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.

1. 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
| Volume 1 | Issue 12 | www.ijrtem.com | 61 |
Thermal and fluid characteristics of three-layer microchannels
heat sinks
3
, Ahmed K. Alshara2
Abul Muhsin A, Rageb,1
Sana J. Yaseen
)University, Iraq(Mechanical, Engineering/ Basrah1,2,
(Civil, Engineering/ Misan University, Iraq)3
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 micro-
channel under constant pumping power of 0.01 W is 3. Skandakumaran et al. (2004)[6] studied single and multi-
layer 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
) Re Reynolds number
Ws total width of heat sink (m) T temperature (K)
Cp specific heat at constant pressure (kJ/kgK) u velocity component in the x direction (m/s)
Dh hydrulic diameter of micro-channel v velocity component in the Y direction (m/s)

2. Thermal and fluid characteristics of three-layer…
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k thermal conductivity (kJ/kgK) w velocity component in the z direction (m/s)
L length of the heat sink (mm) Greek symbols
Nu Nusselt number µ Dynamic viscosity, N.s/m2
P pressure (N/m2
) θ Diveregen angle, degree
𝑞′′
applied heat flux (W/m2
) ρ 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 100µm, length of 26mm and variable height (begins with 100
µm then divergence with the horizontal by angle 0.5̊) 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.
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
Vin(m/s) Tin(̊C) 𝑞̿(W/cm2
) Ksi(W/mºC) Kwater(W/mºC)
1.33 20 90 148 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]
0








z
w
y
v
x
u (1)
Momentum in x, y and z directions respectively are:
)(
1
2
2
2
2
2
2
z
u
y
u
x
u
x
P
z
u
w
y
u
v
x
u
u























(2)
)(
1
2
2
2
2
2
2
z
v
y
v
x
v
y
P
z
v
w
y
v
v
x
v
u























(3)
t
Tin, uin
Tin, uin
Tin, uin
Figure 1: A schematic of heat sink with three channels
(a) Parallel flow (PF) (b) counter 1 flow (CF1) (c) counter 2 (CF2) flow
(a) (c)
(b)
t
Hch
2t
Hch
t
2t
Hch
Tin, uin
Tin, uin
Tin, uin
Tin, uin
Tin, uin
Tin, uin
t
W
L

3. Thermal and fluid characteristics of three-layer…
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)(
1
2
2
2
2
2
2
z
w
y
w
x
w
z
P
z
w
w
y
w
v
x
w
u























(4)
Energy equation:
)( 2
2
2
2
2
2
z
T
y
T
x
T
Cp
k
z
T
w
y
T
v
x
T
u


















(5)
Where the variables u, v, w, ρ, µ, and α 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]:
02
2
2
2
2
2









z
T
y
T
x
T sss (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. 𝑞′′
= 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡.
Inlet temperature T=Tin
−𝑘 𝑠
𝜕𝑇𝑠
𝜕𝑦
= −𝑘 𝑓
𝜕𝑇𝑓
𝜕𝑦
at the fluid–solid interface
𝜕𝑇
𝜕𝑦
= 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. No. of nodes bulk Temperature(K)
1. 60 x162x10 304.78101
2. 70 x182x15 304.7844
3. 80 x212x20 304.79089
4. 90 x262x35 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
30µmx100µmx26mm 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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Figures and Tables
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 𝑁𝑢̅̅̅̅ 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) (K)wT x(mm) (K)bT Channel no.
PF
26 335.428 26 327.86 1
26 333.998 26 326.48 2
26 333.286 26 325.79 3
CF1
8 338.19 2 333.5 1
8 336.634 4 332.007 2
8 335.69 16 328.75 3
306
336
366
396
426
456
25.92 50.92 75.92 100.92 125.92
Maximumtemperature(K)
flow rate x10^3 (1/h)
present
ref[ 13]
present
ref. [13]
Figure 2: Validation of the present work with reference [13], Maximum heated wall temperature
comparison for two uniform channels (parallel and counter flow)

5. Thermal and fluid characteristics of three-layer…
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CF2
18 338.81 22 334.01 1
18 337.29 10 329.97 2
18 336.68 22 331.98 3
Diverge CF
20 338.38 22 337.498 1
20 333.58 10 329.417 2
20 332.48 22 331.64 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
𝑁𝑢̅̅̅̅ along the axial distance for three uniform channels with parallel flow. In case of uniform channels, it began
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 𝑁𝑢̅̅̅̅ 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
Nu/ΔPNuparallel
0.003974.2631
0.003974.26172
0.0039674.2183
Counter1
0.0039574.26011
0.0039644.24542
0.003664.32323
Counter2
0.0039674.38451
0.003954.08562
0.0039664.43123
diverge
0.0040563.64631
0.0040163.512
0.0040543.68533
Table 4: Temperature difference along the heated wall of sink
divergenceCounter2Counter1parallelcase
28.02433.47611.11736.946ΔT
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

6. Thermal and fluid characteristics of three-layer…
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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.
290
295
300
305
310
315
320
325
330
335
340
0 5 10 15 20 25 30
T(K)
X(mm)
ch1
ch2
ch3
ch1
ch2
ch3
Figure 3: Average wall and bulk temperature for three uniform channels along axial distance (PF)
290
300
310
320
330
340
350
0 5 10 15 20 25 30
T(K)
X(mm)
ch1
ch2
ch3
ch1
ch2
ch3
Figure 4: Average wall and fluid temperature for CF1, three uniform channels with axial distance
290
300
310
320
330
340
350
0 5 10 15 20 25 30
T(K)
X(mm)
ch1 ch2
ch3 ch1
ch2 ch3
Figure 5: Average wall and fluid temperature for CF2 three uniform channels

7. Thermal and fluid characteristics of three-layer…
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290
300
310
320
330
340
350
0 3 6 9 12 15 18 21 24 27 30
Tw(K)
X(mm)
parll
count1
count2
Figure 7: Average wall temperatures on the upper heated wall of sink
290
300
310
320
330
340
350
0 5 10 15 20 25 30
T(K)
X(mm)
ch1 ch2
ch3 ch1
ch2 ch3
Figure 6: Average wall and fluid temperature for CF (three divergence channels)
0
2
4
6
8
10
12
14
16
18
0 5 10 15 20 25 30
X(mm)
ch1
ch2
𝑵𝒖̅̅̅̅
Figure 8: Average Nu for parallel flow uniform channel

8. Thermal and fluid characteristics of three-layer…
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Figure 10: Nu/ΔP for three channels along axial distance (all cases)
0
0.0002
0.0004
0.0006
0.0008
0.001
0.0012
0.0014
0.0016
0.0018
0.002
0 3 6 9 12 15 18 21 24 27 30
Nu/ΔP
X(mm)
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
2
4
6
8
10
12
14
16
18
0 5 10 15 20 25 30
X(mm)
ch1
ch2
Figure 9: Average Nu for counter flow 1for uniform channels
𝑵𝒖̅̅̅̅

9. Thermal and fluid characteristics of three-layer…
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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
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[2] Xu. S, Wu. Y, Cai. Q, Yang. L, Li. Y. ''Optimization of the thermal performance of multilayer silicon
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