G011202061070

Invention Journal of Research Technology in Engineering & Management (IJRTEM) ISSN: 2455-3689 www.ijrtem.com Volume 1 Issue 12-Version-2 ǁ October. 2017 ǁ PP 61-70

Thermal and fluid characteristics of three-layer microchannels heat sinks Sana J. Yaseen1 , Abul Muhsin A, Rageb 2, Ahmed K. Alshara3 1,2,

(Mechanical, Engineering/ Basrah University, Iraq) 3 (Civil, Engineering/ Misan University, Iraq)

ABSTRACT : A heat sink with three layers of microchannels with different flow arrangements has been studied numerically using CFD fluent software version 15. The different flow arrangements using uniform and divergence channels on thermal characteristics of heat sinks at the same mass flow rate are investigated. The results indicated that, uniform channels with counter-flow 1 arrangement provide the best temperature uniformity and divergence channels with counter flow gives the best heat sink performance.

KEYWORDS : Multilayered microchannel, Micro heat sink, Counter flow

I.

INTRODUCTION

The progress toward higher circuit density and quicker operation speed, claim a steady increase in the dissipative heat flux. Heat sink of microchannel design is a good choice for cooling of the high-power electronic device with a small volume. But as the devices or systems become smaller, heat flux increases. So an effective cooling strategy was required to dispersal heat [1]. Heat dissipation has become one of the key design tasks [2] and the successful design of micro-channel heat sinks requires dissipate the heat to the environment to maintain micro-devices at an acceptable temperature [3]. A large number of recent studies have carry out to study the basics of microchannel flow in multi-layered microchannels, the characteristics of flow and heat transfer in multi-layered microchannels are studied in the following fields: Vafai and Zhu (1999) [4] investigated counter flow arrangement for two layered microchannel heat sink numerically. They proved that the temperature rise on the base surface was reduced and the pressure drop for the two layered was smaller than that of the one layered heat sink. Wei and Joshi (2003) [5] developed stacked micro-channel heat sink using genetic algorithms. They indicated that the optimal number of layers for microchannel under constant pumping power of 0.01 W is 3. Skandakumaran et al. (2004)[6] studied single and multilayer channeled heat sinks analytically. They found that multi-layer heat sinks have lower thermal resistance compared to single layer. Also, they noticed that increasing the number of layers reducing the overall pressure drop.

Alfieri et al. (2010)[7] studied three dimensional microchannels with cylindrical pin-fins experimentally and numerically. They developed CFD model of conjugate heat transfer in order to dissipated heat reach currently as high as 250 W/ cm2 in multilayer chip stacks of less than 0.3 cm3 volume. The performance of trapezoidal shape double layer microchannel heat sink was investigated by Sharma et al. (2013)[8]. They studied counter and parallel configuration. Their analysis showed that among various trapezoidal configurations, the one with larger side face to face was most suitable. Adewumi et al. (2014)[9] investigated a three-dimensional parallel and counter-flow for fluid flowing in single and two-layer microchannels inserted with circular micro pin fins numerically. Their results showed that the two-layer microchannel with counter flow was the best design in maximising thermal conductance and minimizing the temperature variation on the heated base. Lin et al. (2015) [10] investigated a three-dimensional model of multi-layered microchannel heat sinks numerically. They concluded that as the layer number increases, the multilayered MCHS can achieve a more uniform bottom wall temperature. The objective of the present work is to use heat sink contains three layers of microchannels to obtain good thermal performance for microelectronics devices at low pressure drop and good temperature uniformity on the heat sink.

II.

NOMENCLATURE

Ac cross-sectional area (m2) Ws total width of heat sink (m) Cp specific heat at constant pressure (kJ/kgK) Dh hydrulic diameter of micro-channel

Re Reynolds number T temperature (K) u velocity component in the x direction (m/s) v velocity component in the Y direction (m/s)

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Thermal and fluid characteristics of three-layer‌ k thermal conductivity (kJ/kgK)

w velocity component in the z direction (m/s)

L length of the heat sink (mm) Nu Nusselt number P pressure (N/m2) � ′′ applied heat flux (W/m2)

Greek symbols Âľ Dynamic viscosity, N.s/m2 θ Diveregen angle, degree Ď Fluid density, kg/m3

III.

MODEL DESCRIPTION

A schematic diagram of the heat sink, with length L, height H and total width W, with three layers of microchannels each one with dimensions of width 100Âľm, length of 26mm and variable height (begins with 100 Âľm then divergence with the horizontal by angle 0.5ĚŠ) has been shown in Fig.1(a), (b) and (c). A constant heat flux (q=90W/cm2) applied at the top wall of the sink, all other solid surfaces of the heat sink are assumed adiabatic. The properties of the cooling fluid and solid material are shown in table 1 below.

Tin, uin

t

t

Tin, uin Tin, uin

t Hch

Tin, uin

Tin, uin 2t Hch

Tin, uin 2t Tin, uin

Hch

L

Tin, uin

Tin, uin t W

(a)

(c)

(b)

Figure 1: A schematic of heat sink with three channels (a) Parallel flow (PF) (b) counter 1 flow (CF1) (c) counter 2 (CF2) flow Laminar, steady state flow, incompressible fluid and with negligible viscous dissipation and natural convection are assumed. The fluid and solid regions are assumed with constant properties.

Table 1: The fluid and heat sink properties used in numerical analysis Tin(ĚŠC) 20

Vin(m/s) 1.33

�̿(W/cm2) 90

Ksi(W/mÂşC) 148

Kwater(W/mÂşC) 0.61

Governing equations The governing equations of mass, momentum and energy based on the above assumptions which applied to the fluid region are: Continuity: [8, 11] ď‚św ď‚śu ď‚śv (1)   0 ď‚śx ď‚śy ď‚śz Momentum in x, y and z directions respectively are: 2 ď‚śu ď‚śu ď‚śu ď‚ś 2u ď‚ś 2u 1 ď‚śP ď ­ ď‚ś u (2) u v w   ( 2   ) ď‚śx ď‚śy ď‚śz ď ˛ ď‚śx ď ˛ ď‚śx ď‚śy 2 ď‚śz 2

u

ď‚śv ď‚śx

v

ď‚śv ď‚śy

w

ď‚śv ď‚śz

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

2 1 ď‚śP ď ­ ď‚ś 2v ď‚ś v ď‚ś 2v  ( 2   ) ď ˛ ď‚śy ď ˛ ď‚śx ď‚śy 2 ď‚śz 2

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Thermal and fluid characteristics of three-layer‌ u

ď‚św ď‚śx

v

ď‚św ď‚śy

w

ď‚św ď‚śz



2 1 ď‚śP ď ­ ď‚ś 2 w ď‚ś w ď‚ś2w  ( 2   ) ď ˛ ď‚śz ď ˛ ď‚śx ď‚śy 2 ď‚śz 2

(4)

Energy equation:

u

ď‚śT ď‚śx

v

ď‚śT ď‚śy

w

ď‚śT ď‚śz



k ď ˛ Cp

(

ď‚ś 2T ď‚śx 2



ď‚ś 2T ď‚śy 2



ď‚ś 2T ď‚śz 2

(5)

)

Where the variables u, v, w, Ď , Âľ, and Îą are represent fluid velocity, density, viscosity and thermal diffusivity respectively. While ‘P’ and ‘T’ denote pressure and temperature for fluid.

Steady state energy equation for the solid walls in 3D, is given by [12]:

 2 Ts  2 Ts  2 Ts   0 x 2 y 2 z 2

(6)

IV.

BOUNDARY CONDITIONS

Hydrodynamic Boundary Conditions: uniform velocity at the inlet of channel. At all the walls of channels and sink (no-slip condition), u=0, v=0, w=0.

Thermal Boundary Conditions: adiabatic boundary conditions are applied to all the boundaries of the solid region except the heat sink top wall, where constant heat flux is applied. đ?‘ž ′′ = đ?‘?đ?‘œđ?‘›đ?‘ đ?‘Ąđ?‘Žđ?‘›đ?‘Ą.

Inlet temperature T=Tin đ?œ•đ?‘‡đ?‘ đ?œ•đ?‘‡đ?‘“ −đ?‘˜đ?‘ = −đ?‘˜đ?‘“ at the fluid–solid interface đ?œ•đ?‘Ś

đ?œ•đ?‘‡ đ?œ•đ?‘Ś

đ?œ•đ?‘Ś

= 0. at outlet

V.

MESH INDEPENDENCE AND CODE VALIDATION

The numerical coed is verified in a number of ways to ensure the validity of the numerical analysis. The grid dependence test is first conducted by using several different mesh sizes. First mesh size is (60 x162x10), the second mesh size is (70x182x15), the third is (80x212 x20) and the fourth is (90x262x25) in z, y, x directions respectively.

The results obtained from these meshes at Re =50 are summarized in table. 2 bellows shows the number of nodes and fluid temperature at x=5mm from channel length.

Table.2 The number of nodes and fluid temperature at x=5mm.

Serial No. 1.

2.

3.

4.

No. of nodes 60 x162x10 70 x182x15 80 x212x20 90 x262x35

bulk Temperature(K) 304.78101 304.7844 304.79089 304.83099

From these results it can be seen that the solution becomes independent of grid size and increasing the size of mesh more than the third one do not have a significant effect on the results, so the mesh choosing is the third one. To validate our numerical work, the results of the present study are compared with the numerical results of Sharma et al. [13]. The heat sink presented in [13] contains two uniform microchannels with a 30Âľmx100Âľmx26mm width, height and length respectively. Thermal boundary condition is a constant heat flux of 106 W/ m2 acting at the bottom wall of heat sink. Different flow rate are used at inlet temperature of 305K. Figure 2 represents a maximum wall temperature on the heated surface, it can be seen that, the agreement between results of present model and results of Sharma et al. [13] is accepted since the deviation between the two results equal to 0.45%. The checks indicate that the numerical models are reliable to simulate a double micro channels with parallel and counter flow.

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Thermal and fluid characteristics of three-layer‌ Figures and Tables

Maximum temperature (K)

456

present ref[ 13] present ref. [13]

426 396 366 336 306 25.92

50.92

75.92 flow rate x10^3 (1/h)

100.92

125.92

Figure 2: Validation of the present work with reference [13], Maximum heated wall temperature comparison for two uniform channels (parallel and counter flow)

VI.

RESULTS AND DISCUSSION

The results for three cases studied here done at constant mass flow rate of (39.8x10-6 kg/s), these results can be represented by variation of the average bulk fluid and wall temperature and variation of Ě…Ě…Ě…Ě… đ?‘ đ?‘˘ along the axial distance. Figure 3 represents variation of the average temperature of bulk fluid and average wall along the axial distance for three uniform channels with parallel flow, it can be observed that the temperature increases along the axial distance of channel, and the difference in fluid temperature among the channels belongs to the location of channel from the heated wall, the upper channel has the largest value of the bulk and wall temperature.

Figure 4 shows the variation of average temperature of coolant fluid and wall along the axial distance for three uniform channels with CF1 flow (fluid enters the lower and middle channels from the x-positive direction while enters the upper channel from the opposite direction), it clears that the temperature increased along the channel length till reaches maximum value then reduces, the upper and middle channels has the same behavior since fluid in these channels has the same direction. The temperature of the three fluids in channels begins at inlet temperature in opposite direction then increases till reach its maximum value near the entrance region of the channel that flow alone since the two channels that contain two fluids at the same directions has the larger value of temperature than the singular fluid. So as expected that the two fluids will heated the singular flow alone fluid. Figure 5 is similar to Figure 4 but for counter 2 flows (CF2: fluid in the middle channel flows in opposite direction for the other channels). In this case the maximum value of temperature obtains at the last quarter of channel 2, owing to the fluid direction in these channels. The bulk fluid and wall average temperature for counter flow through three divergence channels shows in Figure 6. In this case the fluids which are flow in the upper and lower channels follow at the same direction, while the middle channel fluid flows in reversed direction called counter flow (CF). As can be seen from this figure the fluid temperature increases from the two sides since cold fluid enters from these sides, then increases till reaches the maximum value of temperature at distance of 14mm. Also, this figure shows the average wall temperature for three divergence channel. The maximum value of temperature occurs at distance of 20mm from the positive x-direction.

Table 2: maximum bulk and average wall temperature for all cases x(mm) PF 26 26 26

Tw(K)

x(mm)

Tb(K)

Channel no.

335.428 333.998 333.286

26 26 26

327.86 326.48 325.79

1 2 3

8 8 8

338.19 336.634 335.69

2 4 16

333.5 332.007 328.75

1 2 3

CF1

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Thermal and fluid characteristics of three-layer‌ CF2 18 18 18 Diverge CF 20 20 20

338.81 337.29 336.68

22 10 22

334.01 329.97 331.98

1 2 3

338.38 333.58 332.48

22 10 22

337.498 329.417 331.64

1 2 3

Figure 7 represents the average temperature for heated wall of sink at different channel shapes and flow arrangements; it can explain the temperature uniformity along the heated sink obtains at CF1. Figure 8 shows Ě…Ě…Ě…Ě… along the axial distance for three uniform channels with parallel flow. In case of uniform channels, it began đ?‘ đ?‘˘ with large value due to small boundary layer at the entrance region then reduces to take a constant value, all channels approximately has the same Nu since it has the same hydraulic diameter and same inlet velocity of fluid. Figure 9 shows Ě…Ě…Ě…Ě… đ?‘ đ?‘˘ along the axial distance for three uniform channels with counter flow. In case of uniform channels with counter flow Nu as the parallel flow case begins with large value from two sides depends on the fluid flow directions. Then reduces to small value, then near the region of the exit for this fluid it belongs to increases again. This behavior results from the hot fluid (singular or double depends on the fluid flow direction) will meet a cold fluid which come from the opposite direction which leads to rise Nu at exit region again. This manner happens in counter flow only. In the same way figure 10 shows the variation of Nu/ΔP along the axial distance of channels, as the fluid flow along the channel this value of Nu reduces with flow direction and pressure drop will increase, so the value of Nu/ΔP reduces along the channels. This value begins with large value from two sides then decreases along the channel due to reduce Nu and due to increase the value of pressure drop along channel length, also for the counter flow N/ΔP begins with large value from reverse direction. The values of Nu and Nu/ΔP for all cases can be represented in table 3. It can be noticed that the maximum value of Nu/ΔP occurs at divergence channels with counter flow. Table 4 shows the difference of maximum temperature and inlet temperature along the heated wall of the heat sink at different cases. From this table it clears that the case of counter1 has the lower temperature difference along the sink, this means that counter1 will give the best temperature uniformity along the heated sink.

Table 3: Values of Nu and Nu/ΔP for all cases parallel 1 2 3 Counter1 1 2 3 Counter2 1 2 3 diverge 1 2 3

case ΔT

Nu 4.263 4.2617 4.218

Nu/ΔP 0.00397 0.00397 0.003967

4.2601 4.2454 4.3232

0.003957 0.003964 0.00366

4.3845 4.0856 4.4312

0.003967 0.00395 0.003966

3.6463 3.51 3.6853

0.004056 0.004016 0.004054

Table 4: Temperature difference along the heated wall of sink parallel Counter1 Counter2 divergence 36.946 11.117 33.476 28.024

Figure 11 represents the temperature contour for different cross sections of uniform and divergence channels and different flow arrangements; PF, CF1 and CF2 at different cross section at x=0, 6, 10, 20 and 26mm along the channel length for the three channels. It noticed that the sink have a regions of low temperature (bold blue color) as like as high temperature (red color), this results in large value of temperatures difference along the heated sink. While others Figures don’t has a blue color region, which result low temperature difference. Also

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Thermal and fluid characteristics of three-layer‌

T(K)

the front view of sinks at parallel flow shows that the whole region at exit has high temperature, which causes a hot spot in this region. But the others flow arrangements not have a hot spot that leads to materials failure.

340 335 330 325 320 315 310 305 300 295 290

ch1 ch2 ch3 ch1 ch2 ch3

0

5

10

15 X(mm)

20

25

30

Figure 3: Average wall and bulk temperature for three uniform channels along axial distance (PF) 350 ch1 ch2 ch3 ch1 ch2 ch3

340

T(K)

330 320 310 300 290 0

5

10

X(mm)

15

20

25

30

Figure 4: Average wall and fluid temperature for CF1, three uniform channels with axial distance 350

ch1 ch3 ch2

340

ch2 ch1 ch3

T(K)

330 320 310 300 290 0

5

10

X(mm)

15

20

25

30

Figure 5: Average wall and fluid temperature for CF2 three uniform channels

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Thermal and fluid characteristics of three-layer‌ 350 340

ch1

ch2

ch3

ch1

ch2

ch3

T(K)

330 320 310 300 290 0

5

10

15 X(mm)

20

25

30

Figure 6: Average wall and fluid temperature for CF (three divergence channels) 350 340

Tw(K)

330 320 310 parll count1 count2

300 290 0

3

6

9

12 X(mm)

15

18

21

24

27

30

Figure 7: Average wall temperatures on the upper heated wall of sink 18 16

ch1

14

ch2

12

Ě…Ě…Ě…Ě… đ?‘ľđ?’–

10 8 6 4 2 0 0

5

10

15

20

25

30

X(mm) Figure 8: Average Nu for parallel flow uniform channel

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Thermal and fluid characteristics of three-layer‌ 18 ch1

16

ch2

14

Ě…Ě…Ě…Ě… đ?‘ľđ?’–

12 10 8 6 4 2 0 0

5

10

15 X(mm)

20

25

30

Figure 9: Average Nu for counter flow 1for uniform channels 0.002

ch1 par ch2 par ch3 par ch1 coun1 ch2 coun1 ch3 coun1 ch1 con2 ch2 con2 ch3 coun2 ch1 div ch2 div ch3 div

0.0018 0.0016 0.0014

Nu/ΔP

0.0012 0.001

0.0008 0.0006 0.0004 0.0002 0 0

3

6

9

12

15 18 X(mm)

21

24

27

30

Figure 10: Nu/ΔP for three channels along axial distance (all cases)

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Thermal and fluid characteristics of three-layer…

Figure 11: Temperature contour for different cross sections (a) PF (b) CF1 (c) CF2 (d) divergence channels with CF

VII.

CONCLUSIONS

The numerical study for the fluid flow and heat transfer in three layer microchannels using parallel and counter flow arrangements on uniform and divergence channels of the heat sink the following conclusions are obtained: 1- The heat transfer performance of microchannel heat sink is affected by the flow arrangements of liquid in uniform and divergence microchannels.

2- The lower temperature difference along the sink is obtained in case of using divergence channel with counter1.

3- Fluid flow with counter1 will give the best temperature uniformity along the heated sink, while divergence channels with counter flow gives the best heat sink performance.

VIII.

RECOMMENDATIONS

The most researchers aiming to obtain good heat sink performance and temperature uniformity, it can recommend using some optimal structures to design the stacked micro-channel heat sink, such as increases the number of layers and using another arrangements of flow inside these layers to increases heat sink performance.

REFERENCES [1] [2]

[3] [4] [5] [6] [7] [8]

Qu. W. Mudawar, I. Lee. S, Y. Wereley. S. T. ''Analysis of three-dimensional heat transfer in microchannel heat sinks''. International Journal of Heat and Mass Transfer. Vol 45.PP:3973–3985. (2002) Xu. S, Wu. Y, Cai. Q, Yang. L, Li. Y. ''Optimization of the thermal performance of multilayer silicon microchannel heat sinks''. Department of Mechatronics Engineering, University of Electronic Science and Technology.

Wei. X. ''Stacked Microchannel Heat Sinks for Liquid Cooling of Microelectronics Devices''. Thesis.

Georgia Institute of Technology. November. (2004).

Vafai. K, Zhu. L. ''Analysis of two layered microchannel heat sink concept in electronic cooling''.

International Journal of Heat and Mass Transfer. PP:1176-1186.(1999) Wei, Joshi. ''Optimization Study of Stacked Micro-Channel Heat Sinks for Micro-Electronic Cooling ''.

IEEE Transctios on Components and Packaging Technoloies.Vo. 26, No. 1.(2003) Skandakumaran. P, Ortega. A, Jamal-Eddine. E, Vaidyanathan. R. ''Multi-Layered Sic Microchannel Heat Sinks- Modeling and Experiment''.inter Society Conferenceon Thermal Phenomena.(2004) Alfieri. F , Tiwari. M. K, Zinovik. I, Poulikakos. D. ''3D Integrated Water Cooling of a Composite Multilayer Stack of Chips''. Journal of HeatTransfer. Vol.132. (2010) Sharma, D. Singh. P. P, Garg. H. ''Numerical Analysis of Trapezoidal Shape double Layer Microchannel Heat Sink''. International Journal of Mechanical and Industrial Engineering (IJMIE) ISSN No. 2231-6477, Vol.3, Iss-1. PP.6-16. (2013).

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Thermal and fluid characteristics of three-layer‌ [9]

[10] [11] [12]

[13]

Adewumi. O. O, Bello-Ochende. T, Meyer. J. P. ''Temperature Variation on The Heated Base of a Solid Substrate Cooled with Different Types of Heat Sink''. 10Th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics.pp:68-78. (2014).

Lin. L, Deng. M. X, Zhang. X. X, Wang. X. D. ''Numerical analysis and parametric study of multilayered microchannel heat sinks''. Advances in mechanical Engineering.Vol. 7, pp 1–10.( 2015).

Patel. V. U, Modi. A. J. ''Optimization of heat sink analysis for electronics cooling''. World Journal of Science and Technology, Vo. 2, No.4. PP:64-69. (2012).

Ismaila. M. F, Rashid. M. A. I , Mahbubb. M. ''Numerical Simulation OF Fluid Flow AND Heat Transfer IN A MEMS-Based Micro Channel Heat Sink . Frontiers in Heat and Mass Transfer (FHMT).

(2012).

Sharama. D, Garg. H, Bajpi. P.P.'' Performance comparison of single and double layer Microchannel Using Liquid Metal Cooling ''. ARME, Vol.1, No.2.pp:9-17. (2012)

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