fin heights, H f [mm]
Fin thickness, W f [mm]
4
10
1
9
20
3
12
30
5
15
40
7
21
50
25
60
A. Ghanbarpour et al. / Renewable Energy 163 (2021) 698e719
701
Fig. 2. Schematic of the computational domain.
symmetry plane:
Table 2
Thermo-physical properties of materials.
Material
r
½kg =m3 Aluminum
Paraffin RT42
Copper
Styrofoam
2719
760 (solid)
880 (fluid)
8978
50
Cp
½j =kg:K
k
½w =m:K
m
871
2000
202.4
0.2
e
0.02534
381
1131
387.6
0.054
e
e
½kg =m:s
vT vT
vui vui
¼
¼0;
¼
¼0
vx vy
vx
vy
Convection boundary condition for other heat sink walls:
kAl
2.2. Boundary and initial conditions
The initial simulation temperature for all the cases is 20 C, this
temperature is selected according to the ambient temperature at
which electronic components usually work [39,40]. Also the pressure at the outlet is equal to the ambient pressure. Thus, the
different boundary conditions in Fig. 2, are as follows:
Constant heat flux boundary condition for the heating plate:
kAl
vT
¼ q’’
vy y¼0
(6)
Adiabatic boundary condition for the heat sink bottom surface
and the vapor chamber walls:
kAl
vT
¼0
vy
(7)
Symmetry boundary condition for the two walls in the heat sink
(8)
vT
¼ h∞ ½T∞ T0 vy
(9)
According to the problem condition, the experimental equations
are taken into account to calculate the convective heat transfer
coefficient. Churchill-Chu [41] correlation which applies to all
Rayleigh numbers is used for the average Nusselt number corresponding to the natural convection over vertical plate.
8
92
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
1
>
>
<
=
6
0:387 RaL
NuL ¼ 0:825 þ
8
2
327 >
>
>
>
>
>
9
>
>
>
16
>
>
6
7 >
>
0:492
>
>
1
þ
4
5 >
>
>
Pr
:
;
(10)
Churchill-Ozoe [42] correlation is also used for forced convection conditions. This correlation can be used for flows with uniform
heat flux and all Prandtl numbers.
Fig. 3. Independency graph (a) mesh independency, (b) time step independency.
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Fig. 4. Comparison between experimental studies [19,34] and present work, (a) base temperature profile of the present work and that of Hosseinizadeh et al. [19], (b) spreading
resistance profile of the present work and that of Velardo et al. [34].
Fig. 5. (a) Temperature versus time for different number of fins, (b) temperature versus number of fins at 60 min.
1=2
0:886 Rex Pr 1=2
Nux ¼ "
2=3 #1=4
Pr
1 þ 0:0207
(11)
the thickness of the vapor chamber and ∅h is the height of the
liquid inside the wick structure of the vapor chamber. The coefficients a, b, g, f and t are also experimental coefficients.
2
Kw ¼
2.3. Calculation of the effective thermal conductivity of vapor
chamber
In order to calculate the effective thermal conductivity of a vapor, an experimental correlation has been used [43].
keff
kb
¼a :
kw b
:
kb
qin
Ps : h0:5
fg
!g t
A f
∅h
:
:
W
W2
(12)
where keff is effective thermal conductivity of the vapor chamber,
kb is the thermal conductivity of the material from which the vapor
chamber is made. kw is the effective thermal conductivity of the
wick structure which can be calculated by applying equation (13)
[44]. qin is the heat source heat flux and Ps is the saturated vapor
pressure of the working fluid, which is water in this study. hfg is the
latent heat of the working fluid, A is the area of vapor chamber, W is
p rc
8 rs
p rc 2
Kl Ks
Ks þ 1 8 rs
ε’ Ks þ Kl ð1 ε’ Þ
(13)
where Kl is the thermal conductivity coefficient of water, Ks is the
thermal conductivity of copper, ε is the wick porosity coefficient, rc
is the contact radius or effective capillary radius and rs is the
spherical radius of the particles. For packaged spheres, the ratio of
the contact radius to the radius of the particle sphere is usually
considered to be 0.41. The coefficient ε’ is also calculated as follow:
ε’ ¼
ε
1p
8
(14)
rc
rs
2.4. Validation and verification
The PISO algorithm is employed for the pressure-velocity
coupling. At the first step of the simulation, the effects of mesh
size and time step on the solution are evaluated. To accomplish this
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Fig. 6. Temperature contours for heat sink with (a) 4 fins, (b) 9 fins, (c) 12 fins, (d) 15 fins, (e) 21 fins, (f) 25 fins.
Fig. 7. (a) Temperature versus time for different fin heights, (b) temperature versus fin height at 60 min.
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Fig. 8. Temperature contours for heat sink with different fin heights (a) 10 mm, (b) 20 mm, (c) 30 mm, (d) 40 mm, (e) 50 mm, (f) 60 mm.
A. Ghanbarpour et al. / Renewable Energy 163 (2021) 698e719
705
Fig. 9. (a) Case temperature versus time for different fin thicknesses, (b) temperature versus fin thickness at 60 min.
Fig. 10. Temperature contours for heat sink with different fin thicknesses (a) 1 mm, (b) 3 mm, (c) 5 mm, (d) 7 mm.
task, a PCM-based heat sink configuration including 9 fins with
20 mm height and 3 mm thickness is considered. As shown in
Fig. 3a, to assure that the mesh size is sufficiently large, four cell
numbers of 389480, 199752, 84672 and 26488 are analyzed. The
mesh with 199752 cells is chosen because it is found that by
increasing the cell number to 199752, the results change negligibly.
Four time step values of 0.001s, 0.005s, 0.01s and 0.05s are also
examined. According to Fig. 3b, the time step of 0.01s is an
appropriate choice to perform the simulation. The convergence is
checked at each time step. The convergence criteria of 106 for
continuity, 104 for momentum and 107 for energy equations are
set. To validate the numerical simulation results with the corresponding experimental data, two experimental studies are taken
into account. Therefore, the PCM simulation is compared with the
experimental data of Hosseinizadeh et al. [19]. For this purpose the
heat sink configuration with 3 fins was simulated and according
Fig. 4a, a maximum difference of 12.8% was observed between
numerical simulation and experimental results. Also the experimental results reported by Velardo et al. [34] is considered as a
benchmark to validate the study for the vapor chamber. The
spreading resistance of the vapor chamber for the heat source with
dimensions of 30 30 mm and under heat inputs of 20, 30 and
40 W was simulated. According to Fig. 4b, the maximum difference
between numerical simulation and experimental results was 13.4%.
Thus, it is found that there is an acceptable agreement between the
numerical results of this study and the experimental data.
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Fig. 11. Base temperature variation for (a) number of fins and fin height, (b) number of fins and fin thickness and (c) fin height and fin thickness.
Fig. 12. (a) Temperature versus time for different number of fins for heat sink integrated with vapor chamber, (b) temperature versus number of fins at 60 min.
3. Results and discussions
3.1. Performance of the heat sink
Heat source temperature variations are investigated by using
three cooling techniques: conventional heat sink, PCM-based heat
sink and heat sink integrated with vapor chamber in both natural
and forced convection modes. The results of this study are
described below.
Heat sink thermal performance under natural convection are
evaluated. The investigated parameters are number, height and
thickness of the fins. Fig. 5 shows the temperature variation of the
heat source for different numbers of fins. It can be seen that by
increasing the number of fins from 4 to 9, 12, 15, 20 and 25, the
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707
Fig. 13. Temperature contours for the heat sink integrated with a vapor chamber with different numbers of fins (a) 4 fins, (b) 9 fins, (c) 12 fins, (d) 15 fins, (e) 21 fins, (f) 25 fins.
Fig. 14. (a) Temperature versus time for different fin heights for the heat sink integrated with a vapor chamber, (b) temperature versus fin height at 60 min.
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Fig. 15. Temperature contours for the heat sink integrated with a vapor chamber with different fin heights (a) 10 mm, (b) 20 mm, (c) 30 mm, (d) 40 mm, (e) 50 mm, (f) 60 mm.
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709
Fig. 16. (a) Temperature versus time for different fin thicknesses for heat sink integrated with vapor chamber, (b) temperature versus fin thickness at 60 min.
Fig. 17. Temperature contours for heat sink integrated with vapor chamber with different fin thicknesses (a) 1 mm, (b) 3 mm, (c) 5 mm, (d) 7 mm.
temperature of the heat source decreases to 34.64%, 44.63%, 51.36%,
59.86% and 63.53%, respectively. In Fig. 6, temperature contour and
the distribution of heat in the body of the heat sink at 60 min can be
seen. As the number of fins increases, the heat transfer between the
heat sink surface and the surrounding air grows. As a result, more
heat is transferred from the heat source to the surrounding air and
consequently the temperature of the heat source decreases. But it is
important to note that, by increasing the number of fins, the heat
sink weight increases. For example, a 25-fin heat sink, which performed the best in reducing the temperature of heat source, benefits from the highest heat transfer area (48680 mm2 and 3.88
times the 4-fin heat sink). On the other hand, this heat sink had the
highest weight among the configurations (241.4 gr and 2.31 times
the 4-fins heat sink), which increases the construction costs.
The next parameter examined is the fin height. According to
Fig. 7, as the fin height increases from 10 to 20, 30, 40, 50 and
60 mm, the temperature of the heat source decreases to 30.59%,
44.78%, 52.92%, 58.15% and 61.77%, respectively. Similar to the
previous case, the reason for the increase in heat sink efficiency is
the increase of heat transfer area with its surrounding environment. The heat transfer area for the heat sink configuration with
the fins height of 60 mm is 52120 mm2 , which is 3.88 times the heat
transfer area of the heat sink employing fins height of 10 mm. In
Fig. 8, the temperature contour and the temperature distribution in
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Fig. 18. Base temperature variation for (a) number of fins and fin height, (b) number of fins and fin thickness and (c) fin height and fin thickness.
Fig. 19. Case temperature versus time for different number of fins for PCM-based heat
sink.
the heat sink body of different heights are shown. In addition to the
increase in the heat transfer area, the heat sink weight variation
should be taken into consideration. As the height of the fin
increased from 10 to 60 mm, its weight boosts as much as 2.36
times.
It is noted that the temperature variation of the heat source for
this parameter is different from the former two parameters. As
shown in Fig. 9, with an increase in fin thickness from 1 to 3 mm,
the highest temperature difference is observed between the two
modes for up to 7 min, which is 11.9 C. But, after that the temperature difference between the cases decreases. Hence, at the end
of the 60 min of the examination, the temperature difference of the
two cases reaches 3.8 C. Comparison between the two heat sinks
with 3 and 5 mm fin thicknesses also shows a similar trend. The
highest temperature difference between the two thicknesses occurs at 10 min. At this time, the temperature difference is 8 C. But,
after that moment, the temperature difference between the two
thicknesses decreases and reaches 2.8 C. Eventually, by an increase
in fin thickness from 5 to 7 mm, the highest temperature difference
and the final temperature difference at 60 min approach to 6 C and
2.6 C, respectively. In Fig. 10, the temperature contours of the heat
sink with different thicknesses of fins at the end of the simulation
are shown.
It can be seen that by increasing the number of fins, fin height
and fin thickness, the heat source temperature decreases. The
A. Ghanbarpour et al. / Renewable Energy 163 (2021) 698e719
711
Fig. 21. Liquid fraction versus time for different numbers of fins.
between the two parameters of the number and height of fins
revealed an approximately the same results in decreasing the temperature of the heat source. The next comparison made is between
the number of fins and their thickness. Therefore a heat sink
enhanced with 12 1-mm-thick fins and the one that utilizes 4 fins of
3 mm thickness are compared. Both heat sinks capacity is
38400 mm3 and their fins’ height is 20 mm. The last comparison is
endeavored between fin height and fin thickness consequences. As a
result, a heat sink having 30 mm fin height and 1 mm fin thickness is
measured up to a unit with 10 mm fin height and 3 mm fin thickness. The two heat sinks’ volume is the same, 39600 mm3, the fin
number of which are equal, 9. According to Fig. 11b and c, the two
parameters of fin number and fin height play a more effective role
than the fin thickness in reducing the heat sink temperature. Adding
the number of fins or increasing the fin height compared to
increasing the fin thickness reduces the temperature of the heat
source by 73% and 74%, respectively. It can be concluded that if a
certain volume of the heat sink constituent material becomes
available, it is advisable to increase the number and height of fins
instead of their thickness to achieve a better performance of the heat
sink.
3.2. Effect of vapor chamber
Fig. 20. Temperature contours for PCM-based heat sink with different number of fins
(a) 4 fins, (b) 9 fins and (c) 12 fins.
reduction in the temperature can be attributed to the increase in
the heat transfer area between the heat sink surface and the surrounding air. But, increasing these parameters results in an increase
in the weight and cost of heat sink manufacturing, which is not
desirable and a trade-off between these factors can be suggested.
A comparison is made between the effects of the parameters on
thermal performance of the heat sink. The first comparison was
made between the two parameters of the number of fins and fin
height. Hence a 12 fins heat sink having 10 mm fin height is
compared with a heat sink enhanced with 4 fins of 30 mm height.
Both configurations volume capacity is 43200 mm3 the fin thickness
of which is equal 3 mm. According to Fig. 11a, the comparison
By examining the temperature distribution in the heat sink
configuration under natural convection, a temperature difference
between 6.7 C and 10.8 C in the heat sink body is observed. This
temperature difference occurs between the contact point of the
heat sink and the heat source (maximum heat sink temperature)
and the farthest distance to this point at the upper end of the fin
(minimum heat sink temperature). The existence of such a temperature difference in heat sink body means that the heat distribution in the body is inadequate, resulting in a decrease in the heat
sink performance. So, to increase efficiency, the heat sink is merged
with a vapor chamber.
In this section, the geometrical parameters of the heat sink integrated with the vapor chamber are investigated. In Fig. 12, the
heat source temperature variation for the heat sink integrated with
the vapor chamber with different numbers of fins is shown. According to this figure, as the number of fins increases from 4 to 9, 12,
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Fig. 22. Liquid fraction contours for PCM-based heat sink with different numbers of fins (a) 4 fins, (b) 9 fins and (c) 12 fins.
15, 21 and 25, the heat source temperature decreases to 34.44%,
44.65%, 50.58%, 59.4% and 63.14%, respectively. As can be seen, the
variation of the heat source temperature for the heat sink integrated with the vapor chamber is similar to the conventional heat
sink mode. According to the temperature contours, shown in
Fig. 13, it can be concluded that the use of vapor chamber results in
a uniform heat distribution throughout the heat sink body. For the
conventional heat sink configurations, the maximum temperature
difference appeared in the heat sink body is normally 6.7 C to 9.1 C.
By integration of the heat sink with the vapor chamber, this temperature difference reduces to the range of 2.1 Ce3.6 C. Hence, the
existence of the vapor chamber results in a more efficient heat
transfer from the heat source to the heat sink, thereby increasing
the efficiency of the cooling system.
Another parameter to consider is the fin height. According to
Fig. 14, the temperature variation of the heat source in the vapor
chamber is similar to that of without vapor chamber. By increasing
the fin height from 10 to 20, 30, 40, 50 and 60 mm, the heat source
temperature decreases by 30.58%, 45.13%, 53.24%, 58.61% and
62.29%, respectively. In this case, the use of vapor chamber has also
led to a more appropriate heat transfer in the heat sink. As shown in
Fig. 15, the addition of a vapor chamber to the heat sink with
different heights reduces the maximum temperature difference in
the heat sink body to the range of 2.4 Ce4.5 C, while this temperature difference for the case without a vapor chamber is between 7.7 C to 9.1 C.
The last parameter to consider is the fin thickness. When
changing the thickness of the fins, it is observed that the trend of
heat source temperature variation is similar to that of the heat sink
without the vapor chamber, as shown in Fig. 16. By increasing the
fin thickness from 1 to 3 mm, after 10 min, the maximum heat
source temperature difference between the two points occurs,
9.3 C. But over time, the heat source temperature difference decreases, and by the end of the 60 min, the temperature difference
between these two points reaches 3.8 C. Increasing the fin thickness from 3 to 5 mm also shows a similar trend in the heat source
A. Ghanbarpour et al. / Renewable Energy 163 (2021) 698e719
713
temperature variations. In fact the maximum heat source temperature difference between the two different configurations is
observed at 13 min, which is 6.6 C. In this case, this difference of
the heat source between the two configurations decreases over
time and at the end of the experiment, at 60 min, the temperature
difference is found to be 2.9 C. Finally, by increasing the fin thickness from 5 to 7 mm, the maximum heat source temperature difference between these two configurations at 18 min and final heat
moment, at 60 min, is observed, 5.1 C and 2.6 C, respectively.
Fig. 17, shows the temperature contour and the heat distribution in
the body of the heat sink for different fin thicknesses. Among the
configurations investigated, the maximum temperature difference
in the heat sink body is observed that is a value between 2.4 C to
5.5 C, while this maximum temperature difference for similar cases
without a vapor chamber is in the range of 6.9 Ce10.8 C.
Pairwise comparison between the parameters in the heat sink
under natural convection consequences is repeated in heat sink
mode integrated with the vapor chamber. The results for the
comparison of the parameters in the vapor application are similar
to those without the vapor chamber. According to Fig. 18(a), the
effect of the two parameters of the number of fins and fin height on
the performance of the heat sink integrated with a vapor chamber
to reduce the heat sink temperature is approximately the same. But,
according to Fig. 18(b) and Fig. 18(c), the two parameters of the
number and the height of the fins have a much more noticeable
effect than the fin thickness on reducing the heat sink temperature
(up to 74%). It can be concluded that, in order to achieve a greater
heat sink efficiency and reduce the heat source temperature, in
both cases of with and without a vapor chamber, it is more efficient
to increase the number or height of the fins rather than increasing
the fin thickness.
The use of vapor chamber attached to the heat sink results in a
more efficient distribution of the heat in the heat sink body and the
excess heat of the heat source is excreted productively.
3.3. Effect of PCM
In this section, the performance of PCM-based heat sink is
studied. Similar to the previous sections, the first parameter
Fig. 24. Temperature contours for PCM-based heat sink with different fin heights (a)
10 mm, (b) 20 mm and (c) 30 mm.
Fig. 23. Case temperature versus time for different fin heights for PCM-based heat
sink.
examined is the number of fins. As shown in Fig. 19, during the first
11 min of the cooling process, heat sink with 12 fins (highest
number of fins) presents the best heat source cooling performance
and the 4 fins heat sink (lowest number of fins) performs the worst
in cooling. As illustrated in Fig. 21, this is the case where the PCM in
the heat sink with 12 fins completely melts. In the 4 fins heat sink, it
will take longer for the PCM to fully melt due to the larger volume
of the PCM, thus more heat at phase change temperature can be
absorbed in this case. But, after the PCM is fully melted in all the
three heat sink configurations, it can be found that the more fins,
the more acceptable performance. Covered with liquid PCM, the
heat sink with 12 fins again shows the best performance after
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A. Ghanbarpour et al. / Renewable Energy 163 (2021) 698e719
Fig. 25. Liquid fraction versus time for different fin heights.
26 min of the cooling process. According to Figs. 21 and 22, it can be
seen that the PCM in the heat sink with more fins begins to melt
later than the other two cases. In addition, earlier than all other
cases, the PCM in this case completely melts. This is due to the fact
that the larger contact surface area between the solid wall and the
PCM is provided when using more fins. In Fig. 20, the temperature
contour of the heat sinks with different numbers of fins at 60 min is
shown.
The next parameter to study is the fin height in a PCM-based
heat sink. Unlike the heat sink mode with different numbers of
fins and fin thicknesses, the PCM volume increases as the fin height
rises. According to Fig. 23, contrary to the number of fins, for heat
sinks with different fin heights, the temperature variation of the
heat source throughout the cooling process shows a uniform result.
From the beginning of the cooling process to the end of the study
period, the heat sink with the greatest fins height showed the best
performance. The superiority of the heat sink with a fin height of
30 mm is more evident over time than the other two configurations. According to Fig. 25 and Fig. 26, it can also be concluded that
the heat sink with a fin height of 30 mm needs more time for
complete melting of PCM. It is due to the larger volume of PCM
inside it, and therefore compared to the other configurations keeps
the heat source temperature in a relatively stable range for a longer
Fig. 26. Liquid fraction contours for PCM-based heat sink with different fin heights (a) 10 mm, (b) 20 mm and (c) 30 mm.
A. Ghanbarpour et al. / Renewable Energy 163 (2021) 698e719
715
Fig. 27. Case temperature versus time for different fin thickness for PCM-based heat
sink.
period. The temperature contour for these three configurations
with different heights of fins is shown in Fig. 24.
The last geometrical parameter examined in this section is the
fin thickness. For this purpose, three different configurations of
PCM-based heat sink are examined. The first heat sink involves fins
of 1 mm thickness and a PCM volume of 64800 mm3, the second
heat sink whose fin thickness is 3 mm contains a PCM volume of
50400 mm3 and the last heat sink with a fin thickness of 5 mm can
include a PCM volume of 36000 mm3. According to Fig. 27, after
13 min of the cooling process, the heat sink with a thicker fin shows
the best heat source cooling performance. As shown in Fig. 29, in a
heat sink with 5 mm fin thickness, the time required for PCM
melting is less than the other two configurations. Thus, after
14 min, the two lower fin thicknesses configurations continue to
have lower temperature variation. Heat sinks with a 1 mm fin
thickness is able to maintain a relatively stable temperature of the
heat source for a longer time due to the larger volume of the PCM.
Thus, between the time of 16 min and 39 min, the best performance
among these three configurations belongs to the heat sink with
1 mm fin thickness. When the PCM is fully melted in all the three
configurations, the heat source temperature for the heat sink with
the lower fin thickness increases more steeply than the other cases.
After 39 min, the heat sink with a greater fin thickness shows the
best performance. Fig. 28, shows the temperature contour of the
different configurations at 60 min and Fig. 29 shows the diagram of
the melting fraction for these three states. As noted, the PCM in the
heat sink with 1 mm fin thickness begins to melt earlier than the
other two configurations and the PCM in the heat sink with 5 mm
fin thickness begins to melt later than the other two configurations.
However, due to the smaller PCM volume in the 5 mm fin thickness,
the time required for PCM melting is the shortest and for the heat
sink with 1 mm fin thickness it is the longest. The reason for the late
onset of PCM melting in the heat sink enhanced with a thicker fin is
that the heat transfer mode in PCM before melting is mainly conduction. Increasing the heat transfer rate, with the increase in the
temperature gradient, affects the onset of the melting process. The
onset of melting for the thicker fins delays compared to the thinner
ones. However, the reason for shorter PCM melting time for the
thicker fins is the multiple onset of PCM melting along the fin
Fig. 28. Temperature contours for PCM-based heat sink with different fin thicknesses
(a) 1 mm, (b) 3 mm and (c) 5 mm.
height. In Fig. 30, the contour of the melting fraction for all the
three evaluated configurations is shown.
The geometrical parameters, studied above, are compared to
each other to investigate which parameter affects the performance
of the heat sink more significantly. In all cases, both the volume of
heat sink constituents and the volume of PCM were considered
constant. The first comparison is made between the two parameters of number of fins and fin height in the PCM-based heat sink. Of
the two configurations, one heat sink with 8 fins with 8 mm height
and the other with 4 fins with 16 mm height are selected. According
to Fig. 31(a), the heat source temperature for the two configurations
is the same when the PCM is completely in solid or liquid states.
But, in the time period from the beginning to the end of the PCM
melting process, different results are obtained. In this range, the
increase in fin height is superior to the increase in its number. As at
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Fig. 29. Liquid fraction versus time for different fin thickness.
13 min progression of the process, the heat source temperature for
the configuration with the longer fins is 6.5 C lower than for the
other case. Next, a comparison is made between the two parameters of the number and thickness of the fins. In this case the first
configuration has 12 fins with a thickness of 1 mm and the other
configuration has 4 fins with a thickness of 3 mm. According to
Fig. 31(b), the heat sink having more fins performs better than the
heat sink with the thicker fins. This advantage is apparently evident
in the PCM melting process. After 8 min of the cooling process, the
heat source temperature for the heat sink with more fins is 12.1 C
lower than the other case. The final comparison is made between
the two parameters of the fin height and fin thickness. Of the two
configurations selected, one has fins with 8 mm height and 3 mm
thickness and other has fins with 12 mm height and 2 mm thickness. As shown in Fig. 31(c), two different modes exhibited relatively similar performance at the beginning of the cooling process
and when the PCM is completely melted. But, over the PCM melting
period, the longer fins perform better than the thicker fins. This
result is due to the fact that the greater the amount of the PCM is
exposed to the longer fins, and as a result the heat transfer by the
longer fins is more uniform than the thicker fins.
Comparing the geometrical parameters, it can be concluded that
the three investigated geometrical parameters shows almost
Fig. 30. Liquid fraction contours for the PCM-based heat sink with different fin thicknesses (a) 1 mm, (b) 3 mm and (c) 5 mm.
A. Ghanbarpour et al. / Renewable Energy 163 (2021) 698e719
717
Fig. 31. Base temperature variation for (a) number of fins and fin height, (b) number of fins and fin thickness and (c) fin height and fin thickness.
similar results in the heat source cooling process. But, in the period
from the beginning to the end of the PCM melting, the best performance belongs to the parameters of height, then number and
finally thickness of the fins, respectively. The reason for the superiority of the height parameter over the other two parameters is
that the amount of PCM exposed to longer fins is greater compared
Fig. 32. Comparison between different methods used to improve heat sink performance under natural convection.
Fig. 33. Comparison between different methods used to improve heat sink performance under forced convection.
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to the other cases. As a result, the heat in this case is more uniformly transferred from the fins to PCM.
3.4. Effect of convection heat transfer mode
In the previous steps, the performance of different heat sink
configurations was examined. In this section, the performance of
these configurations is compared under both natural and forced
convections. For this purpose, heat sink configuration with 9 fins
with 30 mm height and 3 mm thickness is selected as the reference
geometry. According to Fig. 32, which is related to the temperature
of heat source for the natural convection conditions, the different
methods employed have relatively similar effects at the beginning
of the cooling process. Prior to the 6 min of the cooling process, the
advantage of using PCM in heat sinks over the conventional heat
sink mode as well as the heat sink integrated with vapor chamber is
demonstrated. This preference reaches its maximum before the
7 min of the cooling process, so that the heat source temperature
for PCM-based heat sink at 17 min is lower than that of the heat
source in the conventional heat sink and the heat sink integrated
with a vapor chamber. Comparing the PCM-heat sink and air natural convection (free cooling) case, due to the latent heat characteristic of PCM, in PCM-based heat sink, a large amount of heat is
absorbed at an almost constant temperature (without increasing
PCM temperature) which prevents the heat source temperature
from rising. Hence, PCM-based heat sink performs more acceptable
than conventional heat sink (air natural convection). However
when the PCM melts completely, the heat is absorbed as sensible
heat which lowers the performance of the PCM-based heat sink in
comparison with a conventional one. In fact this increase in the
PCM temperature reduces the temperature difference between
PCM and heat sink surface, resulting in poor cooling. But in air
natural convection the hot air which has absorbed heat from the
heat sink surface is replaced with fresh air with a lower temperature (ambient temperature) due to the change in density.
In this part, the previous comparison process is performed in
forced convection mode. For this purpose, along with the configurations selected, a fan is used to create airflow. The velocity of air is
assumed to be 3 m/s. According to Fig. 33, in forced convection
mode, the use of phase change materials is an inappropriate choice.
Despite the advantages of these materials, it can be seen that
conventional heat sink performs much better than the PCM-based
heat sink and even the PCM-based heat sink integrated with vapor
chamber. In fact, when the heat sink is filled with PCM, the heat
transfer mechanism is conduction at the beginning (when PCM is
solid) and then it is a combination of conduction and natural convection. It is clear that when the PCM melts completely its temperature increase gradually. So, comparing the performance of the
system with PCM to the case of forced convection (air flow), it is
observed that the air forced convection removes a higher amount of
heat from the heat sink that is due to higher temperature difference
between the heat sink solid wall and surround fresh air compared
to the PCM trapped where after melting its temperature increases.
Hence, air force convection can provide a more powerful cooling
mechanism than using PCM.
4. Conclusion
Present study numerically investigates the thermal performance of a heat sink using PCM and a vapor chamber. The influence
of using these techniques under the natural and forced convection
conditions is studied. In addition, the effect of three geometrical
parameters including number, height and thickness of fins on heat
sink thermal performance is evaluated. The following is a summary
of the results obtained in this study.
By increasing each of the parameters of the number, height and
thickness of fins, the heat sink cooling performance improves.
But in a fixed volume of heat sink and PCM, the number of fins
and fin height are more effective than fin thickness in reducing
the temperature of electronic components.
Integration of heat sink with a vapor chamber results in a proper
distribution of heat from the heat source throughout the heat
sink body. This proper heat distribution results in a less temperature difference in heat sink body that in turn leads to an
improved heat sink function and heat source temperature fall. In
fact by using a vapor chamber the heat source temperature reduces by 7.9%e9.5%.
In natural convection conditions, before the complete phase
change of PCM, the PCM-based heat sink shows the best performance. But then because of the loss of PCM desirable properties, the existence of PCM doesn’t bring about a positive effect
on improving the heat sink performance and the use of the
vapor chamber is more beneficial.
In forced convection, the use of PCM does not show a positive
effect on the performance of heat sink, and integration of heat
sink with a vapor chamber and even the use heat sink alone
leads to a better performance.
CRediT authorship contribution statement
A. Ghanbarpour: Methodology, Software, Validation, Conceptualization, Visualization, Investigation, Formal analysis, Writing original draft, Writing - review & editing. M.J. Hosseini: Methodology, Software, Validation, Conceptualization, Visualization,
Investigation, Supervision, Formal analysis, Writing - review &
editing. A.A. Ranjbar: Conceptualization, Visualization, Investigation, Supervision, Formal analysis. M. Rahimi: Writing - original
draft, Conceptualization, Visualization, Investigation, Supervision,
Formal analysis, Writing - review & editing. R. Bahrampoury:
Writing - original draft, Writing - review & editing. M. Ghanbarpour: Writing - review & editing.
Declaration of competing interest
The authors declare that they have no known competing
financial interests or personal relationships that could have
appeared to influence the work reported in this paper.
Acknowledgments
My special words of gratitude go to the venerable anonymous
reviewers for their valuable comments.
Nomenclature
Cp
k
t
h
T
!
v
P
!
g
!
S
DH
x; y; z
Nu
Ra
specific heat ðJ =kg KÞ
thermal conductivity ðW =m KÞ
time ðsÞ
specific enthalpy ðJ =kgÞ
temperature ð CÞ
velocity vector ðm =sÞ
pressure ðPaÞ
gravity acceleration ðm =s2 Þ
momentum source term ðN =m3 Þ
latent heat of fusion ðJ =kgÞ
Cartesian coordination
Nusselt number
Rayleigh number
A. Ghanbarpour et al. / Renewable Energy 163 (2021) 698e719
Re
Pr
H
W
Reynolds number
Prandtl number
height ðmmÞ
width ðmmÞ
Greek symbol
density ðkg =m3 Þ
dynamic viscosity kg=ms
volume fraction
thermal expansion coefficient ðK 1 Þ
r
m
a
b
Subscripts
s
Solid
l
Liquid
n
nth phase
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