Optimization and comparison of double-layer and

Applied Thermal Engineering 65 (2014) 124e134

Contents lists available at ScienceDirect

Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng

Optimization and comparison of double-layer and double-side micro-channel heat sinks with nanofluid for power electronics cooling Assel Sakanova a, Shan Yin a, Jiyun Zhao a, *, J.M. Wu b, K.C. Leong c a

EXQUISITUS, Centre for E-City, School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798, Singapore State Key Laboratory for the Strength and Vibration of Mechanical, School of Aerospace, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, China c School of Mechanical and Aerospace Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore b

h i g h l i g h t s
Microchannels are integrated inside the Cu-layer of direct bond copper.
The double-layered and sandwich microchannel structures are comparatively studied.
Optimized geometry and design is obtained based on parametric studies.
Water based Al2O3 nanofluid is investigated for the microchannel cooling.

a r t i c l e i n f o

a b s t r a c t

Article history: Received 5 September 2013 Accepted 4 January 2014 Available online xxx

The tendency of increasing power rating and shrinking size of power electronics systems requires advanced thermal management technology. Introduction of micro-channel heat sink into power electronics cooling has significantly improved the cooling performance. In present work, two advanced micro-channel structures, i.e. double-layer (DL) and double-side (sandwich) with water as coolant, are optimized and compared by computational fluid dynamics (CFD) study. The micro-channels are integrated inside the Cu-layer of direct bond copper (DBC). The effects of inlet velocity, inlet temperature, heat flux are investigated during geometry optimization. The major scaling effects including temperature-dependent fluid properties and entrance effect are considered. Based on the optimal geometry, the sandwich structure with counter flow shows a reduction in thermal resistance by 59%, 52% and 53% compared with single-layer (SL), DL with unidirectional flow and DL with counter flow respectively. Water based Al2O3 (with concentration of 1% and 5%) nanofluid is further applied which shows remarkable improvement for wide channels. Ó 2014 Elsevier Ltd. All rights reserved.

Keywords: CFD Direct bond copper Micro-channel heat sink Nanofluid Power electronic cooling

1. Introduction With the further increasing demands on high temperature power electronics systems, like hybrid electric vehicles (HEV) and aerospace applications, the conventional packaging and cooling technologies become hard to meet the demands. The standard power electronics packaging normally consists of multiple thermally resistive layers. The long heat conduction path and thermal interface materials (TIM) with low thermal conductivity (typically 0.5e3 W/K m) degrade the cooling performance significantly. The conventional cooling technologies, including natural air convection

* Corresponding author. Tel.: þ65 67904508; fax: þ65 67933318. E-mail address: [email protected] (J. Zhao). 1359-4311/$ e see front matter Ó 2014 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.applthermaleng.2014.01.005

and forced air convection, have become hard to cool the high heat flux (100 W/cm2). Some early works on advanced packaging and cooling technologies included: replacement of TIM with solder between DBC (direct bond copper) and heat sink [1], double-side cooling with heat pipes [2] or liquid impingement cooling [3]. The microchannel heat sink (MCHS) exhibits great potential in power electronics cooling since the first fabrication by Tuckerman and Pease, which cooled a heat flux of 790 W/cm2 with a temperature rise of 71  C [4]. The DBC with a sandwich structure of Cu-ceramic-Cu plays a key role in the modularization and integration of power electronic systems. It serves as the mechanical support, electrical isolation, interconnection and heat removal path for the power module. With integration of micro-channels inside DBC, the cooling performance is ultimately improved by minimizing heat conduction path and completely eliminating TIM. The MCHS can be either

A. Sakanova et al. / Applied Thermal Engineering 65 (2014) 124e134

Nomenclature A Br cp Dh f Gz h H k l M N Nu Dp Ppump Pr q Rcap Rconv Rcond Re t T U

area (m2) Brinkmann number specific heat (J/kg K) hydraulic diameter (m) Fanning friction factor Graetz number heat transfer coefficient (W/K m2) height (m) thermal conductivity (W/K m) length (m) Maranzana number number of micro-channels Nusselt number pressure drop (Pa) pumping power (W) Prandtl number heat flux (W/cm2) capacitive thermal resistance (K/W) convective thermal resistance (K/W) conductive thermal resistance (K/W) Reynolds number thickness (m) temperature (K) velocity vector (m/s)

fabricated in the back Cu-layer of DBC [5e7] or in the AlN-layer of DBC [8e10]. The analytical model considering the heat transfer and fluid dynamics of MCHS needs to be developed in order to facilitate geometry design. Some of the early works used 2D simplified model to build the correlation for thermal resistance [11e13]. Hwang et al. [11] enhanced the performance of MCHS for both deep-channel and shallow-channel cases by increasing flow rate which reduced caloric resistance. Knight et al. [12] analytically described the optimization scheme for the earlier works including Tuckerman and Pease (1981) and Goldberg (1984) by varying both fin and channel, the latter was fixed previously. Weisberg et al. [13] numerically analyzed the conjugate heat transfer and presented the design algorithm for the selection of the channel size. At a later time, 3D conjugated heat transfer model was developed to analyze flow and simulate heat transfer performance of MCHS [14e23]. Lee and Garimella [15] proposed correlations for predicting Nusselt and average Nusselt number obtained by 3D numerical simulations for thermally developing flow with the aspect ratio (a) from 1 to 10. They concluded that both the local and average Nusselt number depends on the dimensionless axial distance and a. Chein and Chen [16] numerically investigated the performance of heat sink under 6 different inlet/outlet locations, others conditions were the same. Considering thermal resistance, overall heat transfer coefficient and pressure drop as the main criteria for heat sink fulfillment, it was found that U- and V-types showed better performance than other geometries. Gunnasegaran et al. [17] also numerically investigated the effect of three different channel shapes on heat transfer characteristics. They pointed out that the Poiseuille number as well as heat transfer coefficient augmented with increasing Reynolds number. Under these conditions, the rectangular channels showed the best performance and followed by trapezoidal and triangular. Kim [18] summarized two analytical models and 3D numerical approach. Then the data of two analytical models which included the fin model and porous

u, n, w W x, y, z

125

flow velocity (m/s) width (m) Cartesian coordinates

Greek symbols aspect ratio width ratio thickness of interfacial layer fin efficiency k(N) Hagenbach factor m viscosity (N s/m2) r density (kg/m3) f viscous dissipation 4 volumetric concentration of nanoparticles

a b d h

Subscripts app apparent av average ch channel eff effective f fluid j junction inf inletnanofluid o outlet s solid

medium model were compared with numerical simulation. The optimal values of channel height, width and fin thickness under the constraint of maximum pumping power were obtained. Husain and Kim [19] performed the optimization of MCHS with the help of surrogate analysis and hybrid multi-objective evolutionary approach. Ambatipudi and Rahman [20] varied the channel depth, width, number and flow rate. The results were compared with the experimental works of Harms [21] and Harms et al. [22]. Li and Peterson [23] determined the optimal parameters under a constant pumping power of 0.05 W which were found at channel number N ¼ 100, channel width ratio b ¼ 0.6 and channel aspect ratio a ¼ 12. They provided a fully understanding influence of the optimized spacing and channel dimensions on heat transfer capacity of MCHS. As the channels shrink to micro-size, the well-established theories and analytical correlations for the macro-channel are no longer suitable. By comparing Nusselt number at constant and variable properties, Herwig and Mahulikar [24] concluded that the temperature dependence of thermo-physical properties are important with scaling effects and cannot be negligible in microsize channels. Li et al. [25] numerically compared inlet, average and variable properties for laminar flow in rectangular channels and made the conclusion that variable properties were more accurate in terms of engineering application. Entrance effect should also be taken into account. Qu and Mudawar [26] numerically analyzed 3D fluid flow and heat transfer characteristics in rectangular MCHS. They found the highest heat flux and Nusselt number at inlet while zero in the corners. Lee et al. [27] experimentally investigated heat transfer with hydraulic diameters ranged from 318 to 903 mm. These results had wide disparities with conventional correlations. The effect of viscous dissipation in terms of Brinkman number was studied by Tso and Manulikar [28]. They elaborated Brinkman number for correlating the convective heat transfer in MCHS. Morini and Spiga [29] demonstrated that channel aspect ratio, Brinkman number and Reynolds number were

126

A. Sakanova et al. / Applied Thermal Engineering 65 (2014) 124e134

meaningful to define the effect of viscous dissipation on Nusselt number. The DL structure with counter flow was proposed as a substantial improvement over the SL MCHS by Vafai and Zhu [30]. They found that the streamwise temperature rise gradually declined than that of SL structure, and it also showed smaller pressure drop. Wei et al. [31] conducted numerical simulations to study thermal performance of stacked micro-channels with unidirectional and counter flow, which showed a thermal resistivity as low as 0.09 K/ (W cm2). For the counter flow, the non-uniformity of streamwise temperature distribution was less by 40% than that for unidirectional. Hung et al. [32] analyzed the heat transfer characteristics of DL structure with different substrate materials, working fluids and geometric parameters. They concluded its thermal performance better than SL structure, at the expense of a slight increase in pumping power. A noval approach for efficient cooling of multichip power modules is sandwich structure. This packaging structure consists of two DBC substrates, with power semiconductor devices sandwiched between them, and MCHS can be soldered to backside Culayer of DBC. This technology enables essential improvements in electrical performance due to the elimination of wirebonding interconnections. The thermal performance is also greatly enhanced as the heat generated by the power module can be removed from both sides. Lots of experimental works have been presented on this kind of structure [33e36]. As one of innovative strategies to enhance the heat transfer performance, nanofluid was initially proposed by Choi at Argonne National laboratory [37]. Lots of numerical and experimental works for nanofluid-cooled MCHS have been conducted. Ho et al. [38] concluded that a copper MCHS with an Al2O3-water based nanofluid at high pumping power had a noticeably higher average heat transfer coefficient while friction factor increases insignificantly. Chein and Huang [39] concluded that the introduction of nanofluid in base fluid produced no extra pressure drop due to small size and low particle concentration. Tsai and Chein [40] analyzed the performance of MCHS as a porous media using copperewater (Cue H2O) and carbon nanotube-water (CNTeH2O) nanofluids. Hung and Yan [41] conducted a three-dimensional analysis of DL MCHS with Al2O3 (1%)-water based nanofluid which showed a 26% improvement in thermal performance at fixed pumping power.

Diesselhorst equation [42]. The dynamic viscosity dependence on temperature is obtained by Sherman [43]. Specific heat capacity and thermal conductivity expressions are derived by third-order polynomial fitting results of [44].




rðTÞ ¼ 1000 1 

T þ 15:9414 ðT  276:9863Þ2 508929:2ðT  204:87037Þ

 (1)

mðTÞ ¼ 1:005  103



T 293

8:9

i h  exp 4700 T 1  2931

cp ðTÞ ¼ 3908 þ 3:826T  0:01674T 2 þ 2:330  105 T 3

(2)

(3)

kf ðTÞ ¼ 1:579 þ 0:01544T  3:515  105 T 2 þ 2:678  108 T 3 (4) where T is Kelvin temperature. The velocity inlet is defined with uniform temperature of 297 K and constant velocity of 2 m/s. The pressure outlet is adopted with atmosphere pressure. Constant heat flux 200 W/cm2 is specified at the top of DBC. Symmetrical boundary conditions are assumed on the left and right sides. Therefore, the boundary conditions are listed as below: Channel inlet:

u ¼ uin ; n ¼ 0; w ¼ 0; T ¼ Tin

(5)

Channel outlet:

p ¼ pout

(6)

Coolantesolid interface:

u ¼ n ¼ u ¼ 0; Tf ¼ Ts ; kf

vTf vTs ¼ ks vn vn

(7)

Bottom wall of the heat sink:

qw ¼ ks

vTs vn

(8)

Other solid walls and symmetric boundaries:

2. Numerical method The 3D structure of DBC (typical 300 mme635 mm AlNe300 mm Cu) and cross section of computational domain with rectangular micro-channels in back Cu-layer is shown by Fig. 1. The channel depth is fixed at 300 mm (through Cu-layer) and channel width varies during geometry optimization. Liquid water is used as the working fluid with temperature-dependent properties. The temperature-dependent density is defined by the ThieseneScheele

Heat flux Cu

AlN H

Cu W /2

(a)

W /2

(b)

Fig. 1. (a) 3D structure of DBC, (b) cross section of computational domain.

ks

vTs ¼ 0 vn

(9)

For the purpose of simplifying the analysis, the assumptions taken are listed as below: 1) Single-phase, incompressible laminar flow 2) The effect of gravitational force, heat dissipation caused by viscosity and radiation is negligible 3) Natural convection and radiation are neglected Under these simplifications, 3D steady governing equations for the conjugated heat transfer can be written as follows. Continuity equation

vu vn vw þ ¼ 0 þ vx vy vz

(10)

Momentum equation

!   vu vu vw vP v2 u v2 u v2 u rf u þ n þ w ¼  þ mf þ þ vx vy vz vx vx2 vy2 vz2

(11)

A. Sakanova et al. / Applied Thermal Engineering 65 (2014) 124e134



rf u 

rf

 vn vn vn vP v2 n v2 n v2 n þn þw ¼  þ mf þ þ vy vx vy vz vx2 vy2 vz2

! (12)

Table 1 Physical parameters of experiments and comparison between simulations and experiments. Case

!  vw vw vw vP v2 w v2 w v2 w þn þw ¼  þ mf u þ 2 þ 2 vx vy vz vz vx2 vy vz (13)

127

1 2 3

Wch (mm)

Wwall (mm)

Hch (mm)

P (psi)

q (W/cm2)

Rth (K/W) Experiment [4]

Simulation

56 55 50

44 45 50

320 287 302

15 17 31

181 277 790

0.110 0.113 0.090

0.104 0.105 0.077

Energy equation for the coolant



rf cp:f

vT vT vT u f þn f þw f vx vy vz

 ¼ kf

v2 Tf v2 Tf v2 Tf þ 2 þ 2 vx2 vy vz

! (14)

Energy equation for the solid region

0 ¼ ks

v2 Ts v2 Ts v2 Ts þ 2 þ 2 vx2 vy vz

! (15)

Based on ANSYS Fluent, the 3D conjugate heat transfer problem is numerically solved. Implicit solver option is used to solve the governing equations. The second order upwind scheme is adopted for both energy and momentum discretization. And for pressure discretization, standard interpolation scheme is adopted. The pressureevelocity coupling is implemented by SIMPLE algorithm. The convergence criteria for the x, y, and z directions velocity is 106 while the residuals of energy equations are restricted to 107. To evaluate the mesh density, 3 types of quadrilateral meshes with grid lines of 121  62  41, 141  72  51, 161  82  61 are investigated. The impact of mesh density on the simulation results are shown in Fig. 2. The difference of maximum temperatures is 0.006% between 121  62  41 and 141  72  51, while 0.008% between 121  62  41 and 161  82  61. With respect to pressure drop distribution, the maximum deviation occurs at the end of the channel with 0.14% between 121  62  41 and 141  72  51 and 0.25% between 121  62  41 and 161  82  61. Finally, 121  62  41 grid was selected as the best trade-off between both accuracy and CPU time. To verify the model, we compared the simulation results with experiments [4], as Table 1 illustrates. The differences for the thermal resistance are 5%, 7% and 14% for cases 1, 2 and 3 accordingly.

RePrDh Lx

Gz ¼

(16)

where Re is the Reynolds number and defined as Re ¼ ruavDh/m, Pr is the Prandtl number and defined as Pr ¼ cpm/kf, Dh is the hydraulic diameter and defined as Dh ¼ 2HchWch/(Hch þ Wch). The criterion for the effect of viscous dissipation is proposed by Morini and Spiga [29]

xlim ¼ 2RefBr

Hch Wch D2h

(17)

where xlim is the maximum allowable ratio (e.g. 5%) between temperature rise due to viscous dissipation and solidefluid heat transfer, Br is the Brinkman number and defined by mu2av =qDh : The effect of conjugate heat transfer is given by the Maranzana number, and should be taken into account when M > 0.01 [46].

M ¼


 ks Dh ðHbase þ Hch ÞWpitch 1 1 RePr kf Lx Hch Wch

(18)

The total thermal resistance of MCHS is given by

Rth ¼

Tj  Tin qA

(19)

where Tj is the junction temperature, Tin is the inlet temperature of coolant, qA is the heat flow. The pumping power is given by

Ppump ¼ Dp$V_

(20)

where Dp is the pressure drop of working liquid between inlet and outlet, V is the volumetric flow rate of working liquid with the expression V ¼ NAuav. The dimensionless Fanning friction factor is defined as

3. Analytical results The dimensionless Graetz number determined the importance of entrance effect which should be taken into account when Gz > 10 [45].

(a)

f ¼

Dh Dp 2rav u2av Lx

(21)

(b)

Fig. 2. Comparison of streamwise temperature distribution (a) and pressure drop distribution (b) with different mesh densities.

128

A. Sakanova et al. / Applied Thermal Engineering 65 (2014) 124e134

The thermal resistance of MCHS consists of the following three components.

4. Results and discussions 4.1. Geometry optimization

1) Conductive thermal resistance

Rcond

t ¼ ks As

(22)

where, t is thickness of each layer of the material under the device. 2) Convective thermal resistance

Rconv ¼

1   Nhav Lx 2hfin Hch þ Wch

(23)

where, hfin is fin efficiency and given by

hfin ¼

tanhðmHch Þ mHch

(24)

where, m is given by

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi hav P m ¼ ks Lx Wfin

(25)

And, hav is the average heat coefficient which is defined by

hav ¼

kf;av Nu Dh

(26)

The Nusselt number for the fully developed laminar flow is given by [47]

 NuN ¼ 8:235 1 

2:0421

a

þ

3:0853

a2



2:4765

a3

þ

1:0578

a4



0:1861



a5 (27)

3) Capacitive thermal resistance

Rcap ¼

1

(28)

rf;av cp;av uav Ach

Considering the scaling effects when the channel size shrinks to micro-scale, some correlations were proposed in lot of early works. Rohsenow et al. [48] suggested and Lee et al. [49] verified that flow in MCHS is hydrodynamically fully developed but thermally developing where entrance effects plays a significant role and cannot be neglected. The average Nusselt number, where entrance effect is taken into account is given by Hausen correlation [50].

Nu ¼ NuN þ

0:14Gz 1 þ 0:05Gz2=3

(29)

The pressure drop for the developing flow is depend on apparent friction factor which consists of two parts including the fully developed flow and pressure defect

ru2 2m L Ref Dp ¼ av x2 N uav þ kðNÞ av 2 Dh

(30)

where k(N) is Hagenbach factor and defined by

kðNÞ ¼ 0:6796 þ

1:2197

a

þ

3:3089

a2



9:5921

a3

þ

8:9089

a4



2:9959

a5 (31)

Fig. 3 presents the dependence of pumping power, thermal resistance and pressure drop on channel width ratio and channel number. At the beginning, the thermal resistance declines with b increasing until reaching optimized value of b. Further increasing b has a reverse effect. The lowest value of thermal resistance in terms of b is 0.75, 0.7, 0.6, 0.6, 0.4 for N ¼ 150, 125, 100, 75, 50 respectively. The cause of different optimal value is concluded in two aspects. Firstly, total thermal resistance is a sum of conductive and convective thermal resistances. As thermal conductivity of copper becomes higher than that of coolant, the second component has a greater effect. The convective thermal resistance is inversely proportional to the cross sectional area of the heat sink. Hence, at fixed N as b increasing that means heat transfer area getting larger, which results in a decrease of conductive thermal resistance. Secondly, Rth is reduced significantly with N increasing, which contributes to higher Ppump. However, as a side effect it brings to the higher flow resistance inside the channel, which causes the velocity to slowingdown. Thus, the optimal resistance is a trade-off between the heat transfer area and the channel flow resistance. The lowest thermal resistance is found at N ¼ 125 b ¼ 0.7, Wch ¼ 56 mm, and Wfin ¼ 24 for 1 cm  1 cm Cu-based MCHS, which coincides with the numerical results of [51]. With the aim to prove the selected parameters is the optimal geometry, we compared pumping power, thermal resistance and pressure drop among various configurations with changes in b at N ¼ 125 as illustrates in Figs. 4e7. 4.2. Effect of inlet velocity Fig. 4 presents the dependence of pumping power, thermal resistance and pressure drop on channel width ratio and inlet velocity. Higher pumping power as a penalty of high inlet velocity occurs at u ¼ 3 and 4 m/s and significantly falls as hydraulic diameter increases, as Fig. 4(a) shows. This is due to the gradual decrement in pressure drop with increasing b. As expected, the outlet temperature of heat sink goes down with increasing of Reynolds number, which is due to the increase of inlet velocity, as Fig. 4(b) shows. The temperature drop declines with higher Reynolds number because larger amount of working fluid is capable of carrying out the same portion of heat flux. The lowest thermal resistance is found at b ¼ 0.8 for low velocity (u ¼ 1 m/s), b ¼ 0.6 for channels with high velocity (u ¼ 3 and 4 m/s) and for moderate velocity at b ¼ 0.7 (u ¼ 2 m/s). It is apparent from Fig. 4(c) that pressure drop increases noticeably with increasing inlet velocity and decreases with increasing hydraulic diameter. In all cases pressure drop declines roughly by 4 times from b ¼ 0.4 to b ¼ 0.9. The same pressure drop trend for various Reynolds number was given in experimental work [52]. The lowest thermal resistance occurs at b ¼ 0.7, which is around the average value of pumping power. 4.3. Effect of inlet temperature Fig. 5 presents the dependence of pumping power, thermal resistance and pressure drop on channel width ratio and inlet temperature. As the pumping power is a function of pressure drop, it shows similar decreasing tendency, as Fig. 5(a) shows. By comparison, the thermal resistance only slightly decreases with temperature increasing, as Fig. 5(b) shows. The reason is that the specific heat and thermal conductivity show weakly positive temperature-dependence. Hence, the optimal channel width ratio is 0.7 and independent of inlet temperature of working fluid. From

A. Sakanova et al. / Applied Thermal Engineering 65 (2014) 124e134

0.4 0.3 0.2

N = 150 N = 125 N = 100

0.28

0.1

0.24

N = 75 N = 50

0.20

0.16

200

0.5

0.6

0.7

0.8

Channel width ratio

0.9

100 50 0

0.4

0.5

0.6

0.7

Channel width ratio

(a)

0.8

N = 75 N = 50

150

0.12

0.4

N = 150 N = 125 N = 100

250

Pressure drop (kPa)

Pumping power (W)

0.5

N = 75 N = 50

Thermal resistance (K/W)

N = 150 N = 125 N = 100

0.6

129

0.9

0.4

(b)

0.5 0.6 0.7 0.8 Channel width ratio

0.9

(a)

Fig. 3. Pumping power (a), thermal resistance (b) and pressure drop (c) dependence on channel width ratio for various channel numbers.

1.0

0.5

0.0

0.4

0.5

0.6

0.7

0.8

u = 1m/s u = 2m/s u = 3m/s u = 4m/s

0.24

0.20

u = 1m/s u = 2m/s u = 3m/s u = 4m/s

400

Pressure drop (kPa)

Pumping power (W)

1.5

Thermal resistance (K/W)

u = 1 m/s u = 2 m/s u = 3 m/s u = 4 m/s

2.0

0.16

300 200 100

0.12

0.9

0.4

Channel width ratio

0.5

0.6

0.7

0.8

0

0.9

0.4

0.5

0.7

0.8

0.9

(c)

(b)

(a)

0.6

Channel width ratio

Channel width ratio

Fig. 4. Pumping power (a), thermal resistance (b) and pressure drop (c) at different inlet velocity.

Thermal resistance (K/W)

Pumping power (W)

0.40 0.35 0.30 0.25 0.20 0.15 0.4

0.5

0.6

0.7

0.8

T = 297 K T = 307 K T = 317 K T = 327 K

0.160 0.155 0.150 0.145 0.140

120

80

40

0.135 0.4

0.9

T = 297 K T = 317 K T = 307 K T = 317 K

160

Pressure drop (kPa)

T = 297 K T = 307 K T = 317 K T = 327 K

0.45

0.5

Channel width ratio

0.6

0.7

0.8

0.9

0.4

Channel width ratio

(a)

0.5

(b)

0.6

0.7

0.8

Channel width ratio

0.9

(c)

Fig. 5. Pumping power (a), thermal resistance (b) and pressure drop (c) at different inlet temperature.

0.40

Thermal resistance (K/W)

Pumping power (W)

0.45

0.35 0.30 0.25 0.20

0.4

0.5

0.6

0.7

Channel width ratio

(a)

0.8

q = 100W/cm q = 200W/cm q = 300W/cm q = 400W/cm

0.155

0.9

0.150

q = 100W/cm q = 200W/cm q = 300W/cm q = 400W/cm

200

Pressure drop (kPa)

q = 100W/cm q = 200W/cm q = 300W/cm q = 400W/cm

0.50

0.145 0.140 0.135

160 120 80 40

0.4

0.5

0.6

0.7

Channel width ratio

(b)

0.8

0.9

0.4

0.5

0.6

0.7

Channel width ratio

(c)

Fig. 6. Pumping power (a), thermal resistance (b) and pressure drop (c) at different heat flux.

0.8

0.9

A. Sakanova et al. / Applied Thermal Engineering 65 (2014) 124e134

0.25

N = 150 N = 125 N = 100

N = 75 N = 50

N = 150 N = 125 N = 100

Pressure drop (kPa)

Thermal resistance (K/W)

130

0.20

0.15

0.4

0.5

0.6

0.7

0.8

0.9

N = 75 N = 50

200

100

0

0.4

0.5

0.6

0.7

0.8

0.9

Channel width ratio

Channel width ratio

(b)

(a)

Fig. 7. Comparison of analytical modeling (lines) and CFD simulation (dots) results of thermal resistance (a) and pressure drop (b).

(a)

(b)

(c)

Fig. 8. Cross sections of DL, sandwich and SL MCHS structures. The computational domain is shown inside the dashed lines.

Fig. 5(a) it can be seen that rise of inlet temperature benefits to pressure drop, since the fluid viscosity decreases with temperature increasing which will reduce the friction. And for wide channel, the decreasing tendency of pressure drop is more remarkable. Again, the mean of pumping power for all different b is a value for the lowest thermal resistance.

5.3% and 13.2% for thermal resistance and pressure drop accordingly. It can be concluded that current correlations cannot predict the heat transfer characteristics at high Reynolds number very well, especially for the thermal resistance.

4.4. Effect of heat flux

As Fig. 8(a) shows, DL structure contains two stacking layers of micro-channel. The thickness of Cu-layer between the two microchannel layers shows no much influence on the cooling performance, hence 50 mm thickness is adopted in present work. The power module consisting of multiple power semiconductor devices is soldered to the DBC substrate by 95.5Sne3.8Age0.7Cu with a thickness of 50 mm. In a case if 100 mm thickness chosen it contributes less than 3.7% to the total resistance. Wirebonding technology is in need on top pads for interconnection. While for the sandwich structure, the power module is sandwiched by two DBC substrates to achieve double-side cooling and planar packaging, as Fig. 8(b) shows. The circuit diagram can be patterned on the two DBC substrates and it is possible to eliminate the fragile wirebonding interconnection. For comparison, the SL structure is also investigated in present work, as Fig. 8(c) shows. The thermal conductivity and thickness of packaging materials are given by Table 2. Fluid directions of the two micro-channel layers in DL and sandwich structure can either be the same or opposite. One problem led by the unidirectional flow is the non-uniform temperature distribution due to temperature rise between inlet and outlet. As the electrical properties of semiconductor devices are temperaturesensitive, non-uniform temperature distribution will affect the operating condition. With counter flow, the uniformity of temperature distribution inside the packaging can be expected to improve. Based on the optimized geometry and boundary conditions from the last section, the xey plane temperature distribution of DL,

Fig. 6 presents the dependence of pumping power, thermal resistance and pressure drop on channel width ratio and heat flux. Compared with the effect of inlet temperature aforementioned, similar tendencies for pressure drop and thermal resistance are observed. From the simulation results above, it can be concluded that the optimal geometry is almost independence on the inlet velocity, inlet temperature and heat flux. In addition, even though the channel depth is fixed during geometry optimization, it should be kept clear that deep channel is always beneficial for high heat transfer performance. Nevertheless, the heat transfer efficiency does not improve significantly after the channel depth increases beyond 300 mm. Therefore, the commercial DBC of 300 mm Cue 635 mm AlNe300 mm Cu enables to provide good electrical interconnection, high voltage isolation and operate at a wide range of temperature with high cooling efficiency. Comparison between CFD simulation results and analytical modeling results is given by Fig. 7. For low Reynolds number between 100 and 300, the analytical results of thermal resistance coincide well with that of simulation results. However, for high Reynolds number above 300, the discrepancy is noticeably apparent. The pressure drop discrepancy increases as channel width ratio increases. And the discrepancy slightly increases for high Reynolds number. The discrepancy for the optimal geometry is

4.5. Comparison of double-layer and double-side MCHS

A. Sakanova et al. / Applied Thermal Engineering 65 (2014) 124e134 Table 2 Thermal conductivity and thickness of packaging materials.

Table 3 Simulation results.

Materials

Thermal conductivity (K/W m)

Thickness (mm)

Si 95.5Sne3.8Age0.7Cu Cu AlN

148 57.7 387.6 170

400 50 300 635

sandwich and SL structures are obtained from ANSYS Fluent, as Fig. 9 shows. Compared with the conventional SL structure, the DL structure with unidirectional flow only shows a reduction of 15% in thermal resistance with introduction of one more micro-channel layer. In addition, for DL structure with counter flow, the temperature distribution is not as uniform as expected, since the top micro-channel layer removes more heat than the bottom layer. Similar to the experimental result from Ref. [31], the thermal resistance of counter flow is higher than that of unidirectional flow. For sandwich structure with counter flow, it shows a 15% decrease in thermal resistance compared with that of unidirectional flow, due to the larger heat convection coefficient. It allows the largest decrease of 59% in thermal resistance compared with SL structure. The temperature distribution inside the packaging is almost ideally uniform. In actual situation, as the top and bottom pad sizes of power semiconductor devices are different, the heat transfer is not strictly symmetrical. The detailed simulation results of pressure drop, maximum temperature, thermal resistance and pumping power are given by Table 3. The location of xey plan showing in Fig. 9 below can be found in Fig. 1.

To further enhance the thermal performance of MCHS, the nanofluid is introduced in the working fluid. In this work the most widely used Al2O3ewater nanofluids with 1% and 5% of nanoparticle volume fractions are adopted, with the thermo-physical properties given by Table 4. The temperature-dependent thermal properties of liquid water are replaced by that of nanofluid, which are also temperaturedependent. The density and specific heat are given by

rnf ¼ ð1  4Þrf þ 4rp 4rp cpp þ ð1  4Þrf cpf

rnf

Structure DL (unidirectional) DL (counter) Sandwich (unidirectional) Sandwich (counter) SL

DPtop

DPbot

(kPa)

(kPa)

Tmax (K)

Rth (K/W)

Ppump (W)

77.8 76 76.6

74.5 72.9 76.6

323 324 312

0.132 0.136 0.075

0.64 0.63 0.64

76.2

76.2

310

0.064

0.64

69.9

\

328

0.156

0.29

Lots of work has presented various correlations for dynamic viscosity as well as the thermal conductivity. In this work the experiment-based model by Maiga et al. [53] for dynamic viscosity is used

mnf ¼ 12342 þ 7:34 þ 1 mf ðTÞ

(34)

where mf is base fluid viscosity and can be defined by

mf ðTÞ ¼ 2:414  105  10T140 247:8

(35)

The thermal conductivity of nanofluid is given by the correlation of Xuan and Roetzel [54]

knf ¼ ko þ C * rnf cp;nf 4ðHc =2Þu

(36)

where C* is an empirical constant of Al2O3 and ko is the stagnant effective thermal conductivity of nanofluid, which is defined from Xie et al. [55] as

4.6. Enhanced cooling with nanofluid

cp;nf ¼

131

ko ¼

1 þ 3q4T þ

! 2 3q 42T k 1  q4T f

(37)

with the parameters given by the following expressions

h

q ¼

b1f ð1 þ gÞ3  bp1 =bf1 ð1 þ gÞ3 þ 2b1f bp1

i (38)

(32) (33)

4T ¼ 4ð1 þ gÞ3

(39)

g ¼ d=dp

(40)

where 4 is the volumetric concentration of nanoparticles.

Fig. 9. Temperature distribution of DL structure with unidirectional flow (a), DL structure with counter flow (b), sandwich structure with unidirectional flow (c), sandwich structure with counter flow (d), SL structure (e). Flow direction is shown by the arrow.

132

A. Sakanova et al. / Applied Thermal Engineering 65 (2014) 124e134 Table 4 Thermo-physical properties of Al2O3 (particle size d ¼ 38 nm).

b1f

Property

Value

k M2

f k1 ¼ M  d=dp lnð1 þ MÞ þ Md=dp

Density (kg/m3) Thermal conductivity (W/m K) Specific heat capacity (J/kg K)

3970 36 765



M ¼ kp =kf 1 þ d=dp  1

k  kf ¼ 1 k1 þ 2kf

(42)

bf 1 ¼

kf  k1 kf þ 2k1

(43)

Pumping power (W)

0.6

N = 75 N = 50

0.5 0.4 0.3 0.2

N = 150 N = 75

0.24

N = 125 N = 50

N = 100

250

0.4

0.5

0.6

0.7

Channel width ratio

0.8

N = 75 N = 50

200

0.20

150

0.16

100

0.12

0.1

N = 150 N = 125 N = 100

300

Pressure drop (kPa)

N = 150 N = 125 N = 100

0.7

Thermal resistance (K/W)

kp  k1 kp þ 2k1

(45)

where 4T is the particle volume fraction, d is the thickness of the interfacial layer and dp is the particle diameter. Geometry optimization of Section 4.1 is conducted again with the working fluid water replaced by nanofluid. From Fig. 10, the optimal geometry of Al2O3 (1%)-water nanofluid coincides well with that of water. In addition, it brings benefit in thermal resistance while penalty in pressure drop and pumping power. The increment in pressure drop for large channel number is 11.2% while for small channel number is 8.3%. However, the thermal resistance decrement is more perceptible for large channel number. For instance, the decrement for N ¼ 50 is half than N ¼ 125. Whereas

(41)

bp1 ¼

(44)

0.4

0.9

0.5

0.6

0.7

0.8

50 0

0.9

Channel width ratio

0.4

0.5

0.6

0.8

0.9

(c)

(b)

(a)

0.7

Channel width ratio

Fig. 10. Pumping power (a), thermal resistance (b) and pressure drop (c) dependence on channel width ratio for various channel numbers using water (lines) and Al2O3(1%)ewater (dash line) as the coolants.

Therm al resistance (K /W )

R

th

0.25

R

0.20

R

R R 0.15 0.10 0.05

0.4

0.5

(b)

(a)

0.6

0.7

0.8

0.9

Channel width ratio

(c)

Fig. 11. Components of total thermal resistance for various number of channels using water (lines), Al2O3(1%)ewater (dash line) and Al2O3(5%)ewater (dot-dash line) when channel number is 150 (a), 125 (b) and 50 (c).

310

324

309

322

Pure water Nanofluid 1% Nanofluid 5%

0.12

Friction factor

emperature (K)

326

Temperature (K)

Pure water Nanofluid 1% Nanofluid 5%

311

328

0.08

0.04

320

308 318 0

0.2

0.4

0.6

Distance (cm)

(a)

0.8

1

0

0.2

0.4

0.6

Distance (cm)

(b)

0.8

1

0

0.2

0.4

0.6

0.8

1

Distance (cm)

(c)

Fig. 12. Temperature distribution along the chip for SL structure with pure water (a) sandwich structure (b) and friction factor distribution along the length of the channel for sandwich structure with counter flow (c).

A. Sakanova et al. / Applied Thermal Engineering 65 (2014) 124e134

133

Fig. 13. Temperature distribution of sandwich structure with counter flow for Al2O3 (1%)ewater nanofluid (a) and Al2O3 (5%)ewater nanofluid). Flow direction is shown by the arrow.

for N ¼ 150, the thermal resistance is just slightly lower than that of water coolant at low channel aspect ratio. It reduces more remarkably as channel aspect ratio increases. Same results are obtained in Ref. [56]. The details of the three thermal resistance components are shown in Fig. 11 for better comprehension of the impact of nanofluid. For large channel number (N ¼ 125 and 150), Rcap is the dominant factor which decreases as channel width ratio increases and the same trend is observed for the total thermal resistance. The decrease of Rconv is more remarkable compared with the increase of Rcap in the case when Al2O3 (1%)ewater is used as the coolant, which leads to reduction of total thermal resistance. For N ¼ 125, the total thermal resistance decreases until b ¼ 0.87 where Rconv becomes the dominant factor, as Fig. 11(b) shows. For small channel number (N ¼ 50), Rconv almost play as the dominant factor in the whole domain due to wider channels and smaller effective area of heat convection, as Fig. 11(c) shows. Compared with the pure water, Rcap increases very slightly when nanofluid is employed. However, Rconv is reduced more significantly with nanofluid, especially for wide channels. The enhancement in heat removal performance is owing to the decrease of Rconv is more remarkable compared with the increase in Rcap. Hence it is concluded that introduction of nanofluid shows more remarkable improvement for wide channel. The temperature distribution along the chip for SL structure is depicted on Fig. 12(a). The temperature increase between the inlet and outlet can be clearly observed. The temperature distribution along the chip and streamwise friction factor for sandwich structure with employment of nanofluid is given by Fig. 12(bec). For laminar flow the heat transfer coefficient increases proportionally to thermal conductivity which depends on the nanoparticle concentration in base fluid. However, the enlargement in a nanoparticle volume fraction enhances the viscosity and degrades specific heat. Friction factor decreases along the channel owing to the reduction of pressure drop. It gets the maximum value at entrance, and reaches minimum at the outlet. The presence of Al2O3 (1%)ewater nanofluid provides a slight increase in friction factor, whereas Al2O3 (5%)ewater nanofluid increases friction factor considerably. The xey plane temperature distribution of sandwich structure with Al2O3 (1%)ewater and Al2O3 (5%)ewater nanofluid are shown by Fig. 13. The results indicate that the cooling performance is enhanced by about 10.6% for 1% nanoparticle volume fraction and about 17.3% for 5% nanoparticle volume fraction. This improvement depends on nanofluid thermal conductivity, which is dependent on nanoparticle concentration. The increase in pressure drop is by 70% and 9% for 5% and 1% of particle volume fraction accordingly. The results show that nanofluid provides a higher pressure drop in comparison with water due to the rise in nanofluid viscosity and it more increases at higher Reynolds number and volume concentration of nanofluid. The Equation (34) shows that viscosity is directly-proportional to the volume concentration of nanofluid. The increase in viscosity for Al2O3 (1%)ewater nanofluid is 8.5% and for Al2O3 (5%)ewater nanofluid is 67.3% compare with pure water as a coolant.

5. Conclusions This study numerically optimizes the geometry for Cu-based MCHS integrated with DBC. Thermal resistance at constant channel depth is sensitive to such parameters as the channel number, channel width ratio. The larger quantity of channels the lower thermal resistance is. At a fixed channel number, thermal resistance with increasing the channel width firstly decreases up to optimal value and then increases. The optimal geometry has been found at N ¼ 125, b ¼ 0.7. The selected configuration has been proved by varying the inlet velocity, inlet temperature and heat flux. With the objective to improve heat transfer performance different models has been designed and 3D conjugate heat transfer analysis is performed by CFD. Compared with the conventional SL structure, the DL and sandwich structures show reduction in thermal resistance by 15% and 59% respectively. Temperature distribution for the sandwich structure is almost ideally uniform. The sandwich structure shows best performances in heat removal, uniformity of temperature distribution and reliability. Al2O3 (1% and 5%)ewater based nanofluid is used as a coolant to obtain better heat transfer performance. The results indicate the nanofluids at a higher concentration yield a better cooling performance by about 17.3% at 5% concentration while 10.6% at 1% concentration. However, if smaller channel number is chosen, the greater the thermal resistance decrement will be. References [1] L. Boteler, D. Urciuoli, G. Ovrebo, D. Ibitayo, R. Green, Thermal performance of a dual 1.2 kV, 400 A silicon-carbide MOSFET power module, in: Proc. IEEE Semicond. Therm. Measurement and Management Symp, 2010, pp. 170e175. [2] T.J. Martens, G.F. Nellis, J.M. Pfotenhauer, T.M. Jahns, Double-sided IPEM cooling using miniature heat pipes, IEEE Trans. Compon. Packag. Technol. 28 (2005) 852e861. [3] C.M. Johnson, C. Buttay, S.J. Rashidt, F. Udrea, G.A.J. Amaratunga, P. Ireland, R.K. Malhan, Compact double-side liquid-impingement-cooled integrated power electronic module, in: Proc. IEEE Int. Symp. Power Semicond. Devices and IC’s, 2007, pp. 53e56. [4] D.B. Tuckerman, R.F. Pease, High performance heat sinking for VLAI, IEEE Electron. Devices Lett. EDL-2 (1981) 126e129. [5] S.A. Solovitz, L.D. Stevanovic, R.A. Beaupre, Micro-channel thermal management of high power devices, in: Proc. Annu. IEEE Appl. Power Electron. Conf. Expo, 2006, pp. 885e891. [6] L.D. Stevanovic, R.A. Beaupre, A.V. Gowda, A.G. Pautsch, S.A. Solovitz, Integral micro-channel liquid cooling for power electronics, in: Proc. Annu. IEEE Appl. Power Electron. Conf. Expo, 2010, pp. 1591e1597. [7] S. Yin, K.J. Tseng, J. Zhao, Thermal-mechanical design of sandwich SiC power module with micro-channel cooling, in: Proc. IEEE Int. Conf. Power Electron. Drive Syst, 2013, pp. 535e540. [8] N.R. Jankowski, L. Everhart, B. Morgan, B. Geil, P. McCluskey, Comparing microchannel technologies to minimize the Thermal stack and improve Thermal performance in hybrid electric vehicles, in: Proc. IEEE Vehicle Power Propulsion Conf, 2007, pp. 124e130. [9] D.J. Sharar, N.R. Jankowski, B. Morgan, Thermal performance of a direct-bondcopper aluminum nitride manifold-microchannel cooler, in: Proc. IEEE Intersoc. Conf. Therm. Thermomech. Phenom. Electron. Syst, 2010, pp. 68e73. [10] S. Yin, K.J. Tseng, J. Zhao, Design of AlN-based micro-channel heat sink in direct bond copper for power electronics packaging, Appl. Therm. Eng. 52 (2013) 120e129. [11] L.T. Hwang, I. Turlik, A. Reisman, A thermal module design for advancing packaging, J. Electr. Mater. 16 (1987) 347e355. [12] R.W. Knight, J.S. Goodling, D.J. Hall, Optimal thermal design of forced convection heat sinks e analytical, J. Electron. Packag. 113 (1991) 313e321.

134

A. Sakanova et al. / Applied Thermal Engineering 65 (2014) 124e134

[13] A. Weisberg, H.H. Bau, J.N. Zemel, Analysis of micro channels for integrated cooling, Int. J. Heat. Mass Transf. 35 (1992) 2465e2474. [14] C.W. Chen, J.J. lee, H.S. Kou, Optimal thermal design of microchannel heat sinks by the simulated annealing method, Int. Commun. Heat. Mass Transf. 35 (2008) 980e984. [15] P. Lee, S.V. Garimella, Thermally developing flow and heat transfer in rectangular microchannels of different aspect ratios, Int. J. Heat. Mass Transf. 49 (2006) 3060e3067. [16] R. Chein, J. Chen, Numerical study of the inlet/outlet arrangement effect of micro-channel heat sink performance, Int. J. Therm. Sci. 48 (2009) 1627e 1638. [17] P. Gunnasegaran, H.A. Mohammed, N.H. Shuaib, R. Saidur, The effect of geometrical parameters on heat transfer characteristics of microchannels heat sink with different shapes, Int. Commun. Heat. Mass Transf. 37 (2010) 1078e 1086. [18] S.J. Kim, Method for thermal optimization of microchannel heat sinks, Heat. Transf. Eng. 25 (2004) 37e49. [19] A. Husain, K.-Y. Kim, Optimization of a microchannel heat sink with temperature dependent fluid properties, Appl. Therm. Eng. 28 (2008) 1101e1107. [20] K.K. Ambatipudi, M.M. Rahman, Analysis of conjugate heat transfer in microchannel sinks, Numer. Heat. Transf. 37 (2000) 711e731. [21] T.M. Harms, Heat Transfer and Fluid Flow in Deep Rectangular Liquid-cooled Microchannels Etched in a (110) Silicon Substrate, Master’s thesis, University of Cincinnati, Cincinnati, OH, 1997. } lke, H.T. Henderson, [22] T.M. Harms, M. Kazmierszak, F.M. Gerner, A. Ho J. Pilchowcki, K. Baker, Experimental investigation of heat transfer and pressure drop through deep microchannels in a (110) silicon substrate, Proc. AME Heat Transf. Div. 1 ASME/HTD 351 (1997) 347e357. [23] J. Li, G.P. Peterson, 3-dimensional numerical optimization of silicon-base high performance parallel microchannel heat sink with liquid flow, Int. J. Heat. Mass Transf. 50 (2007) 2895e2904. [24] H. Herwig, S.P. Mahulikar, Variable property effects in single-phase incompressible flow through microchannels, Int. J. Therm. Sci. 45 (2006) 977e981. [25] Z. Li, X. Huai, Y. Tao, H. Chen, Effects of thermal property variations on the liquid flow and heat transfer in microchannel heat sinks, Appl. Therm. Eng. 27 (2007) 2803e2814. [26] W. Qu, I. Mudawar, Analysis of three-dimensional heat transfer in microchannel heat sinks, Int. J. Heat. Mass Transf. 45 (2002) 3973e3985. [27] P.-S. Lee, S.V. Garimella, D. Liu, Investigation of heat transfer in rectangular microchannels, Int. J. Heat. Transf. 48 (2005) 1688e1704. [28] C.P. Tso, S.P. Mahulikar, The use of the Brinkman number for the single phase forced convective heat transfer in microchannels, Int. J. Heat. Mass Transf. 41 (1998) 1759e1769. [29] G.L. Morini, M. Spiga, The role of the viscous dissipation in heated microchannels, J. Heat Transf. 129 (2007) 308e318. [30] K. Vafai, L. Zhu, Analysis of two-layered micro-channel heat sink concept in electronic cooling, Int. J. Heat. Mass Transf. 42 (1999) 1176e1186. [31] X. Wei, Y. Joshi, M.K. Peterson, Experimental and numerical study of a stacked microchannels heat sink for liquid cooling of microelectronic devices, J. Heat. Transf. 129 (2007) 1432e1444. [32] T.C. Hung, W.M. Yan, W.P. Li, Analysis of heat transfer characteristics of double-layered microchannel heat sink, Int. J. Heat. Mass Transf. 55 (2012) 3090e3099. [33] C. Gillot, C. Schaeffer, C. Massit, L. Meysenc, Double-sided cooling for high power IGBT modules using flip chip technology, IEEE Trans. Compon. Packag. Technol. 24 (2001) 698e704.

[34] S. Kicin, M. Laitinen, C. Haederli, J. Sikanen, R. Grinberg, C. Liu, J.-H. Fabrian, A. Hamidi, Low-voltage AC drive based on double-sided cooled IGBT presspack modules, IEEE Trans. Industry Appl. 48 (2012) 2140e2147. [35] P. Ning, Z. Liang, F. Wang, Double-sided cooling design for novel planar module, in: 28th Annual IEEE Applied Power Electronics Conference and Exposition, APEC, 2013, pp. 616e621. [36] S. Zhao, J.K.O. Sin, Double-side packaged, High power IGBTs for improved thermal and switching characteristics, in: The 12th International Symposium on Power Semiconductor Devices and IC’s, 2000, pp. 229e232. [37] S.U.S. Choi, Enhancing thermal conductivity of fluids with nanoparticles, ASME Fluids Eng. Div. 231 (1995) 99e103. [38] C.J. Ho, L.C. Wei, Z.W. Li, An experimental investigation of forced convective cooling performance of a microchannel heat sink with Al2O3/water nanofluid, Appl. Therm. Eng. 30 (2010) 96e103. [39] R. Chein, G. Huang, Analysis of microchannel heat sink performance using nanofluids, Appl. Therm. Eng. 25 (2005) 3104e3114. [40] T.H. Tsai, R. Chein, Performance analysis of nanofluid-cooled microchannel heat sinks, Int. J. Heat. Fluid Flow. 28 (2007) 1013e1026. [41] T.C. Hung, W.M. Yan, Enhancement of thermal performance in double-layered microchannel heat sink with nanofluids, Int. J. Heat. Mass Transf. 55 (2012) 3225e3238. [42] S.C. McCutcheon, J.L. Martin, T.O. Barnwell Jr., Handbook of Hydrology, McGraw-Hill, New York, 1993. [43] F.C. Sherman, Viscous Flow, McGraw-Hill, New York, 1990. [44] T.L. Bergman, A.S. Lavine, F.P. Incropera, D.P. Dewitt, Fundamentals of Heat and Mass Transfer, seventh ed., John Willey & Sons, 2011. [45] G.L. Morini, Scaling effects for liquid flows in microchannels, Heat. Transf. Eng. 27 (4) (2006) 64e73. [46] G. Maranzana, I. Perry, D. Maillet, Mini- and micro-channels: influence of axial conduction in the walls, Int. J. Heat. Mass Transf. 47 (2004) 3993e4004. [47] R.K. Shah, A.L. London, Laminar Flow Forced Convection in Ducts, Academic Press, New York, 1978. [48] W.M. Rohsenow, J.P. Hartnett, E.N. Ganic, Handbook of Heat Transfer Applications, McGraw-Hill, New York, 1985. [49] P.S. Lee, S.V. Garimella, D. Liu, Investigation of heat transfer in rectangular microchannels, Int. J. Heat. Mass Transf. 48 (2005) 1688e1704. [50] J. Li, G.P. Peterson, P. Cheng, Three-dimensional analysis of heat transfer in a micro-heat sink with single phase flow, Int. J. Heat. Mass Transf. 47 (2004) 4215e4231. [51] J. Li, G.P. Peterson, Geometric optimization of a micro heat sink with liquid flow, IEEE Trans. Compon. Packag. Technol. 29 (2006) 145e154. [52] W. Qu, I. Mudawar, Experimental and numerical study of pressure drop heat transfer in a single-phase microchannel heat sink, Int. J. Heat. Mass Transf. 45 (2002) 2549e2565. [53] S.E.B. Maiga, C.T. Nquen, N. Galanis, G. Roy, Heat transfer behavior of nanofluids in a uniformly heated tube, Superlatt. Microstruct. 35 (2004) 543e557. [54] Y. Xuan, W. Roetzel, Conceptions for heat transfer correlation of nanofluids, Int. J. Heat. Mass Transf. 43 (2000) 3701e3707. [55] H. Xie, M. Fujii, X. Zhang, Effect of interfacial nano-layer in the effective thermal conductivity of nano-particle fluid mixture, Int. J. Heat. Mass Transf. 48 (2005) 2926e2932. [56] 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) 87e94.