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Numerical investigation of laminar heat transfer performance of various cooling channel designs
Applied Thermal Engineering 31 (2011) 1293e1304
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Numerical investigation of laminar heat transfer performance of various cooling channel designs Jundika C. Kurnia a, Agus P. Sasmito a, b, *, Arun S. Mujumdar a, b a b
Department of Mechanical Engineering, National University of Singapore, 9 Engineering Drive 1, Singapore 117576, Singapore Mineral, Metal and Material Technology Centre, National University of Singapore, 9 Engineering Drive 1, Singapore 117576, Singapore
a r t i c l e i n f o
a b s t r a c t
Article history: Received 22 October 2010 Accepted 23 December 2010 Available online 12 January 2011
This study addresses the heat transfer performance of various cooling channel designs e.g., parallel, serpentine, wavy, coiled and novel hybrid channels. The cooling channel is designed to be placed on top of an electronic chip which dissipates heat at a constant flux. Laminar flow of a Newtonian fluid in a square cross-section channel is investigated using a three-dimensional computational fluid dynamic approach. Five channels Reynolds number are investigated to quantify the effect of Reynolds number on the performance of the cooling channel designs. Advantages and limitations of each design are discussed in the light of numerical results. Figures of merit, viz. heat transferred per unit pumping power are compared for the wide variety of channels examined. Ó 2011 Elsevier Ltd. All rights reserved.
Keywords: Coils Electronic cooling Heat transfer performance Mathematical model Non-circular tube Square tube
1. Introduction In recent years electronic devices have become indispensable part in every aspect of our daily life. In operating these devices, it is essential to maintain the temperature of electronic components below the recommended upper limit level to achieve optimum performance, maximum efficiency and reliability of the components. Inability in maintaining recommended temperature range will reduce the performance, efficiency and life span of the system and may even lead to catastrophic system failure [1]. With the rapid improvement in microprocessors, this problem has become more serious, not only for the electronic components but also for the power systems that supply energy to the electronic components. In attempts to overcome this problem, various cooling strategies have been proposed and developed [2,3]. Currently, there are five cooling strategies available [2]: (i) liquid cooling [4,5], (ii) forced convection cooling [6,7], (iii) natural convection cooling [8,9], (iv) edge cooling [10,11], and (v) phase change cooling [12,13]. Among these methods, the liquid cooling systems offer considerably higher heat transfer rates due to the superior heat dissipation rate offered by a high Prandtl number fluid such as water. Liquid cooling systems can be generally classified into * Corresponding author. Department of Mechanical Engineering, National University of Singapore, 9 Engineering Drive 1, Singapore 117576, Singapore. Tel.: þ65 65162256. E-mail address: [email protected] (A.P. Sasmito). 1359-4311/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2010.12.036
two main categories, i.e. direct (immersion) cooling and indirect cooling [14,15]. In direct cooling, the processor chip is basically immersed on a coolant chamber. This cooling strategy allows the on-conductive liquid coolant to make a direct contact with the processor chip, which results in the elimination of most of the internal thermal resistance. As a result, it generally offers higher heat transfer rate compared to indirect cooling. However, the heat transfer performance of direct cooling depends upon the thermophysical properties of the coolant which are sometimes lower than that of water. Moreover, cost of all liquid coolants is higher than that of water. In indirect cooling, on the other hand, water can be used as the coolant since it does not make direct contact with the processor chip. Instead, it flows inside a microchannel which is attached to or inserted within the processor chip. As such, the channel walls behave as a separator which increases the thermal resistance. Therefore careful considerations are required in designing a cooling channel which can provide high heat transfer performance. Numerous studies have been conducted to investigate and enhance the heat transfer performance of various cooling channels, e.g. parallel [16e20], serpentine [20e22], tree-shaped [15,23e25], and wavy [26,27]. Recently, Lee et al. [28,29] proposed use of oblique fins in cooling channels to enhance heat transfer performance. In this case, the flow in the channel is always in the developing stage. This results in thinner boundary layers and hence better heat transfer rates. Despite of the wide-ranging studies that have been conducted on the heat transfer performance of the cooling channels, none has arrived at a definitive conclusion yet.
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Nomenclature At cp FoM k _ m p Ppump Q_ Qmc T u Greek
r h m
heat transfer area [m2] specific heat [J kg1 K1] figure of merit thermal conductivity [W m1 K1] mass flow rate [kg s1] pressure [Pa] pumping power [W] total heat transfer rate [W] heat flux dissipation [W m2] temperature [K] velocity [m s1]
fluid density [kg m3] efficiency [%] dynamic viscosity [Pa s]
Therefore, there is still room for further improvement of heat transfer performance of cooling channels by evaluating some novel configurations which is the theme of this work. This paper reports results of numerical modeling of several new cooling channel designs, as illustrated in Fig. 1. They are: conventional parallel (Fig. 1a) and serpentine channels (Fig. 1b), wavy (Fig. 1c) and the recently proposed oblique fin (Fig. 1d) channels, as well as rectangular coils (Fig. 1e) and novel hybrid channels (see Fig. 1feh) which are proposed for the first time in this study. The aim of this study is to determine an optimum cooling channel design that has the highest heat transfer performance. To compare the heat transfer performance of different cooling channels, a figure of merit is defined. Essentially, it is the ratio of heat transferred from the processor chip to the fluid per unit of required pumping power. Aside from figure of merit, uniformity of processor chip temperature needs to be taken into consideration in determining heat transfer performance. Five Reynolds numbers and three heat flux conditions are simulated to evaluate the cooling rate and the heat transfer performance of each cooling channel. Note that the results presented are also relevant to thermal management of Polymer Electrolyte Membrane (PEM) fuel cell stacks and battery stacks as well. 2. Mathematical model The mathematical model (see Fig. 2) comprises two components, viz., the solid separator and cooling channel, which allows for a conjugate heat transfer between solid separator and cooling fluid. A constant heat flux, which represents the heat from electronic component, is prescribed at the bottom of the solid separator. The heat is transferred through separator by conduction and then it is taken away by cooling fluid. The solid separator is assumed to have isotropic thermal conductivity; whereas the cooling fluid is assumed to be incompressible laminar Newtonian flow. Furthermore, to ensure the fidelity of the comparison of heat transfer performance for each channel design, the area of the chip is kept constant for all designs and the total length of each channel design is only differ by value less than 5%. Since this work relates only to laminar flow, a precise numerical solution is adequate to simulate reality very closely. 2.1. Governing equations For the solid wall, the mode of heat transfer addresses heat conduction, the governing equation is described by
sstd
standard deviation of the temperature
Subscripts cd coiled channel with double serpentine ch cooling channel cs coiled channel with serpentine in inlet mc microprocessor chip ob parallel channel with oblique fin oi coiled channel with inner inlet/outlet oo coiled channel with outer inlet/outlet out outlet pa parallel channel s solid separator se serpentine channel w water wv parallel wavy channel
ks V2 T ¼ 0
(1)
where ks is the heat conductivity of separator and T is the temperature. In the cooling channel, fluid flow and convective heat transfer are taken into account. The conservation of mass, momentum and energy are given by
V$ðrw uÞ ¼ 0;
(2)
i h V$ðrw u5uÞ ¼ Vp þ V$ mw Vu þ ðVuÞT ;
(3)
rw cp; w u$VT ¼ kw V2 T;
(4)
where rw is the fluid density, u is the fluid velocity, p is the pressure, mw is the dynamic viscosity of the fluid, cp,w is the specific heat of the fluid and kw is thermal conductivity of the fluid. 2.2. Constitutive relations The working fluid considered in this paper is water. Thermophysical properties of water were obtained as polynomial functions of temperature [30]; the water density is defined by
rw ¼ 3:570 103 T 3 þ 1:88T þ 753:2;
(5)
while the water viscosity is given by
mw ¼ 2:591 105 10T143:2 ; 238:3
(6)
and the thermal conductivity of water is calculated from
kw ¼ 8:354 106 T 2 þ 6:53 103 T 0:5981:
(7)
The specific heat of water is considered constant
cp; w ¼ 4200:
(8)
As stated previously, the heat transfer performance of cooling channel is discussed in terms of the figure of merit, FoM, which is defined as
FoM ¼
Q_ ; Ppump
(9)
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Fig. 1. Cooling channel designs: (a) parallel; (b) serpentine; (c) wavy; (d) oblique fin; (e) coiled with outer inlet/outlet; (f) coiled with inner inlet/outlet; (g) coiled with serpentine and (h) coiled with double serpentine.
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Fig. 2. Computational domain for: (a) parallel; (b) serpentine; (c) wavy; (d) oblique fin; (e) coiled with outer inlet/outlet; (f) coiled with inner inlet/outlet; (g) coiled with serpentine and (h) coiled with double serpentine designs; top (z > 0) corresponds to flow channel and bottom (z < 0) represents solid separator.
where Ppump is the pumping power required to drive flow through the channel and Q_ is the total heat transfer rate, given by
Ppump ¼
Q_ ¼
1
hpump
_ Dp m
(10)
area. As a measure of the uniformity, we compare the standard deviation of the temperature for each flow design defined by
0 1 sstd ¼ B @
Z
At
Z
11=2 C ðT Tave Þ2 dAt A
;
(12)
At
Qmc dAt ;
(11)
At
respectively. Here, hpump is the pump efficiency (assumed to be _ is mass flow rate, Dp is pressure drop in the cooling 70%), m channel; Qmc is the heat flux dissipation and At is the heat transfer
where Tave is average temperature of the surface, given by
Tave ¼
1 At
Z TdAt : At
(13)
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2.3. Boundary conditions
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Table 1 Base case and operating parameters.
The boundary conditions for the flow inside the channel are defined as follows: Inlet: At the inlet, we prescribe inlet mass flow rate and inlet temperature
_ ¼ m _ in ; T ¼ Tin m
(14)
Outlet: At the outlet, we specify the pressure and streamwise gradient of the temperature is set to zero; the outlet velocity is not known a priori but needs to be iterated from the neighboring computational cells.
p ¼ pout ; n$VT ¼ 0:
(15)
Bottom wall: At the bottom of the solid separator (z ¼ 1 103 in Fig. 2), we prescribe a constant heat flux which represents heat arising from electronic chip
n$ðks VTÞ ¼ Qmc :
(16)
Flow channel/solid separator interface: At the interface between flow channel and solid separator (z ¼ 0 in Fig. 2), we set no slip condition for velocities; whereas, temperature between solid and liquid is coupled to allow for conjugate heat transfer
u ¼ 0:
(17)
Flow channel walls: At the walls of the channels, we specify no slip and adiabatic conditions
u ¼ 0; n$ðkw VTÞ ¼ 0:
(18)
Solid separator walls: At the solid separator side walls, we set adiabatic conditions
Parameter
Symbol
Value
Unit
Inlet mass flow rate (Re 100) Inlet mass flow rate (Re 250) Inlet mass flow rate (Re 500) Inlet mass flow rate (Re 750) Inlet mass flow rate (Re 1000) Outlet pressure Inlet temperature Thermal conductivity solid separator Chip heat flux
_ in m _ in m _ in m _ in m _ in m Pout Tin ks Qmc
1.00 104 1.00 104 5.00 104 7.50 104 1.00 103 101,325 25 202.4 104
kg s1 kg s1 kg s1 kg s1 kg s1 Pa C W m1 K1 W m2
Equations (1)e(3) together with appropriate boundary conditions and constitutive relations comprising of five dependent variables e u, v, w, p, and T e were solved using commercial finite volume solver Fluent 6.3.26. User-defined functions (UDF) were written in C language to account for temperature-dependence of the thermo-physical properties of the fluid. The equations were solved with the well-known Semi-Implicit Pressure-Linked Equation (SIMPLE) algorithm, first-order upwind discretization and Algebraic Multi-grid (AMG) method. As an indication of the computational cost, it is noted that on average, around 200e500 iterations are needed for convergence criteria for all relative residuals of 106; this takes 5e30 min on a workstation with a quad-core processor (1.83 GHz) and 4 GB of RAM. 4. Results and discussion The numerical simulations were carried out for typical conditions found in electronic cooling; the base-case conditions together with the physical parameters are listed in Table 1, while the geometry details can be found in Table 2. In the following, eight different channel designs, five different coolant flow rates, and three different heat flux values are simulated to study the impact of these factors on thermal management. The Figure of Merit (FoM) concept was implemented to investigate and compared the cooling performance per unit pumping power. 4.1. Effect of channel geometry
n$ðks VTÞ ¼ 0:
(19)
In this paper, the range of mass flow rate represents Reynolds number w100, 250, 500, 750 and 1000. While the prescribed heat flux is ranging from 104 W m2, which is typical condition found in low heat density electronic equipment or fuel cells, to 5 104 W m2 which represents heat flux from computer chip. 3. Numerics The computational domains (see Fig. 2) were created in AutoCAD 2010; the commercial pre-processor software GAMBIT 2.3.16 was used for meshing, labeling boundary conditions and determines the computational domain. Three different amount of mesh 2.5 105, 5 105 and 1 106 e were implemented and compared in terms of local pressure, velocities, and temperatures to ensure a mesh independent solution. We found that the mesh amount of around 5 105 gives about 1% deviation compared to the mesh size of 1 106; whereas, the results from the mesh size of 2.5 105 deviate up to 7% as compared to those from the finest one. Therefore, a mesh of around 5 105 elements (500 500 200) was sufficient for the numerical investigation purposes: a fine structured mesh near the wall to resolve the boundary layer and an increasingly coarser mesh in the middle of the channel in order to reduce the computational cost.
One of the key factors that determine the cooling performance is the geometry of the flow field as it is directly linked to the velocity Table 2 Geometric parameters. Parameter
Symbol
Value
Chip width Channel width Channel height Separator height Oblique fin angle Oblique fin width Oblique fin pitch Number of sinusoidal wave Amplitude of sinusoidal wave Total length parallel channel Total length serpentine channel Total length parallel wavy channel Total length parallel with oblique fin channel Total length coiled channel with outer inlet/outlet Total length coiled channel with inner inlet/outlet Total length coiled channel with serpentine Total length coiled channel with double serpentine
wchip wch hch hs
wob pob nwv Awv Lpa Lse Lwv Lob
5.10 1.00 1.00 1.00 26 4.49 3.06 10 5.10 1.376 1.351 1.486 1.376
Lco
1.428
m
Lci
1.428
m
Lcs Lcd
1.428 1.428
m m
qob
Unit 102 103 103 103
m m m m
104 103 104
m m e m m m m m
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Fig. 3. Velocity contours and vectors of the cooling channels at z ¼ 5 104 m for (a) parallel; (b) serpentine; (c) wavy; (d) oblique fin; (e) coiled with outer inlet/outlet; (f) coiled with inner inlet/outlet; (g) coiled with serpentine and (h) coiled with double serpentine for Re w500 and Qchip ¼ 104 W m2.
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Fig. 4. Temperature distribution at the surface of cooling channels (z ¼ 0) for (a) parallel; (b) serpentine; (c) wavy; (d) oblique fin; (e) coiled with outer inlet/outlet; (f) coiled with inner inlet/outlet; (g) coiled with serpentine and (h) coiled with double serpentine for Re w500 and Qchip ¼ 104 W m2.
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and temperature profiles inside the channel. In general, a higher flow velocity results in higher convective heat transfer; thus, more heat from the electronic equipment can be dissipated so as to maintain a more uniform temperature distribution within allowable limits. The predicted velocity profiles at the middle of the flow channel (z ¼ 5 104 m) for eight different channel designs are shown in Fig. 3. Here, several features are apparent; foremost among them is that the serpentine (see Fig. 3b), coiled (see Fig. 3eef) and hybrid designs (see Fig. 3geh) exhibit higher and more uniform velocity distributions throughout the cooling plate as compared to the conventional parallel (Fig. 3a), wavy channels (Fig. 3c) and oblique fin channels (Fig. 3d). It is noted that the velocity profile in the middle of the cooling plate for parallel, oblique fin and wavy channels can be one order-of-magnitude lower than that of the inlet velocity, even though a secondary flow exists in the oblique fin channel. This is caused by unequal distribution of mass flow rate in each passage; an alternate design e which is beyond the scope of this paper e can be implemented to improve the uniformity of flow distribution in each passage, see for example Refs. [31,32]. A higher velocity profile is expected to have direct impact on the cooling performance; this is indeed the case, as can be inferred from Fig. 4, which illustrates a trend according to which the surface temperature increases along the flow channel from inlet to outlet region. It is shown that the conventional parallel channel gives the most non-uniform temperature distribution compared to others:
60
a
a “hot spot” zone with significant temperature variation of up to 25 C is located in the central zone (see Fig. 4a). The oblique fins channel, on the other hand, performs better than the parallel channel due to the presence of secondary flows, as can be seen in Fig. 4d. This is in-line with the findings of Lee et al. [28,29] who showed that the oblique fin channel yields better heat transfer rate compared to the parallel channel. However, it should be noted that a non-uniform temperature distribution and “hot spots” with maximum temperature variation of up to 20 C exist in the outlet region, which can be a drawback of this design. For the wavy channel design, it is seen that the maximum temperature is slightly lower (DTmax ¼ 18 C) and the “hot spot” area is smaller as well (see Fig. 4c) compared to the first two designs. While in the serpentine channel design, temperature near the inlet is low (close to inlet temperature), and a high temperature (DTmax ¼ 15 C) exists in the outlet area, as can be seen in Fig. 4b. Thus far, the four rectilinear channel designs e parallel, obliquefin, wavy, and serpentine e have been found to result in nonuniform temperature distribution (hot spots). Now, looking at the results for the various coiled-base designs shown in Fig. 4eeh, one can observe that the coiled-base designs yield a more uniform temperature distribution compared to these four designs. In the coiled-base designs, the structure of fresh and warm fluid passages which are set up alternately together with high flow velocity inside the channel produce a lower maximum temperature and a more
3.5
paralel serpentine wavy oblique fin
50
a
coil outer coil inner coil serpentine coil 2 serpentine
3
σstd, K
ΔTave, K
2.5 40
30
2 1.5 1
20
0.5 10 200
400
600
800
0
1000
200
Re
600
800
1000
Re 9
60
400
b
coil outer coil inner coil serpentine coil 2 serpentine
50
b
paralel serpentine wavy oblique fin
8 7
σstd, K
ΔTave, K
6 40
5 4
30
3 20 2 10 200
400
600
800
1000
Re Fig. 5. Average temperature for (a) rectilinear designs and (b) coiled-base designs at various Reynolds numbers.
1
200
400
600
800
1000
Re Fig. 6. Standard deviation of the temperature for (a) rectilinear designs and (b) coiledbase designs at various Reynolds numbers.
J.C. Kurnia et al. / Applied Thermal Engineering 31 (2011) 1293e1304
uniform temperature distribution. On closer inspection, it is seen that the coiled design with outer inlet/outlet gives slightly higher temperature in the central area (see Fig. 4e), whereas the coiled design with inner inlet/outlet yields slightly lower temperature in the central zone (see Fig. 4f). Furthermore, for the hybrid design (coiled with single and double serpentine), there is no significant difference in terms of the temperature distribution as compared to the coils with outer inlet/outlet design. Therefore, these results suggest that coiled-base channel design is generally suitable for electronic component cooling which requires uniform temperature distribution. Of course, further optimization may be needed for specific applications. 4.2. Effect of mass flow rate A further point of interest in this study is the effect of mass flow rate of coolant fluid as it is directly linked to the convective heat transfer and pumping power required. This study examined five different coolant flow rates which correspond to Re w100, 250, 500, 750 and 1000. Fig. 5 depicts the average temperature for various channel designs at various Reynolds numbers. As expected, the average temperature decreases as the mass flow rate is increased. Interestingly, the average temperature for some channel designs behaves differently at low and high velocities: the average
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Table 3 Figure of merit for various cooling channel design for heat dissipation of 104 W m2. Channel design
Re 100
Re 250
Re 500
Re 750
Re 1000
Parallel Serpentine Parallel wavy Parallel with oblique fins Coiled with outer inlet/outlet Coiled with inner inlet/outlet Coiled with serpentine Coiled with double serpentine
2853 107.5 2275 5730 117.7 113.9 112.5 111.9
284.9 10.1 221.0 568 9.6 9.7 9.7 9.6
51.3 1.8 40.6 96.5 1.7 1.7 1.7 1.7
18.5 0.7 15.1 32.9 0.6 0.6 0.6 0.6
8.7 0.3 7.5 15 0.3 0.3 0.3 0.3
temperature of oblique-fin channel is somewhat lower than the wavy channel at low velocities and increasingly higher at high velocities (see Fig. 5a). Moreover, the average temperature for coiled-base channel design is higher than that of parallel and oblique-fin channels at low velocities; whereas, at high velocities, the coiled-base channel designs produce lower average temperature than parallel and oblique-fin channels. This implies that the coiled-base channel designs are more effective at higher flow velocity conditions. The cooling performance needs to be evaluated not only on the basis of the average temperature, but also on the degree of uniformity of the temperature distribution. As a measure of temperature uniformity, the standard deviation of temperature distribution at various coolant flow rates, defined by Eq. (12), is compared. As seen
4
x 10
a
paralel serpentine wavy oblique fin
6 5
ΔP, Pa
4 3 2 1 0
200
400
600
800
1000
Re 4
x 10 6 5
b
coil outer coil inner coil serpentine coil 2 serpentine
ΔP, Pa
4 3 2 1 0
200
400
600
800
1000
Re Fig. 7. Pressure drop for (a) rectilinear designs and (b) coiled-base designs at various Reynolds numbers.
Fig. 8. Average temperature for (a) rectilinear designs and (b) coiled-base designs at various heat flux conditions.
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in Fig. 6, for all channel designs, the distributions become more uniform as the coolant flow rate is increased. Further, the standard deviation of temperature distribution for coiled-base channel design is lower (see Fig. 6b) compared to that for other designs (see Fig. 6a) over the whole range of flow velocities considered here. This indicates that the coiled-base design yields more uniform temperature distribution than do other designs. It is noteworthy that coiled with inner inlet/outlet design gives more uniform temperature distribution at higher velocities, but they do become more non-uniform at lower velocities. Among the rectilinear channel designs, the serpentine channel yields a more uniform temperature distribution, as seen in Fig. 6a. Moreover, for the wavy and oblique fin channel designs, the temperature distributions are more uniform compared to the parallel channel at higher velocities, but become more non-uniform than those for parallel channel at lower velocities. This provides clear evidence that the oblique-fin and wavy channels are also more effective when used for higher flow rate applications, especially if temperature uniformity is of greater interest e albeit their uniformity of temperature distribution is still far below the coiled-base channel designs. Keeping the pressure drop at a minimum is of interest for reducing the operating cost of thermal management; whence a good channel design should be able to maintain low and uniform temperature, whilst keeping the pressure drop to a minimum. The coiled-base channel design, as shown in Fig. 7, requires the highest
pressure drop to drive the flow; this can be expected from the more complex flow patterns inside the channel. The pressure drop for the serpentine channel is somewhat lower (w10%) compared to that of the coiled-base channel; however, it is still one order-magnitude higher than that of parallel, oblique-fin and wavy channels. The lowest pressure drop is obtained within the oblique fin channel, followed by parallel and wavy channels. We note that if the flow channel does not split, i.e. coiled-base and serpentine designs, the pressure drop required is much higher than that with flow splitting since the coolant fluid is forced to flow to longer passages. In addition, the characteristics between pressure drop and Reynolds number were determined; the slopes for the coiled-base and serpentine channels are steeper than those for parallel, oblique fin and wavy channels. With respect to heat transfer performance and pressure drop in the system, the “Figure of Merit” concept is introduced to account for the effectiveness of heat transfer performance per unit pumping power. Table 3 shows the computed figures of merit for various channel designs at different Reynolds numbers. It is found that apart from the high heat transfer rate and more uniform temperature distribution, the coiled-base channel designs have lower figure of merit. This is due to the fact that coiled-base channels require the highest pressure drop (see Fig. 7). It is followed by the
Fig. 9. Standard deviation of the temperature for (a) rectilinear designs and (b) coiledbase designs at various heat flux conditions.
Fig. 10. Pressure drop for (a) rectilinear designs and (b) coiled-base designs at various heat flux conditions.
J.C. Kurnia et al. / Applied Thermal Engineering 31 (2011) 1293e1304
serpentine channel which has slightly higher figure of merit at high Reynolds numbers, but it gives more non-uniform temperature. The parallel, wavy, and oblique-fin channels, on the other hand, give higher figures of merit, up to around one order-of-magnitude, compared to those for coiled and serpentine channels due to their lower pressure drop. It is noted that oblique-fin channel gives the highest figure of merit, followed by wavy channel and parallel channel at all Reynolds numbers. When designing cooling plates, however, careful balance and consideration has to be given to heat transfer performance and pumping power. If the performance and uniformity is of interest, e.g. for chip cooling, one can consider coiled-base design for the cooling plate. However, if pumping power is the major constraint, e.g. for fuel cell cooling, the oblique-fin channel design may have potential to be used after further optimization of the design. 4.3. Effect of heat flux So far, the simulated heat flux arising from the electronic equipment has been set to 104 W m2, which is a typical condition found in fuel cells and low heat density electronic equipment. Intuitively, the temperature is expected to be increase as the heat flux is raised, as illustrated in Fig. 8. Here, the value of the average temperature is found to be proportional to the prescribed heat flux for all flow channel designs tested. A constant gradient, Tave/Qchip, is observed for all channel designs, irrespective of the prescribed heat flux. For each flow channel design, the coiled-base, serpentine, and wavy channels give lower average temperature and show no discernable difference, whereas the parallel channel design gives the highest average temperature followed by the oblique-fin channel. Proceeding to uniformity of the temperature distribution, Fig. 9, the degree of temperature uniformity is also found to be proportional to the prescribed heat flux; albeit the gradient and the order of temperature uniformity for each flow channel design are slightly different compared to those for the average temperature. Here, the parallel channel exhibits the most non-uniform temperature distribution among others. It is followed by the wavy channel (with around 15% difference), oblique-fin channel (w18% difference), and serpentine channel displaying up to 50% difference in standard deviation. For the coiled-base channel design, it is found that the slope is lower than that of others. Hence, a more uniform temperature distribution is achieved even at higher heat fluxes. In addition, it is noted that the coiled design with inner inlet/outlet gives the best uniformity of temperature distribution, especially for the high heat flux condition. This is mainly due to the inlet position which is placed at the middle of the chip to allow more fresh water to be in contact with chip surface and cover larger heat transfer area and, thus, maintain a more uniform distribution as compare to that of the outer inlet/outlet design. This implies that coiled design with inner inlet/outlet may have potential to be applied for electronic cooling under high heat flux conditions. As the thermo-physical properties of the working fluid is functions of temperature, it is therefore of interest to evaluate the effect of heat flux conditions to the fluid properties and its hydrodynamics. Fig. 10 shows pressure drops required for various channel designs at various heat flux conditions. It is found that, for all cases, the pressure drop decreases when heat flux increases. This is attributed to the decrease of viscosity at higher temperature arising from higher heat flux. Closer inspection notice that for coiled-base design, at the same inlet conditions, the pressure drop required reduces up to around 13% when the heat flux raised from 104 W m2 to 5 104 W m2, followed by serpentine (12%), wavy (11%), parallel (8%), and obliquefin channel (5%). Thus, it can be deduced that coiled-base channel is more effective to be used in high heat flux condition as the pumping power is lower than when it is used at low heat flux conditions.
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5. Concluding remarks A computational study has been conducted to investigate the heat transfer performance of various cooling channel designs. Eight channel configurations, parallel, wavy, oblique-fin, serpentine, and coiled-base channel design, i.e., coil with outer inlet/outlet, coil with outer inlet/outlet, hybrid coil with serpentine channel, and hybrid coil with double serpentine e were investigated and their performance are compared with each other in terms of the figure of merit. It is found that even though coiled-base channel designs give higher and more uniform heat transfer rate, they also impose a significantly higher pressure drop penalty. As a result, the figure of merit of the coiled-base channel design is lower. However, for the application where heat transfer performance and uniformity is of interest and pumping power is not an issue, the coiled-base channel can be a desired choice especially in critical applications where cooling performance is of paramount importance. References [1] R.C. Chu, R.E. Simons, M.J. Ellsworth, R.R. Schmidt, V. Cozzolino, Review of cooling technologies for computer products, IEEE Transactions on Device and Materials Reliability 4 (2004) 568e585. [2] D.S. Steinberg, Cooling Techniques for Electronic Equipment. John Wiley & Sons, United States of America, 1991. [3] C.J.M. Lasance, R.E. Simons, Advances in high-performance cooling for electronics, Electronics Cooling 11 (4) (November 2005).http://www.electronicscooling.com/2005/11/advances-in-high-performance-cooling-for-electronics [accessed August 2010]. [4] H.Y. Zhang, D. Pinjala, T.N. Wong, K.C. Toh, Y.K. Joshi, Single-phase liquid cooled microchannel heat sink for electronic packages, Applied Thermal Engineering 25 (2005) 1472e1487. [5] A.P. Sasmito, E. Birgersson, A.S. Mujumdar, Numerical investigation of liquid water cooling for a proton exchange membrane fuel cell stack, Heat Transfer Engineering 32 (2011) 151e167. [6] A.B. Etemoglu, A brief survey and economical analysis of air cooling for electronic equipments, International Communications in Heat and Mass Transfer 34 (2007) 103e113. [7] A.P. Sasmito, K.W. Lum, E. Birgersson, A.S. Mujumdar, Computational study of forced air-convection in open-cathode polymer electrolyte fuel cells stacks, Journal of Power Sources 195 (2010) 5550e5563. [8] M.M. Mohamed, Air cooling characteristics of a uniform square modules array for electronic device heat sink, Applied Thermal Engineering 26 (2006) 486e493. [9] S. Banerjee, A. Mukhopadhyay, S. Sen, R. Ganguly, Natural convection in a bi-heater configuration of passive electronic cooling, International Journal of Thermal Sciences 47 (2008) 1516e1527. [10] E.A.M. Elshafei, Effect of flow bypass on the performance of a shrouded longitudinal fin array, Applied Thermal Engineering 27 (2007) 2233e2242. [11] T.J. John, B. Mathew, H. Hegab, Parametric study on the combined thermal and hydraulic performance of single phase micro pin-fin heat sinks part I: square and circle geometries, International Journal of Thermal Sciences 49 (2010) 2177e2190. [12] R. Kandasamy, X.-Q. Wang, A.S. Mujumdar, Application of phase change materials in thermal management of electronics, Applied Thermal Engineering 27 (2007) 2822e2832. [13] X.-Q. Wang, C. Yap, A.S. Mujumdar, A parametric study of phase change material (PCM)-based heat sinks, International Journal of Thermal Sciences 47 (2008) 1055e1068. [14] H.B. Jang, I. Yoon, C.H. Kim, S. Shin, S.W. Chung, The impact of liquid cooling on 3D multi-core processors. In: Proceeding of the 2009 International Conference on Computational Design, Lake Tahoe, California, USA. 2009 pp. 472e478. [15] X.-Q. Wang, A.S. Mujumdar, C. Yap, New Approaches to Micro-electronic Component Cooling. Lambert Academic Publishing, Germany, 2009, ISBN 9783838314792. [16] R.W. Johnson, M.D. Landon, Shape optimization of electronic cooling channels. in: C.H. Amon (Ed.), Cooling and Thermal Design of Electronic System. American Society of Mechanical Engineers, New York, 1995, pp. 17e23. [17] A. Husain, K.-Y. Kim, Optimization of a microchannel heat sink with temperature dependent fluid properties, Applied Thermal Engineering 28 (2008) 1101e1107. [18] Z. Li, X. Huai, Y. Tao, H. Chen, Effects of thermal property variations on the liquid flow and heat transfer in microchannel heat sinks, Applied Thermal Engineering 27 (2008) 2803e2814. [19] X.L. Xie, X.L. Huai, Y.J. Tao, H.Z. Chen, Numerical study of laminar heat transfer and pressure drop characteristics in a water-cooled minichannel heat sink, Applied Thermal Engineering 29 (2009) 64e74. [20] F.C. Chen, Z. Gao, R.O. Loufty, M. Hecht, Analysis of optimal heat transfer in a PEM fuel cell cooling plate, Fuel Cells 3 (2003) 181e188. [21] S.H. Yu, S. Sohn, J.H. Nam, C.-J. Kim, Numerical study to examine the performance of multi-pass serpentine flow-fields for cooling plates in polymer electrolyte membrane fuel cells, Journal of Power Sources 194 (2009) 697e703.
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[22] J.-Y. San, K.-L. Pai, Performance of a serpentine heat exchanger: part II e Second-law efficiency, Applied Thermal Engineering 29 (2009) 3088e3093. [23] X.-Q. Wang, A.S. Mujumdar, C. Yap, Thermal characteristics of tree-shaped microchannel nets for cooling of a rectangular heat sink, International Journal of Thermal Sciences 45 (2006) 1103e1112. [24] X.-Q. Wang, A.S. Mujumdar, C. Yap, Numerical analysis of blockage and optimization of heat transfer performance of fractal-like microchannel nets, Journal of Electronic Packaging 128 (2006) 38e45. [25] A. Bejan, S. Lorente, Constructal tree-shaped flow structures, Applied Thermal Engineering 27 (2007) 755e761. [26] M. Lorenzini, G. Fabbri, S. Salvigni, Performance evaluation of a wavy-fin heat sink for power electronics, Applied Thermal Engineering 27 (2007) 969e975. [27] Y. Sui, C.J. Teo, P.S. Lee, Y.T. Chew, C. Shu, Fluid flow and heat transfer in wavy microchannels, International Journal of Heat and Mass Transfer 53 (2010) 2760e2772.
[28] Y.-J. Lee, P.-S. Lee, S.-K. Chou, Enhanced microchannel heat sinks using oblique fins. In: Proceedings of the ASME InterPack Conference, July 19e23, 2009, San Francisco, California, USA. [29] Y.-J. Lee, P.-S. Lee, S.-K. Chou, Experimental investigation of oblique finned microchannel heat sink. In: Proceeding of the Thermal and Thermomechanical Phenomena in Electronic System (ITherm), IEEE Transaction. 2010. [30] W. Kays, M. Crawford, B. Weigand, Convective Heat and Mass Transport, fourth ed. MacGraw Hill, Singapore, 2005. [31] S. Maharudrayya, S. Jayanti, A.P. Deshpande, Pressure drop and flow distribution in multiple-parallel channel configuration used in proton exchange membrane fuel cell stacks, Journal of Power Sources 157 (2006) 358e367. [32] H. Liu, P. Li, J.V. Lew, CFD study on flow distribution uniformity in fuel distributors having multiple structural bifurcations of flow channels, International Journal of Hydrogen Energy 35 (2010) 9186e9198.
Contents lists available at ScienceDirect
Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Numerical investigation of laminar heat transfer performance of various cooling channel designs Jundika C. Kurnia a, Agus P. Sasmito a, b, *, Arun S. Mujumdar a, b a b
Department of Mechanical Engineering, National University of Singapore, 9 Engineering Drive 1, Singapore 117576, Singapore Mineral, Metal and Material Technology Centre, National University of Singapore, 9 Engineering Drive 1, Singapore 117576, Singapore
a r t i c l e i n f o
a b s t r a c t
Article history: Received 22 October 2010 Accepted 23 December 2010 Available online 12 January 2011
This study addresses the heat transfer performance of various cooling channel designs e.g., parallel, serpentine, wavy, coiled and novel hybrid channels. The cooling channel is designed to be placed on top of an electronic chip which dissipates heat at a constant flux. Laminar flow of a Newtonian fluid in a square cross-section channel is investigated using a three-dimensional computational fluid dynamic approach. Five channels Reynolds number are investigated to quantify the effect of Reynolds number on the performance of the cooling channel designs. Advantages and limitations of each design are discussed in the light of numerical results. Figures of merit, viz. heat transferred per unit pumping power are compared for the wide variety of channels examined. Ó 2011 Elsevier Ltd. All rights reserved.
Keywords: Coils Electronic cooling Heat transfer performance Mathematical model Non-circular tube Square tube
1. Introduction In recent years electronic devices have become indispensable part in every aspect of our daily life. In operating these devices, it is essential to maintain the temperature of electronic components below the recommended upper limit level to achieve optimum performance, maximum efficiency and reliability of the components. Inability in maintaining recommended temperature range will reduce the performance, efficiency and life span of the system and may even lead to catastrophic system failure [1]. With the rapid improvement in microprocessors, this problem has become more serious, not only for the electronic components but also for the power systems that supply energy to the electronic components. In attempts to overcome this problem, various cooling strategies have been proposed and developed [2,3]. Currently, there are five cooling strategies available [2]: (i) liquid cooling [4,5], (ii) forced convection cooling [6,7], (iii) natural convection cooling [8,9], (iv) edge cooling [10,11], and (v) phase change cooling [12,13]. Among these methods, the liquid cooling systems offer considerably higher heat transfer rates due to the superior heat dissipation rate offered by a high Prandtl number fluid such as water. Liquid cooling systems can be generally classified into * Corresponding author. Department of Mechanical Engineering, National University of Singapore, 9 Engineering Drive 1, Singapore 117576, Singapore. Tel.: þ65 65162256. E-mail address: [email protected] (A.P. Sasmito). 1359-4311/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2010.12.036
two main categories, i.e. direct (immersion) cooling and indirect cooling [14,15]. In direct cooling, the processor chip is basically immersed on a coolant chamber. This cooling strategy allows the on-conductive liquid coolant to make a direct contact with the processor chip, which results in the elimination of most of the internal thermal resistance. As a result, it generally offers higher heat transfer rate compared to indirect cooling. However, the heat transfer performance of direct cooling depends upon the thermophysical properties of the coolant which are sometimes lower than that of water. Moreover, cost of all liquid coolants is higher than that of water. In indirect cooling, on the other hand, water can be used as the coolant since it does not make direct contact with the processor chip. Instead, it flows inside a microchannel which is attached to or inserted within the processor chip. As such, the channel walls behave as a separator which increases the thermal resistance. Therefore careful considerations are required in designing a cooling channel which can provide high heat transfer performance. Numerous studies have been conducted to investigate and enhance the heat transfer performance of various cooling channels, e.g. parallel [16e20], serpentine [20e22], tree-shaped [15,23e25], and wavy [26,27]. Recently, Lee et al. [28,29] proposed use of oblique fins in cooling channels to enhance heat transfer performance. In this case, the flow in the channel is always in the developing stage. This results in thinner boundary layers and hence better heat transfer rates. Despite of the wide-ranging studies that have been conducted on the heat transfer performance of the cooling channels, none has arrived at a definitive conclusion yet.
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Nomenclature At cp FoM k _ m p Ppump Q_ Qmc T u Greek
r h m
heat transfer area [m2] specific heat [J kg1 K1] figure of merit thermal conductivity [W m1 K1] mass flow rate [kg s1] pressure [Pa] pumping power [W] total heat transfer rate [W] heat flux dissipation [W m2] temperature [K] velocity [m s1]
fluid density [kg m3] efficiency [%] dynamic viscosity [Pa s]
Therefore, there is still room for further improvement of heat transfer performance of cooling channels by evaluating some novel configurations which is the theme of this work. This paper reports results of numerical modeling of several new cooling channel designs, as illustrated in Fig. 1. They are: conventional parallel (Fig. 1a) and serpentine channels (Fig. 1b), wavy (Fig. 1c) and the recently proposed oblique fin (Fig. 1d) channels, as well as rectangular coils (Fig. 1e) and novel hybrid channels (see Fig. 1feh) which are proposed for the first time in this study. The aim of this study is to determine an optimum cooling channel design that has the highest heat transfer performance. To compare the heat transfer performance of different cooling channels, a figure of merit is defined. Essentially, it is the ratio of heat transferred from the processor chip to the fluid per unit of required pumping power. Aside from figure of merit, uniformity of processor chip temperature needs to be taken into consideration in determining heat transfer performance. Five Reynolds numbers and three heat flux conditions are simulated to evaluate the cooling rate and the heat transfer performance of each cooling channel. Note that the results presented are also relevant to thermal management of Polymer Electrolyte Membrane (PEM) fuel cell stacks and battery stacks as well. 2. Mathematical model The mathematical model (see Fig. 2) comprises two components, viz., the solid separator and cooling channel, which allows for a conjugate heat transfer between solid separator and cooling fluid. A constant heat flux, which represents the heat from electronic component, is prescribed at the bottom of the solid separator. The heat is transferred through separator by conduction and then it is taken away by cooling fluid. The solid separator is assumed to have isotropic thermal conductivity; whereas the cooling fluid is assumed to be incompressible laminar Newtonian flow. Furthermore, to ensure the fidelity of the comparison of heat transfer performance for each channel design, the area of the chip is kept constant for all designs and the total length of each channel design is only differ by value less than 5%. Since this work relates only to laminar flow, a precise numerical solution is adequate to simulate reality very closely. 2.1. Governing equations For the solid wall, the mode of heat transfer addresses heat conduction, the governing equation is described by
sstd
standard deviation of the temperature
Subscripts cd coiled channel with double serpentine ch cooling channel cs coiled channel with serpentine in inlet mc microprocessor chip ob parallel channel with oblique fin oi coiled channel with inner inlet/outlet oo coiled channel with outer inlet/outlet out outlet pa parallel channel s solid separator se serpentine channel w water wv parallel wavy channel
ks V2 T ¼ 0
(1)
where ks is the heat conductivity of separator and T is the temperature. In the cooling channel, fluid flow and convective heat transfer are taken into account. The conservation of mass, momentum and energy are given by
V$ðrw uÞ ¼ 0;
(2)
i h V$ðrw u5uÞ ¼ Vp þ V$ mw Vu þ ðVuÞT ;
(3)
rw cp; w u$VT ¼ kw V2 T;
(4)
where rw is the fluid density, u is the fluid velocity, p is the pressure, mw is the dynamic viscosity of the fluid, cp,w is the specific heat of the fluid and kw is thermal conductivity of the fluid. 2.2. Constitutive relations The working fluid considered in this paper is water. Thermophysical properties of water were obtained as polynomial functions of temperature [30]; the water density is defined by
rw ¼ 3:570 103 T 3 þ 1:88T þ 753:2;
(5)
while the water viscosity is given by
mw ¼ 2:591 105 10T143:2 ; 238:3
(6)
and the thermal conductivity of water is calculated from
kw ¼ 8:354 106 T 2 þ 6:53 103 T 0:5981:
(7)
The specific heat of water is considered constant
cp; w ¼ 4200:
(8)
As stated previously, the heat transfer performance of cooling channel is discussed in terms of the figure of merit, FoM, which is defined as
FoM ¼
Q_ ; Ppump
(9)
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Fig. 1. Cooling channel designs: (a) parallel; (b) serpentine; (c) wavy; (d) oblique fin; (e) coiled with outer inlet/outlet; (f) coiled with inner inlet/outlet; (g) coiled with serpentine and (h) coiled with double serpentine.
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Fig. 2. Computational domain for: (a) parallel; (b) serpentine; (c) wavy; (d) oblique fin; (e) coiled with outer inlet/outlet; (f) coiled with inner inlet/outlet; (g) coiled with serpentine and (h) coiled with double serpentine designs; top (z > 0) corresponds to flow channel and bottom (z < 0) represents solid separator.
where Ppump is the pumping power required to drive flow through the channel and Q_ is the total heat transfer rate, given by
Ppump ¼
Q_ ¼
1
hpump
_ Dp m
(10)
area. As a measure of the uniformity, we compare the standard deviation of the temperature for each flow design defined by
0 1 sstd ¼ B @
Z
At
Z
11=2 C ðT Tave Þ2 dAt A
;
(12)
At
Qmc dAt ;
(11)
At
respectively. Here, hpump is the pump efficiency (assumed to be _ is mass flow rate, Dp is pressure drop in the cooling 70%), m channel; Qmc is the heat flux dissipation and At is the heat transfer
where Tave is average temperature of the surface, given by
Tave ¼
1 At
Z TdAt : At
(13)
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2.3. Boundary conditions
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Table 1 Base case and operating parameters.
The boundary conditions for the flow inside the channel are defined as follows: Inlet: At the inlet, we prescribe inlet mass flow rate and inlet temperature
_ ¼ m _ in ; T ¼ Tin m
(14)
Outlet: At the outlet, we specify the pressure and streamwise gradient of the temperature is set to zero; the outlet velocity is not known a priori but needs to be iterated from the neighboring computational cells.
p ¼ pout ; n$VT ¼ 0:
(15)
Bottom wall: At the bottom of the solid separator (z ¼ 1 103 in Fig. 2), we prescribe a constant heat flux which represents heat arising from electronic chip
n$ðks VTÞ ¼ Qmc :
(16)
Flow channel/solid separator interface: At the interface between flow channel and solid separator (z ¼ 0 in Fig. 2), we set no slip condition for velocities; whereas, temperature between solid and liquid is coupled to allow for conjugate heat transfer
u ¼ 0:
(17)
Flow channel walls: At the walls of the channels, we specify no slip and adiabatic conditions
u ¼ 0; n$ðkw VTÞ ¼ 0:
(18)
Solid separator walls: At the solid separator side walls, we set adiabatic conditions
Parameter
Symbol
Value
Unit
Inlet mass flow rate (Re 100) Inlet mass flow rate (Re 250) Inlet mass flow rate (Re 500) Inlet mass flow rate (Re 750) Inlet mass flow rate (Re 1000) Outlet pressure Inlet temperature Thermal conductivity solid separator Chip heat flux
_ in m _ in m _ in m _ in m _ in m Pout Tin ks Qmc
1.00 104 1.00 104 5.00 104 7.50 104 1.00 103 101,325 25 202.4 104
kg s1 kg s1 kg s1 kg s1 kg s1 Pa C W m1 K1 W m2
Equations (1)e(3) together with appropriate boundary conditions and constitutive relations comprising of five dependent variables e u, v, w, p, and T e were solved using commercial finite volume solver Fluent 6.3.26. User-defined functions (UDF) were written in C language to account for temperature-dependence of the thermo-physical properties of the fluid. The equations were solved with the well-known Semi-Implicit Pressure-Linked Equation (SIMPLE) algorithm, first-order upwind discretization and Algebraic Multi-grid (AMG) method. As an indication of the computational cost, it is noted that on average, around 200e500 iterations are needed for convergence criteria for all relative residuals of 106; this takes 5e30 min on a workstation with a quad-core processor (1.83 GHz) and 4 GB of RAM. 4. Results and discussion The numerical simulations were carried out for typical conditions found in electronic cooling; the base-case conditions together with the physical parameters are listed in Table 1, while the geometry details can be found in Table 2. In the following, eight different channel designs, five different coolant flow rates, and three different heat flux values are simulated to study the impact of these factors on thermal management. The Figure of Merit (FoM) concept was implemented to investigate and compared the cooling performance per unit pumping power. 4.1. Effect of channel geometry
n$ðks VTÞ ¼ 0:
(19)
In this paper, the range of mass flow rate represents Reynolds number w100, 250, 500, 750 and 1000. While the prescribed heat flux is ranging from 104 W m2, which is typical condition found in low heat density electronic equipment or fuel cells, to 5 104 W m2 which represents heat flux from computer chip. 3. Numerics The computational domains (see Fig. 2) were created in AutoCAD 2010; the commercial pre-processor software GAMBIT 2.3.16 was used for meshing, labeling boundary conditions and determines the computational domain. Three different amount of mesh 2.5 105, 5 105 and 1 106 e were implemented and compared in terms of local pressure, velocities, and temperatures to ensure a mesh independent solution. We found that the mesh amount of around 5 105 gives about 1% deviation compared to the mesh size of 1 106; whereas, the results from the mesh size of 2.5 105 deviate up to 7% as compared to those from the finest one. Therefore, a mesh of around 5 105 elements (500 500 200) was sufficient for the numerical investigation purposes: a fine structured mesh near the wall to resolve the boundary layer and an increasingly coarser mesh in the middle of the channel in order to reduce the computational cost.
One of the key factors that determine the cooling performance is the geometry of the flow field as it is directly linked to the velocity Table 2 Geometric parameters. Parameter
Symbol
Value
Chip width Channel width Channel height Separator height Oblique fin angle Oblique fin width Oblique fin pitch Number of sinusoidal wave Amplitude of sinusoidal wave Total length parallel channel Total length serpentine channel Total length parallel wavy channel Total length parallel with oblique fin channel Total length coiled channel with outer inlet/outlet Total length coiled channel with inner inlet/outlet Total length coiled channel with serpentine Total length coiled channel with double serpentine
wchip wch hch hs
wob pob nwv Awv Lpa Lse Lwv Lob
5.10 1.00 1.00 1.00 26 4.49 3.06 10 5.10 1.376 1.351 1.486 1.376
Lco
1.428
m
Lci
1.428
m
Lcs Lcd
1.428 1.428
m m
qob
Unit 102 103 103 103
m m m m
104 103 104
m m e m m m m m
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Fig. 3. Velocity contours and vectors of the cooling channels at z ¼ 5 104 m for (a) parallel; (b) serpentine; (c) wavy; (d) oblique fin; (e) coiled with outer inlet/outlet; (f) coiled with inner inlet/outlet; (g) coiled with serpentine and (h) coiled with double serpentine for Re w500 and Qchip ¼ 104 W m2.
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Fig. 4. Temperature distribution at the surface of cooling channels (z ¼ 0) for (a) parallel; (b) serpentine; (c) wavy; (d) oblique fin; (e) coiled with outer inlet/outlet; (f) coiled with inner inlet/outlet; (g) coiled with serpentine and (h) coiled with double serpentine for Re w500 and Qchip ¼ 104 W m2.
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and temperature profiles inside the channel. In general, a higher flow velocity results in higher convective heat transfer; thus, more heat from the electronic equipment can be dissipated so as to maintain a more uniform temperature distribution within allowable limits. The predicted velocity profiles at the middle of the flow channel (z ¼ 5 104 m) for eight different channel designs are shown in Fig. 3. Here, several features are apparent; foremost among them is that the serpentine (see Fig. 3b), coiled (see Fig. 3eef) and hybrid designs (see Fig. 3geh) exhibit higher and more uniform velocity distributions throughout the cooling plate as compared to the conventional parallel (Fig. 3a), wavy channels (Fig. 3c) and oblique fin channels (Fig. 3d). It is noted that the velocity profile in the middle of the cooling plate for parallel, oblique fin and wavy channels can be one order-of-magnitude lower than that of the inlet velocity, even though a secondary flow exists in the oblique fin channel. This is caused by unequal distribution of mass flow rate in each passage; an alternate design e which is beyond the scope of this paper e can be implemented to improve the uniformity of flow distribution in each passage, see for example Refs. [31,32]. A higher velocity profile is expected to have direct impact on the cooling performance; this is indeed the case, as can be inferred from Fig. 4, which illustrates a trend according to which the surface temperature increases along the flow channel from inlet to outlet region. It is shown that the conventional parallel channel gives the most non-uniform temperature distribution compared to others:
60
a
a “hot spot” zone with significant temperature variation of up to 25 C is located in the central zone (see Fig. 4a). The oblique fins channel, on the other hand, performs better than the parallel channel due to the presence of secondary flows, as can be seen in Fig. 4d. This is in-line with the findings of Lee et al. [28,29] who showed that the oblique fin channel yields better heat transfer rate compared to the parallel channel. However, it should be noted that a non-uniform temperature distribution and “hot spots” with maximum temperature variation of up to 20 C exist in the outlet region, which can be a drawback of this design. For the wavy channel design, it is seen that the maximum temperature is slightly lower (DTmax ¼ 18 C) and the “hot spot” area is smaller as well (see Fig. 4c) compared to the first two designs. While in the serpentine channel design, temperature near the inlet is low (close to inlet temperature), and a high temperature (DTmax ¼ 15 C) exists in the outlet area, as can be seen in Fig. 4b. Thus far, the four rectilinear channel designs e parallel, obliquefin, wavy, and serpentine e have been found to result in nonuniform temperature distribution (hot spots). Now, looking at the results for the various coiled-base designs shown in Fig. 4eeh, one can observe that the coiled-base designs yield a more uniform temperature distribution compared to these four designs. In the coiled-base designs, the structure of fresh and warm fluid passages which are set up alternately together with high flow velocity inside the channel produce a lower maximum temperature and a more
3.5
paralel serpentine wavy oblique fin
50
a
coil outer coil inner coil serpentine coil 2 serpentine
3
σstd, K
ΔTave, K
2.5 40
30
2 1.5 1
20
0.5 10 200
400
600
800
0
1000
200
Re
600
800
1000
Re 9
60
400
b
coil outer coil inner coil serpentine coil 2 serpentine
50
b
paralel serpentine wavy oblique fin
8 7
σstd, K
ΔTave, K
6 40
5 4
30
3 20 2 10 200
400
600
800
1000
Re Fig. 5. Average temperature for (a) rectilinear designs and (b) coiled-base designs at various Reynolds numbers.
1
200
400
600
800
1000
Re Fig. 6. Standard deviation of the temperature for (a) rectilinear designs and (b) coiledbase designs at various Reynolds numbers.
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uniform temperature distribution. On closer inspection, it is seen that the coiled design with outer inlet/outlet gives slightly higher temperature in the central area (see Fig. 4e), whereas the coiled design with inner inlet/outlet yields slightly lower temperature in the central zone (see Fig. 4f). Furthermore, for the hybrid design (coiled with single and double serpentine), there is no significant difference in terms of the temperature distribution as compared to the coils with outer inlet/outlet design. Therefore, these results suggest that coiled-base channel design is generally suitable for electronic component cooling which requires uniform temperature distribution. Of course, further optimization may be needed for specific applications. 4.2. Effect of mass flow rate A further point of interest in this study is the effect of mass flow rate of coolant fluid as it is directly linked to the convective heat transfer and pumping power required. This study examined five different coolant flow rates which correspond to Re w100, 250, 500, 750 and 1000. Fig. 5 depicts the average temperature for various channel designs at various Reynolds numbers. As expected, the average temperature decreases as the mass flow rate is increased. Interestingly, the average temperature for some channel designs behaves differently at low and high velocities: the average
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Table 3 Figure of merit for various cooling channel design for heat dissipation of 104 W m2. Channel design
Re 100
Re 250
Re 500
Re 750
Re 1000
Parallel Serpentine Parallel wavy Parallel with oblique fins Coiled with outer inlet/outlet Coiled with inner inlet/outlet Coiled with serpentine Coiled with double serpentine
2853 107.5 2275 5730 117.7 113.9 112.5 111.9
284.9 10.1 221.0 568 9.6 9.7 9.7 9.6
51.3 1.8 40.6 96.5 1.7 1.7 1.7 1.7
18.5 0.7 15.1 32.9 0.6 0.6 0.6 0.6
8.7 0.3 7.5 15 0.3 0.3 0.3 0.3
temperature of oblique-fin channel is somewhat lower than the wavy channel at low velocities and increasingly higher at high velocities (see Fig. 5a). Moreover, the average temperature for coiled-base channel design is higher than that of parallel and oblique-fin channels at low velocities; whereas, at high velocities, the coiled-base channel designs produce lower average temperature than parallel and oblique-fin channels. This implies that the coiled-base channel designs are more effective at higher flow velocity conditions. The cooling performance needs to be evaluated not only on the basis of the average temperature, but also on the degree of uniformity of the temperature distribution. As a measure of temperature uniformity, the standard deviation of temperature distribution at various coolant flow rates, defined by Eq. (12), is compared. As seen
4
x 10
a
paralel serpentine wavy oblique fin
6 5
ΔP, Pa
4 3 2 1 0
200
400
600
800
1000
Re 4
x 10 6 5
b
coil outer coil inner coil serpentine coil 2 serpentine
ΔP, Pa
4 3 2 1 0
200
400
600
800
1000
Re Fig. 7. Pressure drop for (a) rectilinear designs and (b) coiled-base designs at various Reynolds numbers.
Fig. 8. Average temperature for (a) rectilinear designs and (b) coiled-base designs at various heat flux conditions.
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in Fig. 6, for all channel designs, the distributions become more uniform as the coolant flow rate is increased. Further, the standard deviation of temperature distribution for coiled-base channel design is lower (see Fig. 6b) compared to that for other designs (see Fig. 6a) over the whole range of flow velocities considered here. This indicates that the coiled-base design yields more uniform temperature distribution than do other designs. It is noteworthy that coiled with inner inlet/outlet design gives more uniform temperature distribution at higher velocities, but they do become more non-uniform at lower velocities. Among the rectilinear channel designs, the serpentine channel yields a more uniform temperature distribution, as seen in Fig. 6a. Moreover, for the wavy and oblique fin channel designs, the temperature distributions are more uniform compared to the parallel channel at higher velocities, but become more non-uniform than those for parallel channel at lower velocities. This provides clear evidence that the oblique-fin and wavy channels are also more effective when used for higher flow rate applications, especially if temperature uniformity is of greater interest e albeit their uniformity of temperature distribution is still far below the coiled-base channel designs. Keeping the pressure drop at a minimum is of interest for reducing the operating cost of thermal management; whence a good channel design should be able to maintain low and uniform temperature, whilst keeping the pressure drop to a minimum. The coiled-base channel design, as shown in Fig. 7, requires the highest
pressure drop to drive the flow; this can be expected from the more complex flow patterns inside the channel. The pressure drop for the serpentine channel is somewhat lower (w10%) compared to that of the coiled-base channel; however, it is still one order-magnitude higher than that of parallel, oblique-fin and wavy channels. The lowest pressure drop is obtained within the oblique fin channel, followed by parallel and wavy channels. We note that if the flow channel does not split, i.e. coiled-base and serpentine designs, the pressure drop required is much higher than that with flow splitting since the coolant fluid is forced to flow to longer passages. In addition, the characteristics between pressure drop and Reynolds number were determined; the slopes for the coiled-base and serpentine channels are steeper than those for parallel, oblique fin and wavy channels. With respect to heat transfer performance and pressure drop in the system, the “Figure of Merit” concept is introduced to account for the effectiveness of heat transfer performance per unit pumping power. Table 3 shows the computed figures of merit for various channel designs at different Reynolds numbers. It is found that apart from the high heat transfer rate and more uniform temperature distribution, the coiled-base channel designs have lower figure of merit. This is due to the fact that coiled-base channels require the highest pressure drop (see Fig. 7). It is followed by the
Fig. 9. Standard deviation of the temperature for (a) rectilinear designs and (b) coiledbase designs at various heat flux conditions.
Fig. 10. Pressure drop for (a) rectilinear designs and (b) coiled-base designs at various heat flux conditions.
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serpentine channel which has slightly higher figure of merit at high Reynolds numbers, but it gives more non-uniform temperature. The parallel, wavy, and oblique-fin channels, on the other hand, give higher figures of merit, up to around one order-of-magnitude, compared to those for coiled and serpentine channels due to their lower pressure drop. It is noted that oblique-fin channel gives the highest figure of merit, followed by wavy channel and parallel channel at all Reynolds numbers. When designing cooling plates, however, careful balance and consideration has to be given to heat transfer performance and pumping power. If the performance and uniformity is of interest, e.g. for chip cooling, one can consider coiled-base design for the cooling plate. However, if pumping power is the major constraint, e.g. for fuel cell cooling, the oblique-fin channel design may have potential to be used after further optimization of the design. 4.3. Effect of heat flux So far, the simulated heat flux arising from the electronic equipment has been set to 104 W m2, which is a typical condition found in fuel cells and low heat density electronic equipment. Intuitively, the temperature is expected to be increase as the heat flux is raised, as illustrated in Fig. 8. Here, the value of the average temperature is found to be proportional to the prescribed heat flux for all flow channel designs tested. A constant gradient, Tave/Qchip, is observed for all channel designs, irrespective of the prescribed heat flux. For each flow channel design, the coiled-base, serpentine, and wavy channels give lower average temperature and show no discernable difference, whereas the parallel channel design gives the highest average temperature followed by the oblique-fin channel. Proceeding to uniformity of the temperature distribution, Fig. 9, the degree of temperature uniformity is also found to be proportional to the prescribed heat flux; albeit the gradient and the order of temperature uniformity for each flow channel design are slightly different compared to those for the average temperature. Here, the parallel channel exhibits the most non-uniform temperature distribution among others. It is followed by the wavy channel (with around 15% difference), oblique-fin channel (w18% difference), and serpentine channel displaying up to 50% difference in standard deviation. For the coiled-base channel design, it is found that the slope is lower than that of others. Hence, a more uniform temperature distribution is achieved even at higher heat fluxes. In addition, it is noted that the coiled design with inner inlet/outlet gives the best uniformity of temperature distribution, especially for the high heat flux condition. This is mainly due to the inlet position which is placed at the middle of the chip to allow more fresh water to be in contact with chip surface and cover larger heat transfer area and, thus, maintain a more uniform distribution as compare to that of the outer inlet/outlet design. This implies that coiled design with inner inlet/outlet may have potential to be applied for electronic cooling under high heat flux conditions. As the thermo-physical properties of the working fluid is functions of temperature, it is therefore of interest to evaluate the effect of heat flux conditions to the fluid properties and its hydrodynamics. Fig. 10 shows pressure drops required for various channel designs at various heat flux conditions. It is found that, for all cases, the pressure drop decreases when heat flux increases. This is attributed to the decrease of viscosity at higher temperature arising from higher heat flux. Closer inspection notice that for coiled-base design, at the same inlet conditions, the pressure drop required reduces up to around 13% when the heat flux raised from 104 W m2 to 5 104 W m2, followed by serpentine (12%), wavy (11%), parallel (8%), and obliquefin channel (5%). Thus, it can be deduced that coiled-base channel is more effective to be used in high heat flux condition as the pumping power is lower than when it is used at low heat flux conditions.
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5. Concluding remarks A computational study has been conducted to investigate the heat transfer performance of various cooling channel designs. Eight channel configurations, parallel, wavy, oblique-fin, serpentine, and coiled-base channel design, i.e., coil with outer inlet/outlet, coil with outer inlet/outlet, hybrid coil with serpentine channel, and hybrid coil with double serpentine e were investigated and their performance are compared with each other in terms of the figure of merit. It is found that even though coiled-base channel designs give higher and more uniform heat transfer rate, they also impose a significantly higher pressure drop penalty. As a result, the figure of merit of the coiled-base channel design is lower. However, for the application where heat transfer performance and uniformity is of interest and pumping power is not an issue, the coiled-base channel can be a desired choice especially in critical applications where cooling performance is of paramount importance. References [1] R.C. Chu, R.E. Simons, M.J. Ellsworth, R.R. Schmidt, V. Cozzolino, Review of cooling technologies for computer products, IEEE Transactions on Device and Materials Reliability 4 (2004) 568e585. [2] D.S. Steinberg, Cooling Techniques for Electronic Equipment. John Wiley & Sons, United States of America, 1991. [3] C.J.M. Lasance, R.E. Simons, Advances in high-performance cooling for electronics, Electronics Cooling 11 (4) (November 2005).http://www.electronicscooling.com/2005/11/advances-in-high-performance-cooling-for-electronics [accessed August 2010]. [4] H.Y. Zhang, D. Pinjala, T.N. Wong, K.C. Toh, Y.K. Joshi, Single-phase liquid cooled microchannel heat sink for electronic packages, Applied Thermal Engineering 25 (2005) 1472e1487. [5] A.P. Sasmito, E. Birgersson, A.S. Mujumdar, Numerical investigation of liquid water cooling for a proton exchange membrane fuel cell stack, Heat Transfer Engineering 32 (2011) 151e167. [6] A.B. Etemoglu, A brief survey and economical analysis of air cooling for electronic equipments, International Communications in Heat and Mass Transfer 34 (2007) 103e113. [7] A.P. Sasmito, K.W. Lum, E. Birgersson, A.S. Mujumdar, Computational study of forced air-convection in open-cathode polymer electrolyte fuel cells stacks, Journal of Power Sources 195 (2010) 5550e5563. [8] M.M. Mohamed, Air cooling characteristics of a uniform square modules array for electronic device heat sink, Applied Thermal Engineering 26 (2006) 486e493. [9] S. Banerjee, A. Mukhopadhyay, S. Sen, R. Ganguly, Natural convection in a bi-heater configuration of passive electronic cooling, International Journal of Thermal Sciences 47 (2008) 1516e1527. [10] E.A.M. Elshafei, Effect of flow bypass on the performance of a shrouded longitudinal fin array, Applied Thermal Engineering 27 (2007) 2233e2242. [11] T.J. John, B. Mathew, H. Hegab, Parametric study on the combined thermal and hydraulic performance of single phase micro pin-fin heat sinks part I: square and circle geometries, International Journal of Thermal Sciences 49 (2010) 2177e2190. [12] R. Kandasamy, X.-Q. Wang, A.S. Mujumdar, Application of phase change materials in thermal management of electronics, Applied Thermal Engineering 27 (2007) 2822e2832. [13] X.-Q. Wang, C. Yap, A.S. Mujumdar, A parametric study of phase change material (PCM)-based heat sinks, International Journal of Thermal Sciences 47 (2008) 1055e1068. [14] H.B. Jang, I. Yoon, C.H. Kim, S. Shin, S.W. Chung, The impact of liquid cooling on 3D multi-core processors. In: Proceeding of the 2009 International Conference on Computational Design, Lake Tahoe, California, USA. 2009 pp. 472e478. [15] X.-Q. Wang, A.S. Mujumdar, C. Yap, New Approaches to Micro-electronic Component Cooling. Lambert Academic Publishing, Germany, 2009, ISBN 9783838314792. [16] R.W. Johnson, M.D. Landon, Shape optimization of electronic cooling channels. in: C.H. Amon (Ed.), Cooling and Thermal Design of Electronic System. American Society of Mechanical Engineers, New York, 1995, pp. 17e23. [17] A. Husain, K.-Y. Kim, Optimization of a microchannel heat sink with temperature dependent fluid properties, Applied Thermal Engineering 28 (2008) 1101e1107. [18] Z. Li, X. Huai, Y. Tao, H. Chen, Effects of thermal property variations on the liquid flow and heat transfer in microchannel heat sinks, Applied Thermal Engineering 27 (2008) 2803e2814. [19] X.L. Xie, X.L. Huai, Y.J. Tao, H.Z. Chen, Numerical study of laminar heat transfer and pressure drop characteristics in a water-cooled minichannel heat sink, Applied Thermal Engineering 29 (2009) 64e74. [20] F.C. Chen, Z. Gao, R.O. Loufty, M. Hecht, Analysis of optimal heat transfer in a PEM fuel cell cooling plate, Fuel Cells 3 (2003) 181e188. [21] S.H. Yu, S. Sohn, J.H. Nam, C.-J. Kim, Numerical study to examine the performance of multi-pass serpentine flow-fields for cooling plates in polymer electrolyte membrane fuel cells, Journal of Power Sources 194 (2009) 697e703.
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