Effects of channel shape on the cooling performance of hybrid micro-channel and slot-jet module

International Journal of Heat and Mass Transfer 113 (2017) 295–309

Contents lists available at ScienceDirect

International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt

Effects of channel shape on the cooling performance of hybrid micro-channel and slot-jet module Yanjun Zhang, Shuangfeng Wang ⇑, Puxian Ding Key Laboratory of Enhanced Heat Transfer and Energy Conservation of the Ministry of Education, School of Chemistry and Chemical Engineering, South China University of Technology, Guangzhou 510640, Guangdong, China

a r t i c l e

i n f o

Article history: Received 26 February 2017 Received in revised form 17 May 2017 Accepted 24 May 2017 Available online xxxx Keywords: Hybrid micro-channel Slot-jet module Cross-section shape Cooling performance Parameters optimization

a b s t r a c t This paper investigates the effect of channel shape on the micro-channel and slot-jet module with the realizable k-e turbulent model. Cooling performance of three channels with a same cross-section area but different shapes (rectangular, trapezoid and circular) are comparatively discussed. The hybrid module with circular channel has the maximum pressure drop at the same flow rate. While the hybrid module with trapezoid channel achieves the best cooling performance. Its superiority in the cooling performance enlarges with the heat flux rising and the pump power increasing, as compared with the other two hybrid modules. The local thermal resistance in the trapezoid channel exhibits peak-shape distribution, which is very different from the other two shapes channel. In addition, the cooling performance of the trapezoid channel module can be further improved by the optimization of the three geometric parameters (channel height, channel bottom width, and channel corner angle). When the optimal value for the three parameters is respectively adopted, the temperature on the bottom surface of the module can be reduced by 12.22%, 14.85% and 7.15% as compared with the worst design, and the temperature difference can also be reduced by 63.60%, 74.86% and 57.16%. What’s more, the influence level of these parameters is also compared. Before the reference value, the channel height has the greatest influence on the module bottom surface temperature, whereas after the reference value, the corner angle becomes the largest influence factor. As for the temperature difference on the module bottom surface, it is just opposite. Ó 2017 Elsevier Ltd. All rights reserved.

1. Introduction During the past few decades, a rapid advance has been made in the packed electronic devices, solar photovoltaic concentrators, laser diode arrays and other high heat production fields, where a more efficient thermal management system is urgently needed. Micro-channel flow and jet impingement are two traditional strategies employed to dissipate the high heat flux [1]. While, deficiencies still remain in them [2]. High pressure drop and poor temperature uniformity exist in the micro-channel chips. As for the jet impingement, there is a big temperature difference on the cooled surface and an abrupt reduction of the heat transfer coefficient away from the impingement region [3]. Arrays of the jets can be used to decrease the temperature difference, but local heat transfer coefficient will be reduced by the interaction between adjacent jets. Hybrid micro-channel and slot jet is one of the most efficient cooling module, which have the advantage of the micro-channel flow and jet impingement simultaneously. It not only provides a ⇑ Corresponding author. E-mail address: [email protected] (S. Wang). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2017.05.092 0017-9310/Ó 2017 Elsevier Ltd. All rights reserved.

very high heat removal capability, but also maintains a high degree of temperature uniformity on the cooling surface [4]. Lelea [5] numerically investigated the micro-tube heat sink with tangential impingement jet and variable fluid properties. He found that the jet impingement heat sink reached both lower peak temperature and lower temperature difference compared with classical micro-tube heat sink. The fluid viscosity was also found has a great influence on the temperature and velocity field of the heat sink. Barrau et al. [2,6] experimentally and numerically studied on a new hybrid jet impingement/micro-channel cooling scheme. It was shown that the hybrid scheme exhibited excellent cooling performance. Yang et al. [7–9] experimentally and numerically studied the unsteady heat transfer and fluid flow in cylindrical channel with a single row of 10 aligned impinging jets. They found that the flow unsteadiness increased as cross-flows accumulated within the impingement channel. Kayansayan and Kucuka [10] investigated the impingement cooling of a semi-cylindrical concave channel. Heat transfer rate at the impingement surface of the concave channel was found higher than that of the flat channel, because of the effect of the channel curvature. Liu and Feng [11] numerically researched the effect of jet nozzle position on the impinge-

296

Y. Zhang et al. / International Journal of Heat and Mass Transfer 113 (2017) 295–309

Nomenclature ui

q p

l

kf cp

lt rk

ks Tf Ts Tb

DT Q P

fluid velocity, coolant density coolant pressure dynamic viscosity of the coolant thermal conductivity of the coolant specific heat of the coolant turbulent viscosity the turbulent Prandtl number for k solid thermal conductivity coolant temperature wall temperature average temperature of the hybrid module bottom surface temperature difference on the module bottom surface flow rate of the water pump power

ment cooling of gas turbine blade leading edge. They concluded that the side entry jet was desirable to improve the cooling performance of the impingement. Barik et al. [12] explored the heat transfer enhancement using different surface protrusions in the rectangular channel. The heat transfer enhancement rate with triangular protrusions was found to be higher compared to rectangular and trapezoidal protrusions. Husain et al. [13] numerically explored a novel hybrid design with pillars inserted into the rectangular micro-channel. They found pillars in the channel would contribute to a heat transfer rate enhancement. Besides, a kind of manifold micro-channel heat sink was also investigated having favorable capacity to improve the temperature uniformity of the cooled object [14,15]. Sung and Mudawar [4,16–19] experimentally and numerically conducted a series of exploration on the cooling performance of hybrid micro-channel and slot jet module. The rectangular shape micro-channel was used in the hybrid module and the standard k-e model was employed to analyze the fluid flow and heat transfer characteristics of their hybrid scheme. Sung and Mudawar also analyzed the effects of jet pattern on single-phase [20] and two-phase [21] cooling performance of hybrid microchannel. It was shown that the decreasing-jet-size pattern achieved the lowest bottom wall temperatures but the equal-jetsize pattern provided the smallest gradients in bottom wall temperature in the condition of single phase. But the pressure drop in the two-phase region was highest for equal-jet-size pattern followed by the decreasing-jet-size and increasing-jet-size patterns, respectively. However, there are few studies which sufficiently compare the cooling performance of the hybrid micro-channel and slot jet modules with different channel shapes. In this work, a threedimensional numerical model based on the realizable k-e turbulent model is developed to research the fluid flow and the heat transfer characteristics of the hybrid module. The pressure drops and the cooling performances of three kinds of hybrid module with different cross-section shape of channels (rectangular, trapezoid and circular) are comparatively analyzed. Subsequently, three geometric parameters of trapezoid channel including channel height, channel bottom width, and channel corner angle are analyzed to search for the optimal design of the hybrid module. 2. Geometry of the hybrid micro-channel and slot-jet modules with different channels The schematics of the hybrid micro-channel and slot-jet modules with different channels are depicted in Fig. 1. The unit cells

u, v, w Vn

velocity component in the direction of coordinate axis velocity component perpendicular to the solid-fluid interface Ljet length of the jet slot Wjet width of the jet slot Hch channel height channel bottom width Wb Ajet cross-sectional area of the slot-jet a channel corner angle b, w non-dimensional geometric parameters Topt, DTopt temperature and temperature difference at optimal point h local heat transfer coefficient Rcon convection thermal resistance q heat flux

consisting of one slot jet and single micro-channel for each kind of modules are illustrated in Fig. 2. They have an equal channel cross-section area, a same channel length, and a same jet orifice area as well. The fluid from the slot jet strikes at the heated bottom surface and runs rapidly outwards. The geometric parameters of each unit cell are listed in Table 1. It can also be noticed that the micro-channel is thermally and hydro-dynamically symmetrical with respect to the boundary conditions. Thus, only a quarter of unit cell is analyzed, as shown in Fig. 3(1). 3. Mathematical model 3.1. Governing equations Numerical computations were accomplished using the Fluent 6.3 CFD commercial software. The realizable k-e turbulent model [22], which has been proven to be accurate enough in predicting turbulent flow including strong streamline curvature and vortices, was employed to predict the fluid flow and heat transfer characteristics of the present hybrid scheme. The following conditions were assumed for solving the governing equations: (1) steady state, (2) single phase and turbulent flow. The governing equations are written in Cartesian tensor notation as follows. For the fluid region: Continuity equation:

@ qui ¼0 @xi

ð1Þ

where ui is the coolant velocity. Momentum equation:

uj


 @ qui @p @ @ui ¼ þ ð l þ lt Þ @xi @xj @xj @xj

ð2Þ

where q is the coolant density, p is the coolant pressure, l is the dynamic viscosity of the coolant, and lt is the turbulent viscosity. Energy equation:

qcp uj

@T f @ ¼ @xj @xj



  cp lt @T f kf þ Pr t @xj

ð3Þ

where kf is the thermal conductivity of the coolant, cp is the specific heat of the coolant, Tf is the coolant temperature, and Prt = 0.85 is the turbulent Prandtl number. The transport equations of the realizable k-e turbulent model:

297

Y. Zhang et al. / International Journal of Heat and Mass Transfer 113 (2017) 295–309

Fig. 1. Schematic of three kinds of hybrid micro-channel and slot-jet module with different channels: (a) rectangular module, (b) trapezoid module, (c) circular module.

X

0 Slot jet

W

Outlet

Z

(a)

Outlet Heat flux Slot jet

Outlet (b)

Ljet

Outlet

L

Heat flux Slot jet Outlet

Wjet

(c)

Outlet

Ww

Wch

Ww

Heat flux

(1)

(2)

Hjet

Hjet Hjet

Wch Hch

H

Hch

H Wb

Hw

Hw

Hch

R

H

Hw

Y

0

X

Heat flux

Heat flux

Heat flux

(a)

(b)

(c)

(3) Fig. 2. Schematic for each unit cell consisting of one slot jet and single micro-channel: (1) 3D physical module, (2) top view, (3) cross-section view; (a) rectangular, (b) trapezoid, (c) circular.

298

Y. Zhang et al. / International Journal of Heat and Mass Transfer 113 (2017) 295–309

Table 1 The geometric parameters of each unit cell.

Rectangular Trapezoid Circular

L (mm)

Ljet (mm)

W (mm)

Wjet (mm)

Wch (mm)

Ww (mm)

Wb (mm)

H (mm)

Hjet (mm)

Hch (mm)

Hw (mm)

20 20 20

3 3 3

2 2 2

0.4 0.4 0.4

1 1.6

0.5 0.2 0.33

0.4

3.5 3.5 3.16

1 1 1

1.50 1.50 1.16

1 1 1

R (mm)

Cross-sectional area (mm2)

0.77

1.5 1.5 1.5

Solid domain Velocity inlet Pressure outlet

Symmetry Symmetry Fluid domain

(1)

(a)

(b)

(c)

(2) Fig. 3. (1) Schematic of the computational domain with boundary conditions; (2) Local numerical mesh distribution for the computational domain of different kinds of hybrid module: (a) rectangular module, (b) trapezoid module, (c) circular module.

quj



  l @k þ Gk þ Gb  qe kf þ t rk @xj

@k @ ¼ @xj @xj

ð4Þ

where Gk represents the generation of the turbulent kinetic energy due to the mean velocity gradients. and Gb represents the generation of the turbulent kinetic energy due to the buoyancy.

qU j

@e @ ¼ @xj @xj 



  l @e e2 pffiffiffiffiffi þ C 1e þ C 1 qSe  C 2 q kf þ t rk @xj k þ me

e

k

C 3e Gb

ð5Þ

n o pffiffiffiffiffiffiffiffiffiffiffiffi g , g ¼ S ke, S ¼ 2Sij Sij . Sij is the average where C 1 ¼ max 0:43; gþ5

pffiffiffi  pffiffiffi As ¼ 6 cos U, U ¼ 13 arccos 6W , h i qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Sij Sjk Skj @u     @u W ¼ ðS S Þ3=2 , Sij ¼ 12 @xij þ @xji , U ¼ Sij Sij þ Xij Xij , Xij ¼ Xij  A0 ¼ 4:0,

where

ij ij

 2eijk xk , X ij ¼ Xij  2eijk xk .  where Xij is the mean rate-of-rotation tensor viewed in a moving reference frame with the angular velocity xk.

The following values are used for the coefficients in the above equations: C1e = 1.44, C2 = 1.9, rk = 1.0, re = 1.2, PrTKE = 1, PrTDR = 1.2, PrEnergy = 0.85, Prwall = 0.85. For the solid region: Energy equation:

strain rate.

lt ¼ Cu ¼

C u qk

2

e

1 A0 þ As U  ke


 @ @T s ¼0 ks @xj @xj

ð6Þ

where Ts is the wall temperature, and ks is the solid thermal conductivity.

Y. Zhang et al. / International Journal of Heat and Mass Transfer 113 (2017) 295–309

The Semi-Implicit Method for Pressure-Linked Equations (SIMPLE) algorithm [23] was used for couple velocities and pressure. The Enhanced Wall Treatment was employed for Near-Wall Treatment. The residual errors for convergence were set to 106 for governing equations. 3.2. Boundary conditions for the governing equations A constant heat flux q is applied at the bottom surface of the hybrid module:

@T @n

ð7Þ

Ts ¼ Tf ;

v ¼ ujet ;

w ¼ 0;

The temperature difference on the hybrid module bottom surface is defined as:

DT ¼ T b;max  T b;min

ð10Þ

where Tb,max and Tb,min are respectively the maximum temperature and the minimum temperature on the module bottom. The jet Reynolds number is expressed as:

Rejet ¼

qujet Djet l

ð11Þ

2Ljet W jet . jet þW jet

calculated as Djet ¼ L

@T f @T s ks ¼ kf @n @n

where u, v, w is the velocity component in the direction of coordinate axis. Inlet:

u ¼ 0;

ð9Þ

where Djet is the hydraulic diameter of the slot jet, which can be

Solid-liquid interface:

u ¼ v ¼ w ¼ 0;

q T wall  T f

T ¼ T in

where ujet is inlet velocity and its value can be defined as follows [24]: (1) assume an initial value and then numerically solve the governing equations; (2) calculate the pump power P1; (3) compare the difference between P1 with the desired pump power P0, if | P1  P0|/P0 < 0.01, terminate the procedure, otherwise, update ujet and return step (1), and then repeat steps (1) to (3). Outlet:

p ¼ 0 Pa ðGauge pressureÞ At the remaining walls of the numerical approach, adiabatic conditions were applied except for the interfaces between fluid region and solid region. The other boundary conditions are shown in Fig. 3(1). 3.3. Grid arrangement Fig. 3(2) displays the grid arrangement for the computational domain of the three hybrid modules with different channels. A multiple block mesh with hexahedral elements was employed. Local refining is necessary within the boundary layer to ensure the y+ values of the first layer are close to 1. The grid independence test was carried out with heat flux of q = 250 W/cm2 supplied at the bottom surface and different inject Re (Rejet = 6341 for rectangular channel, Rejet = 7046 for trapezoid channel, Rejet = 5531 for circular channel, respectively). Two variables, including the pump power and average temperature on the module bottom surface, were monitored. The grid system with 9,00,000 nodes was founded good enough for the rectangular channel, 1,750,000 nodes for the trapezoid channel, and 1,150,000 nodes for the circular channel respectively. When the further grid refinement was conducted, the changes of the pump power and the temperature were less than 1%. 3.4. Variable definition

3.5. Physical property parameter The hybrid module is made of copper with ks = 387.6 W m1 K . Pure water is served as the coolant and its properties varying with temperature are according to the follow equations. 1

Density (kg m3): q = 809.15 + 1.5481T  0.0031T2; Specific heat (J kg1 K1): Cp = 5580.3–8.9267T + 0.0142T2; Thermal conductivity (W m1 K1): k = 0.93775 + 0.0085505T 1.13  105T2; Viscosity (kg m1 s1): l = 0.025365–0.00014468T + 2.1  107T2. All above equations were fitted according to the data available in Ref. [25]. 3.6. Model validation The present numerical scheme was validated with the experimental data available in Sung and Mudawar’s paper [16], where the rectangular channel was used in the experiment and the HFE-7100 was used as the coolant. The temperatures of four points beneath the bottom wall of the channel were detected by the thermal couple. The experimental results under three different conditions were used as the reference values, as depicted in Fig. 4. The direction X represent the length of the micro-channel where the impingement region occupied the region from 0 to 1.47 mm and the radial flow region is from 1.47 to 10 mm. It shows the temperature distribution in the solid region at the distance of 2.54 mm

Temperature (° C)

q ¼ ks

h¼

299

The pump power P required to drive the fluid though the unit cell can be evaluated as:

P ¼ ujet  Ajet  Dp

ð8Þ

where Ajet = Ljet  Wjet is the cross-sectional area of the slot-jet, and   Dp ¼ D pstatic þ 12 qV 2 is the total pressure-drop across the unit cell. The local heat transfer coefficient can be defined as:

Fig. 4. Comparison of numerical results with the experimental results of Sung and Mudawar.

300

Y. Zhang et al. / International Journal of Heat and Mass Transfer 113 (2017) 295–309

from the solid–fluid interface. The numerical results agree well with the experimental results, indicating that the numerical scheme is capable of predicting the fluid flow and heat transfer of the hybrid micro-channel and slot-jet impingement systems. 4. Result and discussion 4.1. Pressure drop comparison of three hybrid modules Under the same flow rate, the pressure drops of three hybrid modules were depicted in Fig. 5(1). It can be found that the pressure drop in the circular channel is the maximum, and the pressure drop in the rectangular channel is the minimum. The vorticities, whose rotational direction is perpendicular to the main flow direction, become an important factor to the flow resistance in channel. In the circular channel (Fig. 5(2a)), the whole injected fluid could strike the bottom wall and develop vorticities at the affect of the side wall. In the trapezoid channel, only a part of injected fluid can develop vorticities in the wider region of channel. It’s mainly due to the obstacle effect of side

wall (Fig. 5(2c)). As for the rectangular channel (Fig. 5(2b), although the whole impingement jet can touch the bottom wall, the cross-section shape of the channel is not as beneficial for developing vorticities as the circular wall and trapezoid channel. The intensity of vorticities in three shapes channel, in descending order, are respectively circular channel, trapezoid channel and rectangular channel. Consequently, at the same flow rate, the pressure drops in three channels are also arranged in the same order from large to small. 4.2. Cooling performance comparison of three hybrid modules The average temperature and the temperature difference on the bottom surface of the hybrid modules were firstly comparatively explored at a same pump power P = 0.2 W but different heat flux applied at the bottom surface. As shown in Fig. 6(a), the average temperatures on the bottom surface of three hybrid modules rise up with the increase of heat flux. The hybrid module with trapezoid channel has the lowest bottom temperature. While, the rectangular channel achieves approximately a same bottom surface

160000 140000 120000 100000 80000 60000 40000 20000 0 0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

Fig. 5. (1) Comparison of three hybrid modules in pressure drop varying with flow rate; (2) Streamlines in the cross-sections passing through the impingement region, at the pump power P = 0.2 W: (a) circular channel, (b) rectangular channel, (c) trapezoid channel.

301

Y. Zhang et al. / International Journal of Heat and Mass Transfer 113 (2017) 295–309

rectangular trapezoid circular

34

80

32

75

30

70

28

o

Temperature difference ( C )

65

Temperature ( C )

60

o

55 50 45 40 35 30

26 24 22 20 18 16 14 12 10 8 6 4

25 20

rectangular trapezoid circular

2 50

100

150

200

250

300

350

400

0

450

50

100

150

2

200

250

300

q ( W/cm )

q ( W/cm )

(a)

(b)

350

400

450

2

Fig. 6. Comparison of three hybrid modules varying with heat flux, at P = 0.2 W: (a) bottom surface temperature, (b) bottom surface temperature difference.

Table 2 Comparison between trapezoid channel module and the other two hybrid modules in cooling performance at different heat flux. Compared with rectangular channel module

Compared with circular channel module

Heat flux (W/cm2)

Temperature decrease (%)

Temperature difference decrease (%)

Temperature decrease (%)

Temperature difference decrease (%)

50 150 250 350 450

4.15 8.04 10.18 11.84 12.58

42.53 43.78 46.19 48.51 50.03

4.01 7.85 9.94 11.52 12.25

33.77 34.86 37.20 39.56 41.31

rectangular trapezoid circular

90

30 28

85

26 24

Temperature difference ( C )

80

o

Temperature ( C )

o

75 70 65 60 55 50

22 20 18 16 14 12 10 8 6 4

45 40 0.00

rectangular trapezoid circular

2 0.04

0.08

0.12

0.16

0.20

0.24

0.28

0.32

0.36

0.40

0 0.00

0.04

0.08

0.12

0.16

0.20

P (W)

P (W)

(a)

(b)

0.24

0.28

0.32

0.36

0.40

Fig. 7. Comparison of three hybrid modules varying with pump power, at q = 250 W/cm2: (a) bottom surface temperature, (b) bottom surface temperature difference.

temperature with the circular channel module. The temperature difference on the bottom surface increases with the rise of heat flux, as presented in Fig. 6(b). The trapezoid channel module has the minimum temperature difference, while rectangular channel

module has the maximum one. The superiority of trapezoid channel module in cooling performance magnifies with the increase of the heat flux, as compared with the other two hybrid modules, Table 2.

302

Y. Zhang et al. / International Journal of Heat and Mass Transfer 113 (2017) 295–309

Table 3 Comparison between trapezoid channel module and the other two hybrid modules in cooling performance at different pump power. Compared with rectangular channel module

Compared with circular channel module

Pump power (W)

Temperature decrease (%)

Temperature difference decrease (%)

Temperature decrease (%)

Temperature difference decrease (%)

0.0033 0.0253 0.0841 0.2000 0.3885

2.10 4.54 8.02 10.18 11.47

9.25 24.66 36.43 46.19 53.55

3.73 6.60 8.47 9.94 11.19

14.61 19.92 28.25 37.20 44.75

on the bottom surface. Moreover, at each pump power, the trapezoid channel module has the lowest temperature and the minimum temperature difference on the bottom surface. And the cooling performance gap in three hybrid modules is gradually enlarged with the increase of pump power, Table 3. The total convection thermal resistances (defined as

rectangular trapezoid circular

0.45 0.40

Rcon ¼ 1h ¼

0.30 0.25 0.20 0.15 0.10 0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

P(W) Fig. 8. Comparison of convection thermal resistance varying with pump power, at q = 250 W/cm2.

Then, the cooling performance of three hybrid modules was also compared under the different pump power. A certain heat flux q = 250 W/cm2 was applied to the bottom surface of the module. As shown in Fig. 7(a) and (b), an increase of the pump power gives rise to both a decrease of temperature and temperature difference

Rectangular Cricular Trapezoid

Impingement 50

Radial flow region

region

48 46

-1

Rcnv(cm kW )

40

2

o

Temperature ( C)

44 42

38 36 34 32 30 28

0

1

2

3

4

5

6

7

8

9

10

11

T wall T f ) q

in three channels are compared. As shown in

Fig. 8, the convection thermal resistance in three hybrid modules all declines with the increase of pump power. At the low pump power, the circular channel has the minimum convection thermal resistance; while at the high pump power, the trapezoid channel has the maximum thermal resistance. With a same cross-section area, the trapezoid channel has the maximum solid-fluid interface area (i.e. heat transfer area), which is more 4.6% than rectangular channel and more 14.69% than circular channel at the crosssection area of 1.5 mm2. The variation in heat transfer area makes the final temperature performance largely different from the performance of the convection thermal resistance in three shape channels. It also helps the trapezoid channel module get the best cooling performance. Besides, the local heat transfer characteristics in different hybrid modules were further explored, at pump power P = 0.2 W and heat flux q = 250 W/cm2. The curves of local temperature on the solid-fluid interface and local thermal resistance Rcon along the flow direction are respectively illustrated in Fig. 9(a) and (b). Both the local temperature and the local thermal resistance in three channels rise along the flow direction. But there is still some difference in them. The local solid-fluid temperature in the trapezoid channel is the minimum and its increase range along the flow

2

-1

Rcnv (cm kW )

0.35

Rectangular Cricular Trapezoid

Impingement 0.42 0.40 0.38 0.36 0.34 0.32 0.30 0.28 0.26 0.24 0.22 0.20 0.18 0.16 0.14 0.12 0.10 0.08 0.06 0.04

Radial flow region

region

0

1

2

3

4

5

X(mm)

X(mm)

(a)

(b)

6

7

8

9

10

11

Fig. 9. (a) Local temperature distributions on the solid-fluid interface at P = 0.2 W and q = 250 W/cm2, (b) local thermal resistance along the flow direction in different channels at P = 0.2 W and q = 250 W/cm2.

303

Y. Zhang et al. / International Journal of Heat and Mass Transfer 113 (2017) 295–309

interface in trapezoid channel which has been mentioned above. In addition, the local thermal resistance in the trapezoid channel shows the peak-shape distribution, which is very different from that in the rectangular channel and circular channel. While, the local temperature distribution of the solid-fluid interface don’t show same variation trend. It’s mainly due to the high thermal conductivity of the copper that makes the temperature variation along the flow direction not as sharp as the thermal resistance exhibited. The fluid velocity distributions in the flow layer near the interface-1-1 and the interface-1-2 are further researched. The velocity component Vn, whose direction is perpendicular to

direction is also the least. Although the local thermal resistance in the impingement region of the trapezoid channel is a little larger than that in the other two channels, the impingement region is much smaller than the radical flow region. So the average convection thermal resistance in the whole channel with trapezoid shape is the least. With the minimum thermal resistance and the least variation range in it along the flow direction, the trapezoid channel reaches the best cooling performance. It should be noted that the local wall temperature of the trapezoid channel in the impingement region is still the lowest, despite the fact that local convection thermal resistance in this region is a little larger than that in the other two channels. It’s mainly due to the largest solid-fluid 0.06

Vn near interface-1-1 V n near interface-1-2

0.05 0.04 0.03 0.02

Vn (m/s)

0.01

Interface-1-2

0.00 -0.01 -0.02 -0.03 -0.04

Interface-1-1

Water flow direction

-0.05 -0.06 -0.07

(a)

Vn (m/s)

0

Interface-1-2 Interface-1-1

(b)

0.14 0.13 0.12 0.11 0.10 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0.00 -0.01 -0.02 -0.03

1

2

3

4

5

X(mm)

6

7

8

9

10

11

V n near interface-1-1 V n near interface-1-2

Water flow direction

0

1

2

3

4

5

X(mm)

6

7

0.10

8

9

10

11

V n near interface-1-1

0.09 0.08 0.07

Vn (m/s)

0.06 0.05 0.04

Water flow direction

0.03

Interface-1-1

0.02 0.01 0.00 -0.01

0

1

2

3

4

5

X(mm)

6

7

8

9

10

11

Fig. 10. The distributions of velocity component Vn near the solid-fluid interfaces: (a) trapezoid channel, (b) rectangular channel, (c) circular channel. The positive direction of Vn points to the interface vertically.

304

Y. Zhang et al. / International Journal of Heat and Mass Transfer 113 (2017) 295–309

Radial flow region

Impingement region

(a)

(b)

(c)

Fig. 11. Expanded and cutaway view of velocity contours in water flow direction passing though the midsection of the channels at the pump power of P = 0.2 W: (a) trapezoid channel, (b) rectangular channel, (c) circular channel.

Wjet

Top wall

Ww

α Hch Side wall Wb

Heat flux Fig. 12. Geometry parameters studied in hybrid module with trapezoid channel.

the interface, exhibits the peak-shape distribution in the trapezoid channel (Fig. 10(a)). But the Vn in the corresponding part of the rectangular channel and circular channel do not show that peakshape distribution (Fig. 10(b) and (c)). When fluid is injected into

the trapezoid channel, the fluid is separated into two parts for the channel shape (Fig. 5(2c)). One part of the fluid (named vorticity part) forms the vorticities in the wider section of the channel due to the obstacle of the side wall. The other part (named impingement part) strikes the bottom wall directly and runs away in the narrow section of the channel. While in the circular channel and the rectangular channel, the whole fluid injected can impinge at the bottom interface (Fig. 5(2a) and (2b)). That’s why the Rcon in the impingement region of the trapezoid channel is larger than those in the other two channels (Fig. 9(b)). Then, in the trapezoid channel, the two parts of the fluid run into the radial flow region (Fig. 11(a)). The impingement part fluid runs in the lower section of the trapezoid channel and its velocity magnitude increases with getting closer to the channel bottom wall because of the reduction in the cross-section area. Whereas, there is no fluid velocity increase around the bottom wall of the rectangular channel and the circular channel due to their channel shape features (Fig. 11 (b) and (c)). In the trapezoid channel, the impingement part fluid crashes with bottom wall and sidewall violently at the effect of vorticity part. And these kinds of crashes gradually diminish along the water flow direction (Fig. 10(a)). Therefore, the local thermal resistance in the trapezoid channel shows the peak-shape distribution along the water flow direction.

4.3. Parametric study of the hybrid module with trapezoid channel It is demonstrated in the previous section that the hybrid module with trapezoid channel has better cooling performance, compared with the rectangular channel and the circular channel. Thus, structure optimizations were done only on trapezoid channel. Three geometric parameters of the trapezoid channel (height Hch, bottom width Wb, corner angle a, shown in Fig. 12) are analyzed at the constant pumping power of P = 0.2 W and heat flux

305

Y. Zhang et al. / International Journal of Heat and Mass Transfer 113 (2017) 295–309

13

0.16

Rcnv

0.11

8

0.10

7

0.09

6

0.08

5

A

4

Temperature ( oC )

0.12

9

Rcnv (cm2 kW-1)

Velocity magnitude (m/s)

0.13

10

o

Temperature difference ( C )

10

57

9

56

8

55

7

54

6

0.07

53

0.06

52

0.05 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4

5 4

B

3 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4

β

β

(a)

(b)

β=0.75

β=1

12 11

58

0.14

11

13

Temperature( oC )

59

0.15

12

3

60

0.17

Velocity magnitude

Temperature difference ( oC )

14

β=1.25

β=1.5

Symmetry

Top wall

Side wall

β=1.75

β=2

β=2.25

β=2.5

Bottom

(c) Fig. 13. (a) Effects of b on convection thermal resistance and flow velocity in the trapezoid channel, at w = 1, a = 68°, (b) Effects of b on the average temperature and temperature difference on the bottom surface of the hybrid module, at w = 1, a = 68°, (c) Expanded and cutaway view of velocity contours of the fluid region perpendicular to water flow direction at the position X = 5 mm in trapezoid channel with different b.

of q = 350 W/cm2. The two non-dimensional parameters are Hch , w ¼ WW b . defined as follows: b ¼ W jet

jet

4.3.1. Effect of b Effects of b on the convection thermal resistance Rcon and the flow velocity in the trapezoid channel, at w = 1.0, a = 68°, are given in Fig. 13(a). The flow velocity decreases with the increase of b. There is an inflection point A (b = 1.5) at the curves of thermal resistance. The thermal resistance Rcon rises slowly before point A while it rises much quickly after point A. The velocity contours on the slices of the fluid region at the same position (X = 5 mm) of the trapezoid channel with different b are shown in Fig. 13(c). Not only does the flow velocity magnitude on the slices decrease, but also its uniformity deteriorates with b rising. A very non-uniform velocity distribution could be observed in the last four pictures (b = 1.75, 2, 2.25 and 2.5) and the high flow speed region gradually shrinks close to the bottom wall with b enlarging. There are three channel walls (top wall, side

wall and bottom wall) contributing to the heat convection between solid region and fluid region. In the first four figures (b = 0.75, 1, 1.25 and 1.5), all of three walls could be affected by the high flow speed region. Whereas there are only two channel walls (side wall and bottom wall) could be influenced by the high fluid speed region in the last four figures (b = 1.75, 2, 2.25 and 2.5), which consequently made the thermal convection resistance increased significantly. So before point A (b = 1.5), the increase of Rcon mainly attribute to the decrease of the channel flow velocity. When it comes to point A, the increase of Rcon is not only due to the decrease of the channel flow velocity, but also the decrease in heat transfer area (especially in top wall and side wall) that high flow speed region could affect. This kind of variation makes it different at the dividing point A (b = 1.5) that the trend lines of thermal convection resistance varying with b. In addition, the average temperature and the temperature difference varying with b on the bottom surface of the hybrid module are shown in Fig. 13(b). The temperature difference increases with b increasing. While the temperature on the bottom surface

Y. Zhang et al. / International Journal of Heat and Mass Transfer 113 (2017) 295–309

firstly declines with the increase of b before the inflection point B, which is mainly due to the augment of the heat transfer area. After point B, the increasing rate of thermal resistance is larger than the augment of the heat transfer area, thus leading to the temperature rising. The minimum temperature is achieved at b = 1.5 (point B). And it is reduced by 12.22% as compared with the design (b = 0.75). The least temperature difference is achieved at b = 0.75, and it is reduced by 63.6% as compared with the design (b = 4.25).

magnitude on the slices decrease, but also its uniformity deteriorates with w rising. It can be gotten that the high flow speed region gradually shrinks close to the bottom wall with w enlarging. There are three channel walls (top wall, side wall and bottom wall) contributing to the heat convection between solid region and fluid region. In the first three figures (w = 0, 0.5, and 1.0), the high flow speed region nearly overspreads the whole channel and affects all of the three walls. Whereas there are only two channel walls (top wall and bottom wall) could be influenced by the high fluid speed region in the last five figures (w = 1.5, 2.0, 2.5, 3.0 and 3.5), which consequently made the thermal convection resistance increased significantly. So before point A (w = 1.0), the increase of Rcon mainly attribute to the decrease of the channel flow velocity. When it comes to point A, the increase of Rcon is not only due to the decrease of the channel flow velocity, but also the decrease in heat transfer area (especially in side wall) that the high flow speed region could affect. This kind of variation makes it different at the dividing point A (w = 1.0) that the trend lines of thermal convection resistance varying with w.

4.3.2. Effect of w Effects of w on the convection thermal resistance Rcon and the flow velocity in the trapezoid channel, at b = 1.5, a = 68°, are shown in Fig. 14(a). The flow velocity decreases with the increase of w. While, the Rcon firstly rises slowly before point A (w = 1.0) and it rises more quickly after point A. The velocity contours on the slices of the fluid region at the same position (X = 5 mm) of the trapezoid channel with different w are shown in Fig. 14(c). Not only does the flow velocity 13

0.110

62

Velocity magnitude

61

0.100

60

12

59

11

58

10

57

9

0.095 10

0.090

9

0.085

8

0.080

Rcnv(cm2 kW-1)

Velocity magnitude (m/s)

11

0.075

7

A

6 0.0

0.5

1.0

1.5

w

2.0

2.5

3.0

3.5

14

0.105

Temperature ( oC )

Rcnv

12

15

Temperature Temperature difference

13

8

56

7

55

6

54

5

53

0.070

52

0.065

51

4

C B 0.0

0.5

1.0

Temperature difference ( oC )

306

3 1.5

(a)

w

2.0

2.5

3.0

3.5

2

(b)

Symmetry

Top wall

w=0

w=0.5

w=2.5

Side wall

Bottom wall

w=1.5

w=1.0

w=3.0

w=2.0

w=3.5

(c) Fig. 14. (a) Effects of w on the convection thermal resistance and flow velocity magnitude in the trapezoid channel, at b = 1.5, a = 68°, (b) effects of w on the average temperature and the temperature difference on the bottom surface of the hybrid module, at b = 1.5, a = 68°, (c) expanded and cutaway view of velocity contours of the fluid region perpendicular to water flow direction at the position X = 5 mm in trapezoid channel with different w.

307

Y. Zhang et al. / International Journal of Heat and Mass Transfer 113 (2017) 295–309

The average temperature and the temperature difference varying with w on the bottom surface of hybrid module are shown in Fig. 14(b). The temperature difference increases steadily with the rise of w. But the bottom temperature firstly declines with the rise of w. It is mainly due to the augment of the heat transfer area. When it comes to point B (w = 1.0, i.e. equal to the jet slot width), the bottom temperature reaches the minimum value. While, the bottom temperature starts rising rapidly after point C (w = 3.0). Besides the deterioration in velocity field, another important influence factor lies in the length of Ww shortened. As depicted in Fig. 12, the Ww connects the top wall and the side wall. When it gets shorter, the heat conduction from the side wall into the top wall will deteriorate. In other words, it leads to the decrease in the heat transfer area of top wall indirectly. The decrease range of heat transfer area after C becomes larger than it before C. Therefore, the temperature rises more rapidly after point C. The

0.105

10.5 10.0

0.100

57

0.095

56

0.090

9.5

0.085

9.0

0.080

8.5

0.075

8.0 7.5

0.070

A 40

45

50

55

60

α

65

70

75

80

85

Temperature ( oC )

11.0

Rcnv(cm2 kW-1)

Velocity magnitude (m/s)

9.0 Temperature Temperature difference

58

8.5 8.0 7.5 7.0 6.5

55

6.0 5.5

54

5.0 4.5

53

4.0

B

52

0.065 90

35

40

45

50

55

3.5

C 60

α

65

70

Temperature difference ( oC )

Velocity magnitude Rcnv

11.5

35

4.3.3. Effect of a Effect of a on the convection thermal resistance Rcon and the flow velocity in the trapezoid channel, at b = 1.5, w = 1.0, are shown in Fig. 15(a). The flow velocity increases with the increase of a. The Rcon firstly declines rapidly before point A (a = 68°) but the it declines much slowly after point A (a = 68°). The velocity contours on the slices of the fluid region at the same position (X = 5 mm) of the trapezoid channel with different a are shown in Fig. 15(c). Not only does the flow velocity magnitude on the slices increases, but also its uniformity rises with increase of a. It can also be gotten that the high flow speed region

0.110

12.0

7.0

minimum temperature is achieved at w = 1.0, and it is reduced by 14.85% as compared with the design (w = 0). The least temperature difference is achieved at w = 0, and it is reduced by 74.86% as compared with the design (w = 3.5).

75

80

85

3.0 90

(b)

(a) α=43

α=39

Top wall

Symmetry

α=54

α=60

α=68

α=48

α=77

α=86

Side wall

Bottom wall

(c) Fig. 15. (a) Effect of a on the convection thermal resistance and channel fluid velocity magnitude, at b = 1.5, w = 1, (b) effect of a on the average temperature and the temperature difference on bottom surface of the hybrid module, at b = 1.5, w = 1, (c) expanded and cutaway view of velocity contours of the fluid region perpendicular to water flow direction at the position X = 5 mm in trapezoid channel with different a.

308

Y. Zhang et al. / International Journal of Heat and Mass Transfer 113 (2017) 295–309

β

w

β w α

2.4 2.2 2.0

α 70 60

1.8 1.6

50

t (%)

1.4 1.2

Δt (%)

1.0

40 30

0.8 0.6

20

0.4

10

0.2 0.0

0

A

-0.2 -50

-40

-30

-20

-10

0

x (%)

10

20

30

40

50

B -50

-40

-30

-20

-10

(a)

0

x (%)

10

20

30

40

50

(b)

Fig. 16. (a) Comparison of three parameters influence level on the temperature of the hybrid module bottom surface, (b) comparison of three parameters influence level on the temperature difference of the hybrid module bottom surface.

gradually has impact on the whole channel with a enlarging. There are three channel walls (top wall, side wall and bottom wall) contributing to the heat convection between solid region and fluid region. In the first five figures (a = 39°, 43°, 48°, 54° and 60°), the influence of high flow speed region on top wall and side wall is feeble. While in the last three figures (a = 68°, 77°, and 86°), all of three walls could be affected by the high flow speed region. It consequently makes the thermal convection resistance decline significantly. Before point A (a = 68°), the decrease of Rcon is not only due to the increase of the channel flow velocity, but also the increase in heat transfer area (especially in top wall and side wall) that high flow speed region could affect. When it comes to point A, the decrease of Rcon mainly attribute to the increase of the channel flow velocity. This kind of variation makes it different at the dividing point A (a = 68°) that the trend lines of thermal convection resistance varying with a. The average temperature and the temperature difference varying with a on the bottom surface of the hybrid module are shown in Fig. 15(b). The temperature difference continuously decreases with the increase of a. But there are two particular points (B, C), dividing the temperature curves into three sections. Before point B (a = 54°), the temperature firstly declines quickly with the increase of a, mainly due to the decline of thermal resistance. In the second section between B (a = 54°) and C (a = 68°), the temperature declines much slowly, because the reduction of heat transfer area makes up the decline of Rcon. While in the third section, the bottom temperature rises rapidly with the increase of a, which is mainly due to the reduction of heat transfer area. The minimum temperature on the module bottom surface is achieved at a = 68.2°, and it can be reduced by 7.15% as compared with the design (a = 86.18°). The least temperature difference is achieved at a = 86.18°, and it can be reduced by 57.16% as compared with the design (a = 39.04°). 4.4. Comparison of three geometric parameters In the previous subsections, three parameters in the hybrid module with trapezoid channel are studied respectively. It should be noted that the optimal parameter corresponding to minimum temperature Topt differs from that corresponding to minimum temperature difference DTopt. Therefore, the influencing level of these

parameters are compared by using an optimal value (T = 52.36 °C, DT = 5.16 °C) as the reference point, where the best cooling performance can be achieved. Three new parameters are defined as follows:

x¼

m  mopt  100%; mopt

t¼

jT  T opt j  100%; T opt

Dt ¼

m ¼ b; w; or a;

jDT  DT opt j  100%: DT opt

As shown in Fig. 16(a), before the optimal value (point A, T = 52.36 °C), b has the maximum influence on the bottom temperature among the three geometric parameters. While after point A, a becomes the largest influencing factor on the bottom temperature. As for the temperature difference (Fig. 16(b)), a has the maximum effect before the optimal value (point B, DT = 5.16 °C). Whereas after the optimal value, b becomes the most important influence factor on the temperature difference. 5. Conclusions In this study, the cooling performances of hybrid jet and microchannel module with three different cross-section shape channels are numerically investigated by a realizable k-e turbulent module. Key findings are as follows: At the same flow rate, the pressure drop exiting in three hybrid modules, in descending order, are circular channel module, trapezoid channel module and rectangular channel module. The hybrid module with trapezoid channel achieves the lowest temperature and the minimum temperature difference on the bottom surface. And its superiority in the cooling performance enlarges with the increase of heat flux and pump power, as compared with the other two hybrid modules. The local convection thermal resistance in the hybrid module with trapezoid channel presents particular peak-shape distribution along the flow direction. It distinguishes with that in the other two hybrid modules.

Y. Zhang et al. / International Journal of Heat and Mass Transfer 113 (2017) 295–309

The cooling performance of trapezoid channel module can be further improved by optimizing the channel height, channel bottom width, and channel corner angle. When the optimal value for the three parameters are respectively adopted, the bottom surface temperature can be reduced by 12.22%, 14.85% and 7.15% as compared with the worst design, and the bottom surface temperature gradient can also be reduced by 63.6%, 74.86% and 57.16%. Before the optimum value, the channel height has the maximum influence on the bottom temperature. After the optimum point, the channel corner angle has the biggest influence. As for the module bottom temperature difference, it’s just opposite. Conflict of interest statement Neither the entire paper nor any part of its content has been published or has been accepted elsewhere. It is not being submitted to any other journal. All authors have seen the manuscript and approved to submit to your journal. Acknowledgements This work is supported by International Cooperation Project (Grant No. 2016YFE0118100) and Dongguan Innovative Research Team Program (Grant No. 2014607119). References [1] I. Mudawar, Assessment of high-heat-flux thermal management schemes, IEEE Trans. Compon. Pack. Technol. 2001 (2001) 122–141. [2] J. Barrau, M. Omri, D. Chemisana, J. Rosell, M. Ibañez, L. Tadrist, Numerical study of a hybrid jet impingement/micro-channel cooling scheme, Appl. Therm. Eng. 33–34 (2012) 237–245. [3] K.A. Estes, I. Mudawar, Comparison of two-phase electronic cooling using free jets and sprays, ASME, J. Electron, Pack 117 (1995) 323–332. [4] M.K. Sung, I. Mudawar, Experimental and numerical investigation of singlephase heat transfer using a hybrid jet-impingement/micro-channel cooling scheme, Int. J. Heat Mass Transf. 49 (2006) 682–694. [5] D. Lelea, The microtube heat sink with tangential impingement jet and variable fluid properties, Heat Mass Transf. 45 (2009) 1215–1222. [6] J. Barrau, D. Chemisana, J. Rosell, L. Tadrist, M. Ibañez, An experimental study of a new hybrid jet impingement/micro-channel cooling scheme, Appl. Therm. Eng. 30 (2010) 2058–2066.

309

[7] L. Yang, Y. Li, P.M. Ligrani, J. Ren, H. Jiang, Unsteady heat transfer and flow structure of a row of laminar impingement jets, including vorticity development, Int. J. Heat Mass Transf. 88 (2015) 149–164. [8] L. Yang, P. Ligrani, J. Ren, H. Jiang, Unsteady structure and development of a row of impingement jets, including kelvin-helmholtz vorticity development, J. Fluids Eng. 137 (2015) 051201. [9] L. Yang, J. Ren, H. Jiang, P. Ligrani, Experimental and numerical investigation of unsteady impingement cooling within a blade leading edge passage, Int. J. Heat Mass Transf. 71 (2014) 57–68. [10] N. Kayansayan, S. Kucuka, Impingement cooling of a semi-cylindrical concave channel by confined slot-air-jet, Exp. Thermal Fluid Sci. 25 (2001) 383–396. [11] Z. Liu, Z. Feng, Numerical simulation on the effect of jet nozzle position on impingement cooling of gas turbine blade leading edge, Int. J. Heat Mass Transf. 54 (2011) 4949–4959. [12] A.K. Barik, A. Mukherjee, P. Patro, Heat transfer enhancement from a small rectangular channel with different surface protrusions by a turbulent cross flow jet, Int. J. Therm. Sci. 98 (2015) 32–41. [13] A. Husain, M. Ariz, N.Z.H. Al-Rawahi, M.Z. Ansari, Thermal performance analysis of a hybrid micro-channel, -pillar and -jet impingement heat sink, Appl. Therm. Eng. 102 (2016) 989–1000. [14] W. Escher, B. Michel, D. Poulikakos, A novel high performance, ultra thin heat sink for electronics, Int. J. Heat Fluid Flow 31 (2010) 586–598. [15] F. Zhou, Y. Liu, Y. Liu, S.N. Joshi, E.M. Dede, Modular design for a single-phase manifold mini/microchannel cold plate, J. Therm. Sci. Eng. Appl. 8 (2015) 021010. [16] M.K. Sung, I. Mudawar, Single-phase and two-phase cooling using hybrid micro-channel/slot-jet module, Int. J. Heat Mass Transf. 51 (2008) 3825–3839. [17] M.K. Sung, I. Mudawar, Correlation of critical heat flux in hybrid jet impingement/micro-channel cooling scheme, Int. J. Heat Mass Transf. 49 (2006) 2663–2672. [18] M.K. Sung, I. Mudawar, Single-phase and two-phase heat transfer characteristics of low temperature hybrid micro-channel/micro-jet impingement cooling module, Int. J. Heat Mass Transf. 51 (2008) 3882–3895. [19] M.K. Sung, I. Mudawar, Single-phase hybrid micro-channel/micro-jet impingement cooling, Int. J. Heat Mass Transf. 51 (2008) 4342–4352. [20] M.K. Sung, I. Mudawar, Effects of jet pattern on single-phase cooling performance of hybrid micro-channel/micro-circular-jet-impingement thermal management scheme, Int. J. Heat Mass Transf. 51 (2008) 4614–4627. [21] M.K. Sung, I. Mudawar, Effects of jet pattern on two-phase performance of hybrid micro-channel/micro-circular-jet-impingement thermal management scheme, Int. J. Heat Mass Transf. 52 (2009) 3364–3372. [22] T.-H. Shih, W.W. Liou, A. Shabbir, Z. Yang, J. Zhu, A new eddy-viscosity model for high reynolds number turbulent flows-model development and validation, Comput. Fluids 24 (1995) 227–238. [23] S.V. Patankar, Numerical Heat Transfer and Fluid Flow, Hemisphere, Washington, DC, 1980. [24] C.-B. Kim, C. Leng, X.-D. Wang, T.-H. Wang, W.-M. Yan, Effects of slot-jet length on the cooling performance of hybrid microchannel/slot-jet module, Int. J. Heat Mass Transf. 89 (2015) 838–845. [25] T.E. Tan, M. Dou, M. H. Zhou, Principles of Chemical Engineering, third ed., Beijing, 2006.