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slot-jet module
International Journal of Heat and Mass Transfer 89 (2015) 838–845
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Effects of slot-jet length on the cooling performance of hybrid microchannel/slot-jet module Chol-Bom Kim a,b, Chuan Leng a, Xiao-Dong Wang a,⇑, Tian-Hu Wang c, Wei-Mon Yan d,⇑ a
State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources, North China Electric Power University, Beijing 102206, China Department of Mechanical Engineering, Hamhung Hydraulic and Power University, Hamhung, Democratic People’s Republic of Korea c School of Mathematics and Physics, North China Electric Power University, Beijing 102206, China d Department of Energy and Refrigerating Air-Conditioning Engineering, National Taipei University of Technology, Taipei 10608, Taiwan b
a r t i c l e
i n f o
Article history: Received 5 January 2015 Received in revised form 28 May 2015 Accepted 28 May 2015 Available online 14 June 2015 Keywords: Hybrid Microchannel Slot-jet Temperature uniformity Thermal resistance
a b s t r a c t In this work, a three-dimensional numerical model based on the k–x SST turbulent model is developed to investigate the single-phase cooling performance of hybrid microchannel/slot-jet module at a constant pumping power of 0.05 W. Two different hybrid modules are analyzed, and the difference between them lies in whether there exist plate fins beneath the slot jet. The temperature uniformity of cooled object and global thermal resistance are evaluated for the two hybrid modules at various slot-jet lengths. The results show that local Nusselt number distribution exhibits a bell shape for the hybrid module with plate fin, while it has a double-peak shape for the hybrid module without plate fin. When with plate fin, a larger slot-jet length of 7800 lm yields the best cooling performance. Oppositely, when without plate fin, a smaller length of 606 lm is beneficial to achieve the better cooling performance. The optimal hybrid module with plate fin has the thermal resistance of 0.105 K W1 and the bottom wall temperature gradient of 0.27 °C, which are lower than those of the hybrid module without plate fin. Furthermore, the cooling performance of hybrid module can be further improved by optimization of geometric parameters of the heat sink. When the optimal channel number, channel aspect ratio, and width ratio of channel-to-pitch are adopted respectively, the thermal resistance of the hybrid module with plate fin can be reduced by 26.38% to 27.78% as compared with the worst geometry, while the bottom wall temperature gradient can be reduced by 86.79% to 87.46%. Ó 2015 Elsevier Ltd. All rights reserved.
1. Introduction Thermal management of electronic devices is one of the important issues for electronics packaging. The rapid advances in micro-electronics technology lead to an increasing heat flux that needs to be removed from the chip surfaces. There is also a desire to improve the temperature uniformity of the cooled object, because the thermal stress caused by large temperature gradient can damage reliability of the devices. Recently several schemes have been proposed to enhance single-phase high heat flux cooling. Among these schemes, microchannel heat sink and jet impingement are regarded as two promising candidates for the cooling of high-performance microprocessors, laser diode arrays, radars, X-ray anodes, solar photovoltaic concentrators, laser and ⇑ Corresponding authors. Tel./fax: +86 10 62321277 (X.-D. Wang). Tel./fax: +886 939259149 (W.-M. Yan). E-mail addresses: [email protected] (X.-D. Wang), [email protected] (W.-M. Yan). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2015.05.108 0017-9310/Ó 2015 Elsevier Ltd. All rights reserved.
microwave directed energy weapons, and hybrid-vehicle power electronics [1]. Both the microchannel heat sink and jet impingement provide very high heat removal capability, but they still present some serious drawbacks [2,3]. The microchannel heat sink can yield heat removal rates comparable to the jet impingement using far smaller coolant flow rates and more compact structure, however, it also causes a high temperature rise along the flow path of coolant and needs a high pressure drop [1,4]. Using a dielectric liquid, the jet impingement produces a very high heat transfer coefficient in the impingement region [5]. The abrupt reduction in cooling effectiveness away from the impingement region can yield large temperature variations along the surface of the cooled object [6]. Therefore the jet impingement requires jet arrays to ensure a relatively good level of temperature uniformity. There are two disadvantages for the jet array. First, after the cool fluid impinges on the cooled surface and dissipates the heat from the surface, the fluid temperature increase inevitably. However, it is difficult to remove the heated fluid from the impinging region due to dense
C.-B. Kim et al. / International Journal of Heat and Mass Transfer 89 (2015) 838–845
jet arrangement which inevitably causes a reduced heat transfer capacity [7]. Second, the interaction between adjacent jets also leads to a significant reduction in the local heat transfer coefficient. Many studies have attempted to reduce these unfavorable effects and at the same time to enhance the heat transfer associated with the two cooling technologies [8–13]. Recently, a hybrid cooling scheme with the combination of microchannel heat sink and jet impingement technologies (referred to as hybrid microchannel/jet-impingement module) was proposed which is expected to both achieve a more uniform temperature distribution on the surface of the cooled object and reduce global thermal resistance of the cooling system [14–19]. Jang et al. [14] for the first time evaluated the cooling performance of the hybrid microchannel/jet-impingement module experimentally. Their results indicated that the thermal resistance of the hybrid module is only 6.1 K W1 with about 48.5% reduction as compared with the conventional microchannel heat sink with a parallel flow at a constant pumping power of 0.072 W. Moreover, the pressure drop of the hybrid module is decreased by about 90.5% and the temperature difference across the base surface is decreased by about 87.6%. Subsequently, Jang and Kim [15] suggested two correlations for the thermal resistance and the pressure drop across the hybrid module. The correlations are compared with their experimental results, and both are shown to match with experimental results to within ±10%. Sung and Mudawar [16,17] investigated the cooling performance of a hybrid microchannel/slot-jet module both experimentally and numerically. They adopted the so-called standard k–e turbulent model to analyze the flow and heat transfer of coolant. Their numerical predictions showed that lower surface temperatures can be achieved by decreasing the jet width and microchannel height, and the hybrid module can maintain surface temperature gradients below 2 °C for heat fluxes up to 50 W cm2. Barrau et al. [18] conducted an experimental study on hybrid microchannel/jet-impingement cooling scheme. Their experiments confirmed that the hybrid scheme has the favorable capacity to improve the temperature uniformity of the cooled object. Barrau et al. [19] also used the k–x SST turbulent model to carry out a parametric analysis of longitudinal distribution and channel height. However, the effect of jet size was not discussed in their work. The hybrid microchannel/jet-impingement cooling module has been shown to significantly improve the temperature uniformity of the cooled object; however, the relevant studies are still very insufficient up to now. Especially, the temperature uniformity, pressure drop, and thermal resistance for the hybrid module can be further improved by optimizing the jet and channel sizes. In this
839
work, a three-dimensional numerical model based on the k–x SST turbulent model is developed to investigate the cooling performance of two different hybrid cooling modules at a constant pumping power. The slot-jet length is first optimized for both the modules and the corresponding cooling performances are compared. Subsequently, effects of three geometric parameters of microchannels, including channel number N, channel aspect ratio a, and width ratio of channel-to-pitch b are analyzed to search for the optimal design of the hybrid module. 2. Geometry for hybrid microchannel/slot-jet module The schematics of two kinds of hybrid microchannel/slot-jet cooling modules are illustrated in Figs. 1 and 2. The coolant impinges on the microchannel heat sink through a slot jet (along the negative y-axis). The slot jet is characterized by its length and width of Ljet and Wjet. The heat sink has a dimension of Lx Ly Lz and is composed of N channels and N + 1 fins. The heights of the channel and fin are Hc, while the widths of the channel and fin are Wc and Wf, respectively. The thickness is d1 for the bottom horizontal fin and d2 for the top horizontal fin. The difference between the two cooling modules lies in whether the solid fins exist beneath the slot jet. The geometric parameters of the hybrid module are listed in Table 1. Among these parameters, the parameters of microchannel heat sink come from Ref. [20], in which an optimal structure of heat sink is obtained at a constant pumping power of 0.05 W by an inverse problem optimization algorithm. The bottom of the heat sink is attached to a cooled surface such as integrated circuits or electronic chips with a uniform heat flux qw = 100 W cm2. 3. Description of the numerical model 3.1. Hybrid microchannel/slot-jet module model Barrau et al. [19] and Menter [21] have demonstrated that the k–x SST model is very effective for predicting the performance of the hybrid cooling module, and hence the present work adopts the same k–x SST turbulent model. The following assumptions are made: (1) steady state; (2) single phase and turbulent flow; (3) constant fluid and solid properties; (4) negligible gravitational force, radiation heat transfer, and contact resistance on the interfaces between the hybrid module and the cooled object. Based on the above assumptions, the governing equations are expressed in the Cartesian tensor notation as follows.
Fig. 1. Schematic of microchannel/slot-jet cooling module with plate fins beneath the slot-jet: (a) cooling module; (b) top and side views of the unit cell.
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Fig. 2. Schematic of microchannel/slot-jet cooling module without plate fins beneath the slot-jet: (a) cooling module; (b) top and side views of the unit cell.
Table 1 The geometric parameters of hybrid cooling module. Lx (mm)
Ly (mm)
Lz (mm)
Hc (lm)
Wc (lm)
Wf (lm)
Ljet (lm)
Wjet (lm)
d1 (lm)
d2 (lm)
10
0.9
10
692
84
56
1739800
9940
100
108
The constants of set 2 (u2) are (Standard k–e):
Continuity equation for the coolant:
@ui ¼0 @xi
ð1Þ
where ui are Cartesian component of velocity. Momentum equation for the coolant:
quj
@ui @p @ @ui ¼ þ ð l þ lt Þ @xi @xj @xj @xj
b
@T @ ¼ @xj @xj
cp lt @T kf þ Prt @xj
ð3Þ
where T is the coolant temperature, cp is the specific heat of the coolant, kf is the thermal conductivity of the coolant, and Prt = 0.85 is the turbulent Prandtl number. The k–x SST model is used for closure of the Reynolds stress tensor. The transport equations of the k–x SST model
@k @ @k ¼ P b qxk þ ðl þ rk lt Þ @xj @xj @xj @ x qc @ @x quj ¼ P bqx2 þ ð l þ rx lt Þ @xj @xj lt @xj 1 @k @ x þ 2ð1 F 1 Þqrx2 x @xj @xj
quj
lt ¼ q
k
ð4Þ
ð5Þ
ð7Þ
The constants of set 1 (u1) are (Wilcox k–x):
rk1 ¼ 0:5; rx1 ¼ 0:5; b1 ¼ 0:075; b ¼ 0:09; b rx1 j2 ffiffiffiffiffi j ¼ 0:41; c1 ¼ 1 p b
b
ð9Þ
ð8Þ
ð10Þ
where Ts is the fin temperature, and ks is the thermal conductivity of the fin. The boundary conditions for the governing equations are given as follows. Inlet:
u ¼ 0;
v ¼ v in ;
w ¼ 0;
T ¼ T in
ð11aÞ
Outlet:
p ¼ pout
ð11bÞ
Coolant–solid interface:
T ¼ Ts;
kf
@T @T s ¼ ks @n @n
ð11cÞ
Bottom wall of the heat sink:
qw ¼ ks
where P is the production term of turbulent viscosity and F1 is the blending function. Any constant (u) in the model is calculated from the constants u1 and u2 as follows:
u ¼ F 1 u1 þ ð1 F 1 Þu2
@ @T s ¼0 ks @xj @xj
u ¼ v ¼ w ¼ 0;
ð6Þ
x
b
Energy equation for solid region:
ð2Þ
where q and l are the density and dynamic viscosity of the coolant, lt is the turbulent viscosity, and p is the coolant pressure. Energy equation for coolant:
qcp uj
rk2 ¼ 1:0; rx2 ¼ 0:856; b2 ¼ 0:0828; b ¼ 0:09; b rx2 j2 ffiffiffiffiffi j ¼ 0:41; c2 ¼ 2 p
@T s @y
ð11dÞ
Other solid walls and symmetric interface:
0¼
@T s @n
ð11eÞ
In this work, the pumping power remains a constant value of X = 0.05 W. However, the coolant inlet velocity needs to be specified to solve the governing equations 1–5 and (10). The inlet velocity is determined as follows: (1) assume an initial value of the inlet velocity vin, and then numerically solve the governing equations )1–5 and (10) with the boundary conditions Eq. (11); (2) calculate the pumping power X0 = NvinAjetDp, where Ajet = LjetWjet is the cross-sectional area of the slot-jet and Dp is the pressure drop
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70
60
Solid block: experimental results in Ref. [19] Dash line: numerical results in Ref. [19] Solid line: present results
55
test 4
65
Nux ¼
Tb (°C)
40 35
test 3
ðT b T c Þ d1
test 2
qeff ¼ ks
test 1
where Tb is the temperature of bottom wall of the hybrid module. The temperature gradient along the bottom wall of the hybrid module is defined as follows:
30 25 20
ð13Þ
where qeff is the effective heat flux, Dh,c is the channel hydraulic diameter expressed as Dh,c = 2HcWc/(Hc + Wc), and Tc is the temperature of the channel bottom wall. The effective heat flux can be calculated by:
50 45
qeff Dh;c kf ðT c T in Þ
0
5
10
15
20
25
ð14Þ
DT b ¼ T b; max T b;min
30
x (mm) Fig. 3. Temperature profile on the bottom wall of the hybrid module at various test conditions.
across the hybrid module; (3) if |X0 X|/X < 0.01, terminate the procedure, otherwise, update vin and return step (1), and then repeat steps (1) to (3). In the present simulations, governing equations 1–5 and (10) are transformed into a finite difference form using the control volume method and are solved iteratively with an iteration criterion for convergence of 106. Various mesh combinations are examined before simulations. The present code is tested for grid independence by calculating the bottom wall minimum temperature in the hybrid module. It is found that a grid size of 203,000 ensures a grid-independent solution. Local refining is necessary at the boundary layer to ensure that the value of the near-wall parameter y+ is close to 1. 3.2. Model validation In order to validate the numerical model, the temperature profiles on the bottom wall of the hybrid module predicted by the present model are compared with experimental and numerical results in Ref. [19] at four different test conditions, as shown in Fig. 3. For fair comparison, the geometry and operating conditions of the hybrid module used in the present model are completely identical to those in Ref. [19]. The comparison shows a good agreement between the present results and the measured and predicted results in Ref. [19].
ð15Þ
where Tb,max = Tmax and Tb,min are the maximum and minimum temperature on bottom wall of the hybrid module. The jet Reynolds number is calculated based on the coolant inlet velocity and hydraulic diameter of the slot jet:
Re ¼
qv in Dh l
ð16Þ
where Dh is the hydraulic diameter of the slot jet. For the hybrid module without plate fin beneath the slot jet, we have Dh = 2LjetWjet/(Ljet + Wjet). However, for the hybrid module with plate fin, the slot jet is separated into N smaller jets due to existence of the plate fin, and these smaller jets separately impinge on the bottom wall of N channels, thus, the jet hydraulic diameter for the each channel should be calculated by Dh = 2LjetWc/(Ljet + Wc). Similarly, the jet inlet velocity in Eq. (16) for the hybrid module with plate fin should be modified as v 0in = vinLjetWjet/(NLjetWc). 4.1. Effects of jet length for hybrid module with plate fin beneath the slot jet This section analyzes the effects of slot-jet length on the cooling performance of the hybrid module with plate fin. Fig. 4 shows the variation of Tb along the bottom wall centerline of the hybrid module with various slot-jet lengths at a constant pumping power of X = 0.05 W. For the small slot length of Ljet = 173 lm, the lowest Tb occurs at the stagnation point with Tb,min = 22.07 °C, then Tb increases sharply when away from the impingement region and the highest Tb appears at the channel outlet with Tb,max = 31.05 °C. As shown in Fig. 4, increasing Ljet increases the temperature in impingement region; however, the temperature rise becomes slow when away from the impingement region as compared with small Ljet. For Ljet = 7800 lm, Tb,min and Tb,max are
4. Results and discussion
RT ¼
T max T min T max T in ¼ qw A qw L x L z
32 31 30 29 28 Tb (°C)
The heat sink is made of silicon with ks = 148 W m1 K1. Pure water is the coolant with kf = 0.613 W m1 K1, l = 0.000855 kg m1 s1, q = 997 kg m3, cp = 4179 J kg1 K1 and Tin = 290 K. A uniform heat flux of qw = 100 W cm2 is applied to the heat sink bottom wall. The hybrid module operates at a constant pumping power of X = 0.05 W. The performance of hybrid module can be evaluated by global thermal resistance, local Nusselt number, and temperature gradient along the bottom wall of the hybrid module. The global thermal resistance RT is defined as follows:
27 26 25
L jet=9800 μ m
24
L jet=7800 μ m
23
ð12Þ
where Tmax and Tmin = Tin are the maximum and minimum temperatures observed in the hybrid module, and A = Lx Lz is the base area of the hybrid module. The local Nusselt number is defined as [17,18]:
L jet=1384 μ m
22 21
L jet=173 μ m 0
1
2
3
4
5
6
7
8
9
10
x (mm) Fig. 4. Temperature profiles along centerline (y = 0 and z = (Wc + Wf)/2) on the bottom wall of the hybrid module with plate fin.
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Table 2 The performance of the hybrid module with plate fin beneath slot jet for various jet lengths at a constant pumping power of 0.05 W. Lje (lm)
Wjet (lm)
Dh (lm)
v 0in
9800 7800 5536 2768 1384 692 346 173
84 84 84 84 84 84 84 84
167 166 165 163 158 150 135 113
0.164 0.188 0.243 0.441 0.820 1.526 2.499 3.568
(m s1)
Re
Dp (kPa)
Tb,max (°C)
Tb,min (°C)
DTb (°C)
RT (K W1)
32 37 46 83 151 266 394 482
5.197 5.706 6.285 6.978 7.332 7.939 9.677 13.260
28.05 27.49 27.67 27.87 28.05 28.33 29.10 31.05
27.47 27.22 26.46 24.98 23.94 23.37 22.59 22.07
0.58 0.27 1.21 2.89 4.11 4.96 6.51 8.98
0.111 0.105 0.107 0.109 0.111 0.113 0.121 0.141
Fig. 5. Flow fields velocity at z = (Wc + Wf)/2 for (a) Ljet = 173 lm and (b) Ljet = 1384 lm.
27.22 and 27.49 °C, respectively, the temperature gradient DTb is only 0.27 °C, indicating a more uniform temperature distribution on the bottom wall can be achieved by a larger Ljet. It is worth noting that Tb,min does not occur at the stagnation point for the cases
with Ljet = 7800, and 9800 lm because Ljet approaches the channel length. The pressure drop across the hybrid module and jet inlet velocity at various slot lengths are shown in Table 2. For the case of Ljet = 173 lm, the jet inlet velocity and pressure drop are 3.568 m s1 and 13.260 kPa, respectively. As Ljet increases, the jet inlet velocity and pressure drop both reduce because the pumping power remains a constant value of 0.05 W. For example, jet inlet velocity reduces to 0.164 m s1, and the pressure drop decreases to 5.197 kPa for Ljet = 9800 lm. The flow fields at z = (Wc + Wf)/2 for Ljet = 173 lm and Ljet = 1384 lm are illustrated in Fig. 5. When Ljet = 173 lm, a larger jet inlet velocity causes the jet fluid to approach closer to the impinging surface (Fig. 5(a)), leading to the significant decrease of temperature in the impingement region. However, most momentum of the jet fluid is lost after impingement, leading to the sharply decreased velocity away from the impinging region. At smaller jet inlet velocity, on the contrary, the jet fluid occupies the upper region of the flow channel due to the weaker attachment of the jet fluid to the impinging surface (Fig. 5(b)). The jet fluid cannot approach to the impinging surface as closer as the larger jet inlet velocity, thus significantly weaken the heat transfer on the impinging surface. In this case, the momentum lost is smaller than that of the larger inlet velocity, thus the velocity decrease more slowly away from the impinging region. Consequently, a more uniform temperature distribution on the bottom wall can be achieved by a larger Ljet. The variation of Tb along the bottom wall centerline for various slot-jet lengths can be further justified by Fig. 6 which shows the local Nusselt number along the channel bottom wall. The jet hydraulic diameter ranges from 113 to 167 lm for various jet lengths in the present simulations (Table 2), which belongs to micro-scale impinging jet according to Ref. [22]. The experimental tests of Choo et al. [22] showed that when Re < 2500, the local Nusselt number distribution for the micro-scale impinging jet
60
70
Ljet=1384 μm,
Ljet=9800 μm Ljet=7800 μm
60
Ljet=606 μm,
Ljet=173 μm,
50
Ljet=346 μm
Ljet=173 μm without channel
Ljet=1384 μm Ljet=173 μm
40
40
Nux
Nux
50
30
30
20
20
10
10
0
1
2
3
4
5
6
7
8
9
10
x (mm) Fig. 6. Local Nusselt number along the channel bottom wall at various slot lengths for the hybrid module with plate fin.
0
0
1
2
3
4
5
6
7
8
9
10
x (mm) Fig. 7. Local Nusselt number along the channel bottom wall at various slot lengths for the hybrid module without plate fin.
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Fig. 8. Schematic of jet impingement without microchannel.
has a bell shape. The present predictions of Nusselt number distribution shown in Fig. 6 agree with the report by Choo et al. well. Since the increase in Ljet decreases the jet inlet velocity, the local Nusselt number is lower thus the bottom wall temperature Tb is higher in the impingement region for larger Ljet. For example, the local Nusselt number at the stagnation point is 64.8 for Ljet = 173 lm, while it reduced to 34.5 for Ljet = 1384 lm. For a typical impinging jet, the flow field can be divided into three separate regions: free jet region, impingement region, and radial flow region (Fig. 5). When coolant flows from the impingement region into the radial flow region, the radial velocity decreases rapidly which results in a thickening of the boundary layer and a heat transfer deterioration along the radial direction. A smaller Ljet corresponds to a smaller width of the impingement region and a larger width of the radial flow region. Thus, the Nusselt number is lower in the radial flow region for smaller Ljet due to the rapid decay of the heat transfer coefficient along the radial direction. The temperature gradient on the bottom wall of the hybrid module and the global thermal resistance for various jet lengths are listed in Table 2. Increasing the jet length significantly reduces both the temperature gradient and the global thermal resistance. The optimal jet length is found to be 7800 lm, which leads to the lowest thermal resistance of RT = 0.105 K W1 and the smallest temperature gradient of DTb = 0.27 °C. 4.2. Effects of jet length for hybrid module without plate fin beneath the slot jet This section analyzes the effects of slot-jet length on the cooling performance of the hybrid module without plate fin. The local Nusselt number along the bottom wall centerline for various jet lengths is shown in Fig. 7. It can be seen that the local Nusselt number exhibits a double-peak distribution and its maximums do not occur at the stagnation point. The double-peak structure
in the macro-scale impinging jet was observed at a high Reynolds number of Re P 40,000 or a small nozzle-to-plate spacing of Y/Dh < 1 [23–25], where Y denotes the distance of the nozzle from the plate. In the present simulations, the jet hydraulic diameter ranges from 340 to 9869 lm for various jet lengths, hence, the jets belong to macro-scale impinging jet and the corresponding Reynolds number varies from 1263 to 1709. The nozzle-to-plate spacing is smaller than 1 when Ljet varies from 606 to 9800 lm, while it is larger than 1 for Ljet = 173 and 346 lm. Thus, the double-peak distribution of the local Nusselt number should indeed occur for the cases with 606 lm 6 Ljet 6 9800 lm. However, the double-peak distribution is also observed in Fig. 7 for the cases with Ljet = 173 and 346 lm, which seems to be in contradiction with the experimental results in Ref. [23–25]. In order to explain why the double-peak distribution occurs for small Ljet, an extra simulation is conducted. The geometry of the new system simulated is shown in Fig. 8. It can be seen that only microchannels are removed from the new system, however, the other parameters such as the jet width and length, nozzle-to-plate spacing, and jet Reynolds number remain the same with the case with Ljet = 173 lm. As shown in Fig. 7, the local Nusselt number again exhibits a bell shape for the new simulation due to Re = 1263 < 40,000 and Y/Dh = 2.35 > 1, which agrees the previous experimental results in Refs. [23–25]. Thus, the double-peak distribution for small Ljet may be attributed to the fact that the microchannels located in the radial flow region produce a perturbation to the jet flow field. As shown in Table 3, for the case of Ljet = 173 lm, the jet inlet velocity and pressure drop across the hybrid module are 3.185 m s1 and 9.192 kPa, respectively. As Ljet increases, the jet inlet velocity and pressure drop are all decreased. For example, the jet inlet velocity is reduced to 0.149 m s1, and the pressure drop is reduced to 3.453 kPa for the case of Ljet = 9800 lm. The variation of jet inlet velocity leads to a significant difference in the local Nusselt number for various jet lengths, as shown in Fig. 7. For the very small Ljet = 173 lm, due to its large jet inlet velocity the local Nusselt number in the impingement region is higher, however, rapid decay of the heat transfer coefficient results in a lower local Nusselt number in the radial flow region compared with other jet lengths. For larger Ljet = 346, 606, and 1384 lm, although the local Nusselt number reduces significantly with the increase of Ljet in the impingement region, it is almost the same in the radial flow region. Fig. 9 shows the temperature distribution along the bottom wall centerline of the hybrid module without plate fin. The temperature distribution along the bottom wall exhibits a double-valley shape, which is just opposite to the Nusselt number distribution shown in Fig. 7. For various jet lengths, Tb firstly decreases with increasing the radial distance from the stagnation point to the shifted valley and then increases monotonically beyond the shifted valley. Tb,min is 22.82 °C for Ljet = 173 lm, 23.90 °C for Ljet = 346 lm, 24.61 °C for Ljet = 606 lm, and 25.79 °C for Ljet = 1384 lm. It should be noted that Tb,max occurs at different location for various jet
Table 3 The performance of the hybrid module without plate fin beneath slot jet for various jet lengths at a constant pumping power of 0.05 W. Ljet (lm)
Wjet (lm)
Dh (lm)
vin (m s1)
Re
Dp (kPa)
Tb,max (°C)
Tb,min (°C)
DTb (°C)
RT (K W1)
9800 5536 2768 1384 692 606 346 173
9940 9940 9940 9940 9940 9940 9940 9940
9869 7111 4330 2430 1294 1142 669 340
0.149 0.169 0.284 0.525 1.018 1.152 1.942 3.185
1709 1401 1434 1487 1536 1535 1514 1263
3.453 5.419 6.413 6.856 7.205 7.219 7.579 9.192
90.55 82.02 57.09 38.39 29.02 27.97 28.12 28.82
49.39 28.09 26.89 25.79 24.78 24.61 23.90 22.82
41.16 53.93 30.20 12.60 4.24 3.36 4.22 6.00
0.736 0.650 0.401 0.214 0.120 0.111 0.111 0.118
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can be explained by the following two reasons. First, the pressure drops are 5.706, 7.219, and 14.040 kPa for the hybrid modules with and without plate fin and the conventional microchannel heat sink, respectively. Hence, the hybrid modules have larger coolant flow rates than the conventional microchannel heat sink at the same pumping power. Second, because the inlet is located at the center of the heat sink for the hybrid modules, the coolant flow path is only a half of that for the conventional heat sink.
40 L jet=1384 μ m L jet=606 μ m
36
L jet=346 μ m
Tb (°C)
L jet=173 μ m 32
28
4.4. Effects of heat sink geometric parameters
6
7
8
9
10
Fig. 9. Temperature profiles along centerline (y = 0 and z = (Wc + Wf)/2) on the bottom wall of the hybrid module without plate fin.
lengths. For the small Ljet = 173 and 346 lm, Tb,max are 28.82 and 28.12 °C, respectively, and they all occur at the channel outlet. For the mediate Ljet = 606 lm, Tb,max = 27.97 °C occurs at the channel outlet, however, this temperature is almost the same with that at the stagnant point (27.96 °C). For the large Ljet = 1384 lm, Tb,max = 38.39 °C occurs at the stagnation point. The temperature gradient on the bottom wall of the hybrid module and global thermal resistance for various jet lengths are listed in Table 3. Both the temperature gradient and global thermal resistance are firstly decrease and then increases with the jet length increased. The optimal jet length is 606 lm, which has the lowest thermal resistance of RT = 0.111 K W1 and the smallest temperature gradient of DTb = 3.36 °C. 4.3. Comparison between two hybrid modules and conventional heat sink Fig. 10 shows the optimal thermal resistance and bottom wall temperature gradient for the two hybrid modules with and without the plate fin and the conventional microchannel heat sink at a constant pumping power of X = 0.05 W. The hybrid module with plate fin exhibits the best performance with (RT)opt = 0.105 K W1 and (DTb)opt = 0.27 °C, and then followed by the hybrid module without plate fin with (RT)opt = 0.111 K W1 and (DTb)opt = 3.36 °C. The conventional microchannel heat sink has the worst performance, the optimal RT is 0.144 K W1 and the optimal DTb is 8.93 °C. The superior performance for the two hybrid modules
1.80 1.60
ΔTb (°C)
8.93
0.108
1.20
1.32
-1
0.104
ΔTb (°C)
70
80
90 N
0.27
with plate fin
120
N = 71, β = 0.60, L jet= 5500 μ m, Ω =0.05 W
0.1064 0.1056 8
9
10
α
(c)
3.00
11
12
13
14
N = 71, α = 8.24, L jet= 5500 μ m, Ω =0.05 W
0.144 0.132
2.00
0.120
1.00
without plate fin
heat sink
Fig. 10. The optimal RT and DTb for the two hybrid modules with and without plate fin and the conventional microchannel heat sink at X = 0.05 W.
0.1072
1.14
4.00 ΔTb (°C)
0.105
110
1.20
7
0.111
100
0.1080
(b)
1.26
0.144 3.36
0.112
1.40
60
RT (K W )
0.116
(a) α = 8.24, β = 0.60, L jet= 5500 μ m, Ω =0.05 W
-1
5 x (mm)
RT (K W )
4
-1
3
RT (K W )
2
-1
1
RT (K W )
0
The bottom wall temperature uniformity and thermal resistance of hybrid module depends on the geometric structure of microchannel heat sink. Therefore, this section analyzes the effects of geometric parameters of the heat sink on the cooling performance of hybrid module at a constant pumping power of X = 0.05 W. Only the hybrid module with plate fin is discussed here due to its better performance than the hybrid module without plate fin. Two non-dimensional parameters are defined as follows: a = Hc/Wc is the channel aspect ratio, and b = Wc/(Wc + Wf) is the width ratio of channel-to-pitch. The optimal design with N = 71, a = 8.24, and b = 0.60 for the conventional microchannel heat sink (Lx = 10 mm, Ly = 0.9 mm, and Lz = 10 mm) at X = 0.05 W has been obtained by Wang et al. [20], and this design is adopted in the present simulations. For comparison purpose, a baseline case with N = 71, a = 8.24, and b = 0.60 is chosen, in single parameter analysis only one parameter of interest is changed with the other two parameters as same as the baseline case. The thermal resistance and bottom wall temperature gradient as function of N, a or b are shown in Fig. 11. For each geometric parameter, there is an optimal value at which the optimal performance of the hybrid module can be achieved. However, it should be noted that the optimal parameter value corresponding to (RT)min differs from that corresponding to (DTb)min. With N = 92, a = 10.75 or b = 0.55, the hybrid module with plate fin achieves the lowest RT, which is reduced by 30.57%, 26.60%, and 29.19%, as compared with the worst design. Similarly, the most uniform bottom wall temperature distribution is achieved at N = 96, a = 11.12 or b = 0.59 for the hybrid module, and DTb is reduced by 70.71%, 70.99%, and 69.46%, as compared with the worst design.
ΔTb (°C)
24
0.108 0.35
0.40
0.45
0.50
β
0.55
0.60
0.65
0.70
Fig. 11. Effects of heat sink geometric parameters on RT and DTb: (a) N; (b) a; (c) b; (d) c.
C.-B. Kim et al. / International Journal of Heat and Mass Transfer 89 (2015) 838–845
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5. Conclusion
References
In this study, single-phase cooling performances for two kinds of hybrid microchannel/slot-jet modules are numerically investigated by a three-dimensional k–x SST turbulent model. The temperature uniformity of cooled object and the global thermal resistance are evaluated for the two hybrid modules at various slot-jet lengths with a constant pumping power of 0.05 W. The key findings from the study are as follows:
[1] I. Mudawar, Assessment of high-heat-flux thermal management schemes, IEEE Trans. Compon. Packag. Technol. 24 (2001) 122–141. [2] S.G. Kandlikar, A.V. Bapat, Evaluation of jet impingement, spray and microchannel chip cooling options for high heat flux removal, Heat Transfer Eng. 28 (2007) 911–923. [3] D. Lee, K. Vafai, Comparative analysis of jet impingement and microchannel cooling for high flux applications, Int. J. Heat Mass Transfer 42 (1999) 1555– 1568. [4] M.E. Steinke, S.G. Kandlikar, Single-phase liquid heat transfer in plain and enhanced microchannels, Int. J. Therm. Sci. 45 (2006) 1073–1083. [5] D.C. Wadsworth, I. Mudawar, Cooling of a multichip electronic module by means of confined two-dimensional jets of dielectric liquid, ASME J. Heat Transfer 112 (1990) 891–898. [6] K.A. Estes, I. Mudawar, Comparison of two-phase electronic cooling using free jets and sprays, ASME J. Electron. Pack. 117 (1995) 323–332. [7] L.B.Y. Aldabbagh, I. Sezai, Three-dimensional numerical simulation of an array of impinging laminar square jets with spent fluid removal, Int. J. Therm. Sci. 43 (2004) 241–247. [8] K. Vafei, L. Zhu, Analysis of two-layered microchannel heat sink concept in electronic cooling, Int. J. Heat Mass Transfer 42 (1999) 2287–2297. [9] J.H. Ryu, D.H. Choi, S.J. Kim, Three-dimensional numerical optimization of a manifold microchannel heat sink, Int. J. Heat Mass Transfer 46 (2003) 1553– 1562. [10] G. Hetsroni, A. Mosyak, Z. Segal, G. Ziskind, A uniform temperature heat sink for cooling of electronic devices, Int. J. Heat Mass Transfer 45 (2002) 3275– 3286. [11] L. Lin, Y.Y. Chen, X.X. Zhang, X.D. Wang, Optimization of geometry and flow rate distribution for double-layer microchannel heat sink, Int. J. Therm. Sci. 78 (2014) 158–168. [12] X.D. Wang, B. An, L. Lin, D.J. Lee, Inverse geometric optimization for geometry of nanofluid-cooled microchannel heat sink, Appl. Therm. Eng. 55 (2013) 87– 94. [13] X.D. Wang, B. An, J.L. Xu, Optimal geometric structure for nanofluid-cooled microchannel heat sink under various constraint conditions, Energy Convers. Manage. 65 (2013) 528–538. [14] S.P. Jang, S.J. Kim, K.W. Paik, Experimental investigation of thermal characteristics for a microchannel heat sink subject to an impinging jet, using a micro-thermal sensor array, Sens. Actuators A 105 (2003) 211–224. [15] S.P. Jang, S.J. Kim, Fluid flow and thermal characteristics of a microchannel heat sink subject to an impinging air jet, ASME J. Heat Transfer 127 (2005) 770–779. [16] M.K. Sung, I. Mudawar, Experimental and numerical investigation of singlephase heat transfer using a hybrid jet-impingement/microchannel cooling scheme, Int. J. Heat Mass Transfer 49 (2006) 682–694. [17] M.K. Sung, I. Mudawar, Single-phase and two-phase cooling using hybrid microchannel/slot-jet module, Int. J. Heat Mass Transfer 51 (2008) 3825–3839. [18] J. Barrau, D. Chemisana, J. Rosell, L. Tadrist, M. Ibanez, An experimental study of a new hybrid jet impingement/microchannel cooling scheme, Appl. Therm. Eng. 30 (2010) 2058–2066. [19] J. Barrau, M. Omri, D. Chemisana, J. Rosell, M. Ibanez, L. Tadrist, Numerical study of a hybrid jet impingement/microchannel cooling scheme, Appl. Therm. Eng. 33–34 (2012) 237–245. [20] Z.H. Wang, X.D. Wang, W.M. Yan, Y.Y. Duan, D.J. Lee, J.L. Xu, Multi-parameters optimization for microchannel heat sink using inverse problem method, Int. J. Heat Mass Transfer 54 (2011) 2811–2819. [21] F.R. Menter, Two-equation eddy-viscosity turbulence models for engineering applications, AIAA J. 32 (1994) 1598–1605. [22] K.S. Choo, Y.J. Youn, S.J. Kim, D.H. Lee, Heat transfer characteristics of a microscale impinging slot jet, Int. J. Heat Mass Transfer 52 (2009) 3169–3175. [23] Q. Liu, A.K. Sleiti, J.S. Kapat, Application of pressure and temperature sensitive paints for study of heat transfer to a circular impinging air jet, Int. J. Therm. Sci. 47 (2008) 749–757. [24] R.J. Goldstein, A.I. Behbahani, K.K. Heppelmann, Streamwise distribution of the recovery factor and the local heat transfer coefficient to an impinging circular air jet, Int. J. Heat Mass Transfer 29 (1986) 1227–1235. [25] D. Lytle, B.W. Webb, Air jet impingement heat transfer at low nozzle-plate spacings, Int. J. Heat Mass Transfer 37 (1994) 1687–1697.
(1) For the hybrid module with plate fin, the jet hydraulic diameter ranges from 113 to 167 lm and the jet belongs to micro-scale impinging jet. Since Reynolds number is lower than the micro-scale critical value of 2500, the local Nusselt number distribution has a bell shape. For the hybrid module without plate fin, the jet belongs to macro-scale impinging jet because the jet hydraulic diameter varies from 340 to 9869 lm. The local Nusselt number exhibits a double-peak shape which is mainly due to the microchannels in the radial flow region produces a perturbation to jet flow field. (2) The hybrid module with plate fin has a better cooling performance than the hybrid module without plate fin. The slot-jet length has different effect on the cooling performance for the two kinds of hybrid modules due to distinct local Nusselt number distributions. Increasing the slot-jet length improves the bottom wall temperature uniformity and reduces the thermal resistance significantly for the hybrid module with plate fin. Oppositely, a relatively small slot-jet length is recommended for another hybrid module. (3) The cooling performance can be further improved by optimizing the channel number, channel aspect ratio, and width ratio of channel-to-pitch. For the hybrid module with plate fin, when the optimal value for the three parameters is respectively adopted, the thermal resistance is reduced by 30.57% 26.60%, and 29.19% as compared with the worst design, while the bottom wall temperature gradient is reduced by 70.71%, 70.99%, and 69.46%.
Conflict of interest None declared.
Acknowledgments This study was partially supported by the National Natural Science Foundation of China (No. 51276060), the 111 Project (No. B12034), Program for New Century Excellent Talents in University (No. NCET-11-0635), and the Fundamental Research Funds for the Central Universities (No. 13ZX13).
Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Effects of slot-jet length on the cooling performance of hybrid microchannel/slot-jet module Chol-Bom Kim a,b, Chuan Leng a, Xiao-Dong Wang a,⇑, Tian-Hu Wang c, Wei-Mon Yan d,⇑ a
State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources, North China Electric Power University, Beijing 102206, China Department of Mechanical Engineering, Hamhung Hydraulic and Power University, Hamhung, Democratic People’s Republic of Korea c School of Mathematics and Physics, North China Electric Power University, Beijing 102206, China d Department of Energy and Refrigerating Air-Conditioning Engineering, National Taipei University of Technology, Taipei 10608, Taiwan b
a r t i c l e
i n f o
Article history: Received 5 January 2015 Received in revised form 28 May 2015 Accepted 28 May 2015 Available online 14 June 2015 Keywords: Hybrid Microchannel Slot-jet Temperature uniformity Thermal resistance
a b s t r a c t In this work, a three-dimensional numerical model based on the k–x SST turbulent model is developed to investigate the single-phase cooling performance of hybrid microchannel/slot-jet module at a constant pumping power of 0.05 W. Two different hybrid modules are analyzed, and the difference between them lies in whether there exist plate fins beneath the slot jet. The temperature uniformity of cooled object and global thermal resistance are evaluated for the two hybrid modules at various slot-jet lengths. The results show that local Nusselt number distribution exhibits a bell shape for the hybrid module with plate fin, while it has a double-peak shape for the hybrid module without plate fin. When with plate fin, a larger slot-jet length of 7800 lm yields the best cooling performance. Oppositely, when without plate fin, a smaller length of 606 lm is beneficial to achieve the better cooling performance. The optimal hybrid module with plate fin has the thermal resistance of 0.105 K W1 and the bottom wall temperature gradient of 0.27 °C, which are lower than those of the hybrid module without plate fin. Furthermore, the cooling performance of hybrid module can be further improved by optimization of geometric parameters of the heat sink. When the optimal channel number, channel aspect ratio, and width ratio of channel-to-pitch are adopted respectively, the thermal resistance of the hybrid module with plate fin can be reduced by 26.38% to 27.78% as compared with the worst geometry, while the bottom wall temperature gradient can be reduced by 86.79% to 87.46%. Ó 2015 Elsevier Ltd. All rights reserved.
1. Introduction Thermal management of electronic devices is one of the important issues for electronics packaging. The rapid advances in micro-electronics technology lead to an increasing heat flux that needs to be removed from the chip surfaces. There is also a desire to improve the temperature uniformity of the cooled object, because the thermal stress caused by large temperature gradient can damage reliability of the devices. Recently several schemes have been proposed to enhance single-phase high heat flux cooling. Among these schemes, microchannel heat sink and jet impingement are regarded as two promising candidates for the cooling of high-performance microprocessors, laser diode arrays, radars, X-ray anodes, solar photovoltaic concentrators, laser and ⇑ Corresponding authors. Tel./fax: +86 10 62321277 (X.-D. Wang). Tel./fax: +886 939259149 (W.-M. Yan). E-mail addresses: [email protected] (X.-D. Wang), [email protected] (W.-M. Yan). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2015.05.108 0017-9310/Ó 2015 Elsevier Ltd. All rights reserved.
microwave directed energy weapons, and hybrid-vehicle power electronics [1]. Both the microchannel heat sink and jet impingement provide very high heat removal capability, but they still present some serious drawbacks [2,3]. The microchannel heat sink can yield heat removal rates comparable to the jet impingement using far smaller coolant flow rates and more compact structure, however, it also causes a high temperature rise along the flow path of coolant and needs a high pressure drop [1,4]. Using a dielectric liquid, the jet impingement produces a very high heat transfer coefficient in the impingement region [5]. The abrupt reduction in cooling effectiveness away from the impingement region can yield large temperature variations along the surface of the cooled object [6]. Therefore the jet impingement requires jet arrays to ensure a relatively good level of temperature uniformity. There are two disadvantages for the jet array. First, after the cool fluid impinges on the cooled surface and dissipates the heat from the surface, the fluid temperature increase inevitably. However, it is difficult to remove the heated fluid from the impinging region due to dense
C.-B. Kim et al. / International Journal of Heat and Mass Transfer 89 (2015) 838–845
jet arrangement which inevitably causes a reduced heat transfer capacity [7]. Second, the interaction between adjacent jets also leads to a significant reduction in the local heat transfer coefficient. Many studies have attempted to reduce these unfavorable effects and at the same time to enhance the heat transfer associated with the two cooling technologies [8–13]. Recently, a hybrid cooling scheme with the combination of microchannel heat sink and jet impingement technologies (referred to as hybrid microchannel/jet-impingement module) was proposed which is expected to both achieve a more uniform temperature distribution on the surface of the cooled object and reduce global thermal resistance of the cooling system [14–19]. Jang et al. [14] for the first time evaluated the cooling performance of the hybrid microchannel/jet-impingement module experimentally. Their results indicated that the thermal resistance of the hybrid module is only 6.1 K W1 with about 48.5% reduction as compared with the conventional microchannel heat sink with a parallel flow at a constant pumping power of 0.072 W. Moreover, the pressure drop of the hybrid module is decreased by about 90.5% and the temperature difference across the base surface is decreased by about 87.6%. Subsequently, Jang and Kim [15] suggested two correlations for the thermal resistance and the pressure drop across the hybrid module. The correlations are compared with their experimental results, and both are shown to match with experimental results to within ±10%. Sung and Mudawar [16,17] investigated the cooling performance of a hybrid microchannel/slot-jet module both experimentally and numerically. They adopted the so-called standard k–e turbulent model to analyze the flow and heat transfer of coolant. Their numerical predictions showed that lower surface temperatures can be achieved by decreasing the jet width and microchannel height, and the hybrid module can maintain surface temperature gradients below 2 °C for heat fluxes up to 50 W cm2. Barrau et al. [18] conducted an experimental study on hybrid microchannel/jet-impingement cooling scheme. Their experiments confirmed that the hybrid scheme has the favorable capacity to improve the temperature uniformity of the cooled object. Barrau et al. [19] also used the k–x SST turbulent model to carry out a parametric analysis of longitudinal distribution and channel height. However, the effect of jet size was not discussed in their work. The hybrid microchannel/jet-impingement cooling module has been shown to significantly improve the temperature uniformity of the cooled object; however, the relevant studies are still very insufficient up to now. Especially, the temperature uniformity, pressure drop, and thermal resistance for the hybrid module can be further improved by optimizing the jet and channel sizes. In this
839
work, a three-dimensional numerical model based on the k–x SST turbulent model is developed to investigate the cooling performance of two different hybrid cooling modules at a constant pumping power. The slot-jet length is first optimized for both the modules and the corresponding cooling performances are compared. Subsequently, effects of three geometric parameters of microchannels, including channel number N, channel aspect ratio a, and width ratio of channel-to-pitch b are analyzed to search for the optimal design of the hybrid module. 2. Geometry for hybrid microchannel/slot-jet module The schematics of two kinds of hybrid microchannel/slot-jet cooling modules are illustrated in Figs. 1 and 2. The coolant impinges on the microchannel heat sink through a slot jet (along the negative y-axis). The slot jet is characterized by its length and width of Ljet and Wjet. The heat sink has a dimension of Lx Ly Lz and is composed of N channels and N + 1 fins. The heights of the channel and fin are Hc, while the widths of the channel and fin are Wc and Wf, respectively. The thickness is d1 for the bottom horizontal fin and d2 for the top horizontal fin. The difference between the two cooling modules lies in whether the solid fins exist beneath the slot jet. The geometric parameters of the hybrid module are listed in Table 1. Among these parameters, the parameters of microchannel heat sink come from Ref. [20], in which an optimal structure of heat sink is obtained at a constant pumping power of 0.05 W by an inverse problem optimization algorithm. The bottom of the heat sink is attached to a cooled surface such as integrated circuits or electronic chips with a uniform heat flux qw = 100 W cm2. 3. Description of the numerical model 3.1. Hybrid microchannel/slot-jet module model Barrau et al. [19] and Menter [21] have demonstrated that the k–x SST model is very effective for predicting the performance of the hybrid cooling module, and hence the present work adopts the same k–x SST turbulent model. The following assumptions are made: (1) steady state; (2) single phase and turbulent flow; (3) constant fluid and solid properties; (4) negligible gravitational force, radiation heat transfer, and contact resistance on the interfaces between the hybrid module and the cooled object. Based on the above assumptions, the governing equations are expressed in the Cartesian tensor notation as follows.
Fig. 1. Schematic of microchannel/slot-jet cooling module with plate fins beneath the slot-jet: (a) cooling module; (b) top and side views of the unit cell.
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Fig. 2. Schematic of microchannel/slot-jet cooling module without plate fins beneath the slot-jet: (a) cooling module; (b) top and side views of the unit cell.
Table 1 The geometric parameters of hybrid cooling module. Lx (mm)
Ly (mm)
Lz (mm)
Hc (lm)
Wc (lm)
Wf (lm)
Ljet (lm)
Wjet (lm)
d1 (lm)
d2 (lm)
10
0.9
10
692
84
56
1739800
9940
100
108
The constants of set 2 (u2) are (Standard k–e):
Continuity equation for the coolant:
@ui ¼0 @xi
ð1Þ
where ui are Cartesian component of velocity. Momentum equation for the coolant:
quj
@ui @p @ @ui ¼ þ ð l þ lt Þ @xi @xj @xj @xj
b
@T @ ¼ @xj @xj
cp lt @T kf þ Prt @xj
ð3Þ
where T is the coolant temperature, cp is the specific heat of the coolant, kf is the thermal conductivity of the coolant, and Prt = 0.85 is the turbulent Prandtl number. The k–x SST model is used for closure of the Reynolds stress tensor. The transport equations of the k–x SST model
@k @ @k ¼ P b qxk þ ðl þ rk lt Þ @xj @xj @xj @ x qc @ @x quj ¼ P bqx2 þ ð l þ rx lt Þ @xj @xj lt @xj 1 @k @ x þ 2ð1 F 1 Þqrx2 x @xj @xj
quj
lt ¼ q
k
ð4Þ
ð5Þ
ð7Þ
The constants of set 1 (u1) are (Wilcox k–x):
rk1 ¼ 0:5; rx1 ¼ 0:5; b1 ¼ 0:075; b ¼ 0:09; b rx1 j2 ffiffiffiffiffi j ¼ 0:41; c1 ¼ 1 p b
b
ð9Þ
ð8Þ
ð10Þ
where Ts is the fin temperature, and ks is the thermal conductivity of the fin. The boundary conditions for the governing equations are given as follows. Inlet:
u ¼ 0;
v ¼ v in ;
w ¼ 0;
T ¼ T in
ð11aÞ
Outlet:
p ¼ pout
ð11bÞ
Coolant–solid interface:
T ¼ Ts;
kf
@T @T s ¼ ks @n @n
ð11cÞ
Bottom wall of the heat sink:
qw ¼ ks
where P is the production term of turbulent viscosity and F1 is the blending function. Any constant (u) in the model is calculated from the constants u1 and u2 as follows:
u ¼ F 1 u1 þ ð1 F 1 Þu2
@ @T s ¼0 ks @xj @xj
u ¼ v ¼ w ¼ 0;
ð6Þ
x
b
Energy equation for solid region:
ð2Þ
where q and l are the density and dynamic viscosity of the coolant, lt is the turbulent viscosity, and p is the coolant pressure. Energy equation for coolant:
qcp uj
rk2 ¼ 1:0; rx2 ¼ 0:856; b2 ¼ 0:0828; b ¼ 0:09; b rx2 j2 ffiffiffiffiffi j ¼ 0:41; c2 ¼ 2 p
@T s @y
ð11dÞ
Other solid walls and symmetric interface:
0¼
@T s @n
ð11eÞ
In this work, the pumping power remains a constant value of X = 0.05 W. However, the coolant inlet velocity needs to be specified to solve the governing equations 1–5 and (10). The inlet velocity is determined as follows: (1) assume an initial value of the inlet velocity vin, and then numerically solve the governing equations )1–5 and (10) with the boundary conditions Eq. (11); (2) calculate the pumping power X0 = NvinAjetDp, where Ajet = LjetWjet is the cross-sectional area of the slot-jet and Dp is the pressure drop
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70
60
Solid block: experimental results in Ref. [19] Dash line: numerical results in Ref. [19] Solid line: present results
55
test 4
65
Nux ¼
Tb (°C)
40 35
test 3
ðT b T c Þ d1
test 2
qeff ¼ ks
test 1
where Tb is the temperature of bottom wall of the hybrid module. The temperature gradient along the bottom wall of the hybrid module is defined as follows:
30 25 20
ð13Þ
where qeff is the effective heat flux, Dh,c is the channel hydraulic diameter expressed as Dh,c = 2HcWc/(Hc + Wc), and Tc is the temperature of the channel bottom wall. The effective heat flux can be calculated by:
50 45
qeff Dh;c kf ðT c T in Þ
0
5
10
15
20
25
ð14Þ
DT b ¼ T b; max T b;min
30
x (mm) Fig. 3. Temperature profile on the bottom wall of the hybrid module at various test conditions.
across the hybrid module; (3) if |X0 X|/X < 0.01, terminate the procedure, otherwise, update vin and return step (1), and then repeat steps (1) to (3). In the present simulations, governing equations 1–5 and (10) are transformed into a finite difference form using the control volume method and are solved iteratively with an iteration criterion for convergence of 106. Various mesh combinations are examined before simulations. The present code is tested for grid independence by calculating the bottom wall minimum temperature in the hybrid module. It is found that a grid size of 203,000 ensures a grid-independent solution. Local refining is necessary at the boundary layer to ensure that the value of the near-wall parameter y+ is close to 1. 3.2. Model validation In order to validate the numerical model, the temperature profiles on the bottom wall of the hybrid module predicted by the present model are compared with experimental and numerical results in Ref. [19] at four different test conditions, as shown in Fig. 3. For fair comparison, the geometry and operating conditions of the hybrid module used in the present model are completely identical to those in Ref. [19]. The comparison shows a good agreement between the present results and the measured and predicted results in Ref. [19].
ð15Þ
where Tb,max = Tmax and Tb,min are the maximum and minimum temperature on bottom wall of the hybrid module. The jet Reynolds number is calculated based on the coolant inlet velocity and hydraulic diameter of the slot jet:
Re ¼
qv in Dh l
ð16Þ
where Dh is the hydraulic diameter of the slot jet. For the hybrid module without plate fin beneath the slot jet, we have Dh = 2LjetWjet/(Ljet + Wjet). However, for the hybrid module with plate fin, the slot jet is separated into N smaller jets due to existence of the plate fin, and these smaller jets separately impinge on the bottom wall of N channels, thus, the jet hydraulic diameter for the each channel should be calculated by Dh = 2LjetWc/(Ljet + Wc). Similarly, the jet inlet velocity in Eq. (16) for the hybrid module with plate fin should be modified as v 0in = vinLjetWjet/(NLjetWc). 4.1. Effects of jet length for hybrid module with plate fin beneath the slot jet This section analyzes the effects of slot-jet length on the cooling performance of the hybrid module with plate fin. Fig. 4 shows the variation of Tb along the bottom wall centerline of the hybrid module with various slot-jet lengths at a constant pumping power of X = 0.05 W. For the small slot length of Ljet = 173 lm, the lowest Tb occurs at the stagnation point with Tb,min = 22.07 °C, then Tb increases sharply when away from the impingement region and the highest Tb appears at the channel outlet with Tb,max = 31.05 °C. As shown in Fig. 4, increasing Ljet increases the temperature in impingement region; however, the temperature rise becomes slow when away from the impingement region as compared with small Ljet. For Ljet = 7800 lm, Tb,min and Tb,max are
4. Results and discussion
RT ¼
T max T min T max T in ¼ qw A qw L x L z
32 31 30 29 28 Tb (°C)
The heat sink is made of silicon with ks = 148 W m1 K1. Pure water is the coolant with kf = 0.613 W m1 K1, l = 0.000855 kg m1 s1, q = 997 kg m3, cp = 4179 J kg1 K1 and Tin = 290 K. A uniform heat flux of qw = 100 W cm2 is applied to the heat sink bottom wall. The hybrid module operates at a constant pumping power of X = 0.05 W. The performance of hybrid module can be evaluated by global thermal resistance, local Nusselt number, and temperature gradient along the bottom wall of the hybrid module. The global thermal resistance RT is defined as follows:
27 26 25
L jet=9800 μ m
24
L jet=7800 μ m
23
ð12Þ
where Tmax and Tmin = Tin are the maximum and minimum temperatures observed in the hybrid module, and A = Lx Lz is the base area of the hybrid module. The local Nusselt number is defined as [17,18]:
L jet=1384 μ m
22 21
L jet=173 μ m 0
1
2
3
4
5
6
7
8
9
10
x (mm) Fig. 4. Temperature profiles along centerline (y = 0 and z = (Wc + Wf)/2) on the bottom wall of the hybrid module with plate fin.
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Table 2 The performance of the hybrid module with plate fin beneath slot jet for various jet lengths at a constant pumping power of 0.05 W. Lje (lm)
Wjet (lm)
Dh (lm)
v 0in
9800 7800 5536 2768 1384 692 346 173
84 84 84 84 84 84 84 84
167 166 165 163 158 150 135 113
0.164 0.188 0.243 0.441 0.820 1.526 2.499 3.568
(m s1)
Re
Dp (kPa)
Tb,max (°C)
Tb,min (°C)
DTb (°C)
RT (K W1)
32 37 46 83 151 266 394 482
5.197 5.706 6.285 6.978 7.332 7.939 9.677 13.260
28.05 27.49 27.67 27.87 28.05 28.33 29.10 31.05
27.47 27.22 26.46 24.98 23.94 23.37 22.59 22.07
0.58 0.27 1.21 2.89 4.11 4.96 6.51 8.98
0.111 0.105 0.107 0.109 0.111 0.113 0.121 0.141
Fig. 5. Flow fields velocity at z = (Wc + Wf)/2 for (a) Ljet = 173 lm and (b) Ljet = 1384 lm.
27.22 and 27.49 °C, respectively, the temperature gradient DTb is only 0.27 °C, indicating a more uniform temperature distribution on the bottom wall can be achieved by a larger Ljet. It is worth noting that Tb,min does not occur at the stagnation point for the cases
with Ljet = 7800, and 9800 lm because Ljet approaches the channel length. The pressure drop across the hybrid module and jet inlet velocity at various slot lengths are shown in Table 2. For the case of Ljet = 173 lm, the jet inlet velocity and pressure drop are 3.568 m s1 and 13.260 kPa, respectively. As Ljet increases, the jet inlet velocity and pressure drop both reduce because the pumping power remains a constant value of 0.05 W. For example, jet inlet velocity reduces to 0.164 m s1, and the pressure drop decreases to 5.197 kPa for Ljet = 9800 lm. The flow fields at z = (Wc + Wf)/2 for Ljet = 173 lm and Ljet = 1384 lm are illustrated in Fig. 5. When Ljet = 173 lm, a larger jet inlet velocity causes the jet fluid to approach closer to the impinging surface (Fig. 5(a)), leading to the significant decrease of temperature in the impingement region. However, most momentum of the jet fluid is lost after impingement, leading to the sharply decreased velocity away from the impinging region. At smaller jet inlet velocity, on the contrary, the jet fluid occupies the upper region of the flow channel due to the weaker attachment of the jet fluid to the impinging surface (Fig. 5(b)). The jet fluid cannot approach to the impinging surface as closer as the larger jet inlet velocity, thus significantly weaken the heat transfer on the impinging surface. In this case, the momentum lost is smaller than that of the larger inlet velocity, thus the velocity decrease more slowly away from the impinging region. Consequently, a more uniform temperature distribution on the bottom wall can be achieved by a larger Ljet. The variation of Tb along the bottom wall centerline for various slot-jet lengths can be further justified by Fig. 6 which shows the local Nusselt number along the channel bottom wall. The jet hydraulic diameter ranges from 113 to 167 lm for various jet lengths in the present simulations (Table 2), which belongs to micro-scale impinging jet according to Ref. [22]. The experimental tests of Choo et al. [22] showed that when Re < 2500, the local Nusselt number distribution for the micro-scale impinging jet
60
70
Ljet=1384 μm,
Ljet=9800 μm Ljet=7800 μm
60
Ljet=606 μm,
Ljet=173 μm,
50
Ljet=346 μm
Ljet=173 μm without channel
Ljet=1384 μm Ljet=173 μm
40
40
Nux
Nux
50
30
30
20
20
10
10
0
1
2
3
4
5
6
7
8
9
10
x (mm) Fig. 6. Local Nusselt number along the channel bottom wall at various slot lengths for the hybrid module with plate fin.
0
0
1
2
3
4
5
6
7
8
9
10
x (mm) Fig. 7. Local Nusselt number along the channel bottom wall at various slot lengths for the hybrid module without plate fin.
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Fig. 8. Schematic of jet impingement without microchannel.
has a bell shape. The present predictions of Nusselt number distribution shown in Fig. 6 agree with the report by Choo et al. well. Since the increase in Ljet decreases the jet inlet velocity, the local Nusselt number is lower thus the bottom wall temperature Tb is higher in the impingement region for larger Ljet. For example, the local Nusselt number at the stagnation point is 64.8 for Ljet = 173 lm, while it reduced to 34.5 for Ljet = 1384 lm. For a typical impinging jet, the flow field can be divided into three separate regions: free jet region, impingement region, and radial flow region (Fig. 5). When coolant flows from the impingement region into the radial flow region, the radial velocity decreases rapidly which results in a thickening of the boundary layer and a heat transfer deterioration along the radial direction. A smaller Ljet corresponds to a smaller width of the impingement region and a larger width of the radial flow region. Thus, the Nusselt number is lower in the radial flow region for smaller Ljet due to the rapid decay of the heat transfer coefficient along the radial direction. The temperature gradient on the bottom wall of the hybrid module and the global thermal resistance for various jet lengths are listed in Table 2. Increasing the jet length significantly reduces both the temperature gradient and the global thermal resistance. The optimal jet length is found to be 7800 lm, which leads to the lowest thermal resistance of RT = 0.105 K W1 and the smallest temperature gradient of DTb = 0.27 °C. 4.2. Effects of jet length for hybrid module without plate fin beneath the slot jet This section analyzes the effects of slot-jet length on the cooling performance of the hybrid module without plate fin. The local Nusselt number along the bottom wall centerline for various jet lengths is shown in Fig. 7. It can be seen that the local Nusselt number exhibits a double-peak distribution and its maximums do not occur at the stagnation point. The double-peak structure
in the macro-scale impinging jet was observed at a high Reynolds number of Re P 40,000 or a small nozzle-to-plate spacing of Y/Dh < 1 [23–25], where Y denotes the distance of the nozzle from the plate. In the present simulations, the jet hydraulic diameter ranges from 340 to 9869 lm for various jet lengths, hence, the jets belong to macro-scale impinging jet and the corresponding Reynolds number varies from 1263 to 1709. The nozzle-to-plate spacing is smaller than 1 when Ljet varies from 606 to 9800 lm, while it is larger than 1 for Ljet = 173 and 346 lm. Thus, the double-peak distribution of the local Nusselt number should indeed occur for the cases with 606 lm 6 Ljet 6 9800 lm. However, the double-peak distribution is also observed in Fig. 7 for the cases with Ljet = 173 and 346 lm, which seems to be in contradiction with the experimental results in Ref. [23–25]. In order to explain why the double-peak distribution occurs for small Ljet, an extra simulation is conducted. The geometry of the new system simulated is shown in Fig. 8. It can be seen that only microchannels are removed from the new system, however, the other parameters such as the jet width and length, nozzle-to-plate spacing, and jet Reynolds number remain the same with the case with Ljet = 173 lm. As shown in Fig. 7, the local Nusselt number again exhibits a bell shape for the new simulation due to Re = 1263 < 40,000 and Y/Dh = 2.35 > 1, which agrees the previous experimental results in Refs. [23–25]. Thus, the double-peak distribution for small Ljet may be attributed to the fact that the microchannels located in the radial flow region produce a perturbation to the jet flow field. As shown in Table 3, for the case of Ljet = 173 lm, the jet inlet velocity and pressure drop across the hybrid module are 3.185 m s1 and 9.192 kPa, respectively. As Ljet increases, the jet inlet velocity and pressure drop are all decreased. For example, the jet inlet velocity is reduced to 0.149 m s1, and the pressure drop is reduced to 3.453 kPa for the case of Ljet = 9800 lm. The variation of jet inlet velocity leads to a significant difference in the local Nusselt number for various jet lengths, as shown in Fig. 7. For the very small Ljet = 173 lm, due to its large jet inlet velocity the local Nusselt number in the impingement region is higher, however, rapid decay of the heat transfer coefficient results in a lower local Nusselt number in the radial flow region compared with other jet lengths. For larger Ljet = 346, 606, and 1384 lm, although the local Nusselt number reduces significantly with the increase of Ljet in the impingement region, it is almost the same in the radial flow region. Fig. 9 shows the temperature distribution along the bottom wall centerline of the hybrid module without plate fin. The temperature distribution along the bottom wall exhibits a double-valley shape, which is just opposite to the Nusselt number distribution shown in Fig. 7. For various jet lengths, Tb firstly decreases with increasing the radial distance from the stagnation point to the shifted valley and then increases monotonically beyond the shifted valley. Tb,min is 22.82 °C for Ljet = 173 lm, 23.90 °C for Ljet = 346 lm, 24.61 °C for Ljet = 606 lm, and 25.79 °C for Ljet = 1384 lm. It should be noted that Tb,max occurs at different location for various jet
Table 3 The performance of the hybrid module without plate fin beneath slot jet for various jet lengths at a constant pumping power of 0.05 W. Ljet (lm)
Wjet (lm)
Dh (lm)
vin (m s1)
Re
Dp (kPa)
Tb,max (°C)
Tb,min (°C)
DTb (°C)
RT (K W1)
9800 5536 2768 1384 692 606 346 173
9940 9940 9940 9940 9940 9940 9940 9940
9869 7111 4330 2430 1294 1142 669 340
0.149 0.169 0.284 0.525 1.018 1.152 1.942 3.185
1709 1401 1434 1487 1536 1535 1514 1263
3.453 5.419 6.413 6.856 7.205 7.219 7.579 9.192
90.55 82.02 57.09 38.39 29.02 27.97 28.12 28.82
49.39 28.09 26.89 25.79 24.78 24.61 23.90 22.82
41.16 53.93 30.20 12.60 4.24 3.36 4.22 6.00
0.736 0.650 0.401 0.214 0.120 0.111 0.111 0.118
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can be explained by the following two reasons. First, the pressure drops are 5.706, 7.219, and 14.040 kPa for the hybrid modules with and without plate fin and the conventional microchannel heat sink, respectively. Hence, the hybrid modules have larger coolant flow rates than the conventional microchannel heat sink at the same pumping power. Second, because the inlet is located at the center of the heat sink for the hybrid modules, the coolant flow path is only a half of that for the conventional heat sink.
40 L jet=1384 μ m L jet=606 μ m
36
L jet=346 μ m
Tb (°C)
L jet=173 μ m 32
28
4.4. Effects of heat sink geometric parameters
6
7
8
9
10
Fig. 9. Temperature profiles along centerline (y = 0 and z = (Wc + Wf)/2) on the bottom wall of the hybrid module without plate fin.
lengths. For the small Ljet = 173 and 346 lm, Tb,max are 28.82 and 28.12 °C, respectively, and they all occur at the channel outlet. For the mediate Ljet = 606 lm, Tb,max = 27.97 °C occurs at the channel outlet, however, this temperature is almost the same with that at the stagnant point (27.96 °C). For the large Ljet = 1384 lm, Tb,max = 38.39 °C occurs at the stagnation point. The temperature gradient on the bottom wall of the hybrid module and global thermal resistance for various jet lengths are listed in Table 3. Both the temperature gradient and global thermal resistance are firstly decrease and then increases with the jet length increased. The optimal jet length is 606 lm, which has the lowest thermal resistance of RT = 0.111 K W1 and the smallest temperature gradient of DTb = 3.36 °C. 4.3. Comparison between two hybrid modules and conventional heat sink Fig. 10 shows the optimal thermal resistance and bottom wall temperature gradient for the two hybrid modules with and without the plate fin and the conventional microchannel heat sink at a constant pumping power of X = 0.05 W. The hybrid module with plate fin exhibits the best performance with (RT)opt = 0.105 K W1 and (DTb)opt = 0.27 °C, and then followed by the hybrid module without plate fin with (RT)opt = 0.111 K W1 and (DTb)opt = 3.36 °C. The conventional microchannel heat sink has the worst performance, the optimal RT is 0.144 K W1 and the optimal DTb is 8.93 °C. The superior performance for the two hybrid modules
1.80 1.60
ΔTb (°C)
8.93
0.108
1.20
1.32
-1
0.104
ΔTb (°C)
70
80
90 N
0.27
with plate fin
120
N = 71, β = 0.60, L jet= 5500 μ m, Ω =0.05 W
0.1064 0.1056 8
9
10
α
(c)
3.00
11
12
13
14
N = 71, α = 8.24, L jet= 5500 μ m, Ω =0.05 W
0.144 0.132
2.00
0.120
1.00
without plate fin
heat sink
Fig. 10. The optimal RT and DTb for the two hybrid modules with and without plate fin and the conventional microchannel heat sink at X = 0.05 W.
0.1072
1.14
4.00 ΔTb (°C)
0.105
110
1.20
7
0.111
100
0.1080
(b)
1.26
0.144 3.36
0.112
1.40
60
RT (K W )
0.116
(a) α = 8.24, β = 0.60, L jet= 5500 μ m, Ω =0.05 W
-1
5 x (mm)
RT (K W )
4
-1
3
RT (K W )
2
-1
1
RT (K W )
0
The bottom wall temperature uniformity and thermal resistance of hybrid module depends on the geometric structure of microchannel heat sink. Therefore, this section analyzes the effects of geometric parameters of the heat sink on the cooling performance of hybrid module at a constant pumping power of X = 0.05 W. Only the hybrid module with plate fin is discussed here due to its better performance than the hybrid module without plate fin. Two non-dimensional parameters are defined as follows: a = Hc/Wc is the channel aspect ratio, and b = Wc/(Wc + Wf) is the width ratio of channel-to-pitch. The optimal design with N = 71, a = 8.24, and b = 0.60 for the conventional microchannel heat sink (Lx = 10 mm, Ly = 0.9 mm, and Lz = 10 mm) at X = 0.05 W has been obtained by Wang et al. [20], and this design is adopted in the present simulations. For comparison purpose, a baseline case with N = 71, a = 8.24, and b = 0.60 is chosen, in single parameter analysis only one parameter of interest is changed with the other two parameters as same as the baseline case. The thermal resistance and bottom wall temperature gradient as function of N, a or b are shown in Fig. 11. For each geometric parameter, there is an optimal value at which the optimal performance of the hybrid module can be achieved. However, it should be noted that the optimal parameter value corresponding to (RT)min differs from that corresponding to (DTb)min. With N = 92, a = 10.75 or b = 0.55, the hybrid module with plate fin achieves the lowest RT, which is reduced by 30.57%, 26.60%, and 29.19%, as compared with the worst design. Similarly, the most uniform bottom wall temperature distribution is achieved at N = 96, a = 11.12 or b = 0.59 for the hybrid module, and DTb is reduced by 70.71%, 70.99%, and 69.46%, as compared with the worst design.
ΔTb (°C)
24
0.108 0.35
0.40
0.45
0.50
β
0.55
0.60
0.65
0.70
Fig. 11. Effects of heat sink geometric parameters on RT and DTb: (a) N; (b) a; (c) b; (d) c.
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5. Conclusion
References
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(1) For the hybrid module with plate fin, the jet hydraulic diameter ranges from 113 to 167 lm and the jet belongs to micro-scale impinging jet. Since Reynolds number is lower than the micro-scale critical value of 2500, the local Nusselt number distribution has a bell shape. For the hybrid module without plate fin, the jet belongs to macro-scale impinging jet because the jet hydraulic diameter varies from 340 to 9869 lm. The local Nusselt number exhibits a double-peak shape which is mainly due to the microchannels in the radial flow region produces a perturbation to jet flow field. (2) The hybrid module with plate fin has a better cooling performance than the hybrid module without plate fin. The slot-jet length has different effect on the cooling performance for the two kinds of hybrid modules due to distinct local Nusselt number distributions. Increasing the slot-jet length improves the bottom wall temperature uniformity and reduces the thermal resistance significantly for the hybrid module with plate fin. Oppositely, a relatively small slot-jet length is recommended for another hybrid module. (3) The cooling performance can be further improved by optimizing the channel number, channel aspect ratio, and width ratio of channel-to-pitch. For the hybrid module with plate fin, when the optimal value for the three parameters is respectively adopted, the thermal resistance is reduced by 30.57% 26.60%, and 29.19% as compared with the worst design, while the bottom wall temperature gradient is reduced by 70.71%, 70.99%, and 69.46%.
Conflict of interest None declared.
Acknowledgments This study was partially supported by the National Natural Science Foundation of China (No. 51276060), the 111 Project (No. B12034), Program for New Century Excellent Talents in University (No. NCET-11-0635), and the Fundamental Research Funds for the Central Universities (No. 13ZX13).