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Characteristic Study on the Optimization of Micro Pin-Fin

Heat Sink with Staggered Arrangement

T. J. John1 and B. Mathew

2

College of Engineering and Science, Louisiana Tech University, Ruston, LA, 71272

H. Hegab3

College of Engineering and Science, Louisiana Tech University, Ruston, LA, 71272

The effect of the Pin-fin shapes on the overall performance of the micro Pin-fin heat sink

with staggered arrangement is studied in this paper. Six different shapes of micro Pin-fins,

square, rectangle, circle, rhombus, triangle and ellipse are subjected to study in this paper.

The optimization processes are carried out using computer simulations performed using

COVE*TORWARE™. The study is carried out over a range of Reynolds number ranging

from 50 to 500 and a figure of merit term (FOM) consisting of both the thermal resistance

and the pumping power is developed for the overall performance evaluation of different

models. A weighted average scheme is used for developing the FOM term. The results of the

study revealed that at low values of Reynolds numbers (Re<200) circle has the best

performance and at high values of Re (Re>200) rectangle showed the best performance.

*omenclature

C = specific heat capacity (J/kg K)

h = total height of the heat sink (m)

k = thermal conductivity(W/K m)

L = length of the heat sink (m)

n = constant

P = pressure (N/m2)

PP = pumping power (W)

∆P = pressure drop across the heat sink

q = heat input (W)

R = resistance (K/W)

T = temperature (K)

V = velocity of the fluid flow (m/s)

W = width of the heat sink (m)

V& = volumetric flow rate (m3/s)

ρ = density of the fluid (kg/m3)

SUBSCRIPT

F = fluid

S = solid

In = inlet

1 Doctoral Student, Micro and Nano Systems Track, College of Engineering and Science, LA Tech, Ruston, LA

71272; Email: tjj007@latech.edu, Ph: +1-813-514-9618. 2 Doctoral Student, Micro and Nano Systems Track, College of Engineering and Science, LA Tech, Ruston, LA

71272; Email: bma017@latech.edu, Ph: +1-318-514-9618. 3 Associate Professor, Mechanical Engineering Program, College of Engineering and Science, LA Tech, Ruston, LA

71272; Email: hhegab@latech.edu, Ph: +1-318-257-3791, Fax: +1-318-257-4922.

10th AIAA/ASME Joint Thermophysics and Heat Transfer Conference28 June - 1 July 2010, Chicago, Illinois

AIAA 2010-4781

Copyright © 2010 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

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out = outlet

wall = wall

th = thermal

non = non dimensional

stu = with structure

without_stu = without structure

I. Introduction

everal methods of heat dissipation from devices by using external heat sinks with the help of air and liquids have

been proposed by numerous researchers. Among the different heat sink designs proposed in the past few

decades, Pin-fin heat sinks are the most promising one. An extensive amount of work has been done on the Pin-fin

heat sinks and researchers have developed several effective Pin-fin structures, and many of these structures has been

gone through the optimization procedures [1-4]. Most of the work done in the Pin-fin heat sinks was confined to the

macro scale till the beginning of this decade [2-4]. While trying to optimize a macro level heat sink, the major factor

of concern is the thermal resistance across the heat sink and most of the studies in the field of Pin-fin heat sink

optimizations were focused on the minimization of the thermal resistance across the heat sink. Though few of the

studies have considered the pressure drop across the heat sink due to the liquid flow through it; as the cross sectional

area available for the liquid flow is higher in a macro level heat sink pressure drop across the device was not a major

factor in the optimization studies. However, as the manufacturing techniques used in the micro scale has developed

vigorously and as the electronic industry is striving towards the miniaturization of the devices, the ease and need for

developing micro scale heat sinks have increased in the last decade. Accordingly, some researchers started working

on the development and optimization of the micro scale heat sinks recently [5, 6].

Park et al. developed a numerical model for the optimization of the Pin-fin heat sink by keeping the objective of

optimization as the minimization of the thermal resistance and pressure drop in 2004 [2]. The study was based on

Pin-fins with rectangular shapes and the study concluded that both the height and width of the fins are affecting the

thermal resistance as well as the pressure drop in the heat sink. K. Park et al studied the effect of Pin-fin shapes on

the thermal resistance and the pressure drop inside a Pin-fin heat sink with the use of computational fluid dynamics

[3]. Two shapes of pins, circle and rectangle were considered in the study and the study concluded that the

rectangular Pin-fins outperformed the circular fins in the performance of the thermal resistance. An optimization

based on the entropy generation by five different Pin-fin shapes (Elliptical, rhombus, circle, rectangle and square)

inside a heat sink was conducted in 2006 by Abdel-Rehim [4]. Circular and elliptical pins were showing the best

thermal performance and copper was found to be the best material for the heat sink manufacturing. A study done by

Yova Peles et al. on the optimization of the micro Pin-fin heat sink using silicon as the substrate revealed some

interesting observations. At high Reynolds number heat sinks with high density of Pin-fins are preferred and less

denser Pin-fins are preferred at low Reynolds number [6]. The study also showed that the pin efficiency of the Pin-

fin heat sinks is low at micro level and this issue can be resolved by using shorter Pin-fins. An extension of the

earlier study was reported by the same group in 2007 and this time the thermal resistance and the pressure drop of

the Pin-fin heat sinks were studied with four different shapes of fin structures (circle, hydrofoil, cone, and rectangle)

and silicon was again used as the substrate for this study [5]. T. J. John at el. conducted investigation on the effect of

the micro Pin-fin geometries on the performance evaluation of the micro Pin-fin heat sinks in 2009 [7]. Six different

geometries were studied under two different condition, constant liquid flow rate and constant pressure drop.

Geometries selected for the study were square, circle, rectangle, ellipse, triangle and rhombus. The substrate

material used was silicon and a figure of merit (FOM) term was developed as an evaluation criterion for the micro

heat sink. The study reported that at very low flow rate the thermal resistance factor is the dominating term in

determining FOM and ellipse was the best performer among the all structures. At intermediate flow rates the circular

pin had the best performance and as the flow rate increased the pumping pressure became the dominating factor in

FOM and the rectangle pin-fin dominated the evaluation.

The major concern of the researchers while developing a micro Pin-fin heat sink is managing the huge pressure

drop developed across the device during its operation. So while determining the major factors involved in the

optimization process of a micro Pin-fin heat sink both thermal resistance and pressure drop plays an equally

important role. In this paper the authors have studied the effect of six different Pin-fin shapes on the thermal

resistance and pressure drop inside a micro Pin-fin heat-sink with staggered arrangement of pin-fins. Liquid is used

as the cooling agent in this optimization study. The liquid flow rate through the device is varied over a range of

values for the optimization purpose. The Reynolds number of the liquid flow at the entrance of the Pin-fin device is

S

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kept constant for all the six models and the liquid flow rate corresponding to each value of the Reynolds number is

calculated using the cross sectional area available for the liquid flow. The optimization processes are carried out

using computer simulations generated using COVENTORWARE™. The heat sink under consideration in this study

has a length and width of 1 cm each and has a thickness of 500 micrometer. Only a small section of the total micro

heat-sink is modeled for the optimization of the pin-fin shapes for the ease of analysis and due to the memory

constrains of the computers. The model consists of two sections, the substrate and the fluid. The substrate had a total

depth of 500 micrometers, width of 400 micrometers, and length of 1 cm. The pin fins are 150 micrometers tall and

the cross sectional width towards the center of all the pin-fin shapes except triangle is kept constant at 100

micrometers. For triangle the base width is kept as 100 micrometer. The axial pitch (PA) is set as 500 micrometers

and the transverse pitch (PT) is kept constant as 100 micrometers. Silicon is used as the substrate, and uniform heat

flux of 250 kW/m2 is applied at the bottom of the structure. Simulations are carried out for Reynolds numbers

ranging from 50 to 500. Water with initial temperature of 278.15K was used as the coolant in the heat-sink. Six

different shapes: square, circle, rectangle, triangle, oval and rhombus were analyzed in the optimization study.

Simulations were conducted and the nondimensional overall thermal resistance of the heat sink, and the

nondimensional pumping pressure was calculated from the results. A heat sink of same dimensions without pin-fin

structures is developed for the purpose of nondimensionalizing thermal resistance and pumping pressure obtained

from the different models. A figure of merit (FOM) was developed using the nondimensional thermal resistance and

nondimensional pumping power for each structure with different pin-fin shapes. All the results obtained in this study

is discussed in the sections below

II. Theory

A top view of the pin-fin heat sink, and cross sectional views of the heat sink along the z and x axis is shown in

fig. 1. The total length of the heat sink along the x axis is L, the width is W, and the total height is H1. Certain

assumptions are made for the ease of solving the models and those assumptions are given below.

1. The micro fluidic device is operating under steady condition.

2. The fluid does not undergo phase change while flowing through the micro fluidic device.

3. The fluid flow is under nonslip condition (kn < 0.001).

4. The fluid is assumed to be incompressible.

The solution of the developed model is obtained using COVENTORWARE™by solving four governing

equations. The equations used are continuity equation (Eq. 1), momentum equation (Eq. 2), and two energy

equations, one each for the substrate and the liquid part (Eqs. 3 & 4).

0=⋅∇ Vr

(1)

VPVVrrr

2)( ∇+−∇=∇⋅ µρ (2)

FFFP TkTCV 2∇=⋅∇r

ρ (3)

02 =∇ SS Tk (4)

The boundary conditions assumed for solving the above governing equations are as follows. The velocity of the

liquid flow in the x-direction (Vx) at the inlet of the heat sink is calculated from the liquid flow rate (input

parameter) and the cross sectional area of the device (Eq. 5) by assuming uniform flow rate at the inlet. The pressure

at the outlet is taken as zero. In the actual situation, the pressure at the outlet is not zero, but in this model the

concern is only about the pressure drop across the device, and hence this assumption is valid (Eq. 6). As the

minimum cross sectional area available for the liquid flow in the device is large enough to have a kn <0.001, so the

velocity towards the walls of the device (Eq. 7). Both the pressure and the velocity conditions are the default

boundary condition for the COVENTORWARE™.

vVin&& = (5)

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0=outP (6)

0=wallVr

(7)

Figure 1. Cross sectional view of the heat sink (W = 200 µm, H1 = 500 µm, H2 = 100 µm, L = 10000µm, A) top

view, B) along the x-axis, and C) along the z-axis

B.

C.

Substrate

Liquid Liquid

H2

H1

Y

Z

W1

W2

X

Y L

H1

H2

Liquid

B'

A.

A A'

B PA

PT

W

L Z

X

H1

H2

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",0,

qy

Tk

zyx

SS =∂

∂−

=

(8)

0=∂

∂

Ω∂ T

y

TS (9)

The heat transfer from the inlet side and the outlet side of the substrate is negligible so the heat transfer through

these sides is considered to be zero (Eq. 10). Both sides of the heat sink are assigned a symmetric boundary

condition (the model developed is a small portion of the entire heat sink under study, so repeatability of the

developed model is assumed). COVENTORWARE™ assumes the heat transfer in the symmetric walls to be zero

(Eq. 11).

0,,0,,

=∂

∂=

∂

∂

== zyx

S

zyLx

S

x

T

x

T (10)

0,10,0,10,

=∂

∂=

∂

∂

=≤≤=≤≤ WzHyx

S

zHyx

S

z

T

z

T (11)

Equations 12 to 16 gives the boundary conditions used to solve the energy equation for the liquid. The inlet

temperature of the liquid is kept constant as 278.15K (Eq. 12). It is assumed that there is no heat transfer from the

fluid at the outlet to the surroundings, i.e. an adiabatic condition is assumed at this face. This can be mathematically

represented as shown in Eq. 13.

inzyxF TT == ,,0

(12)

0,,

=∂

∂

= zyLx

F

x

T (13)

As discussed in the case of the boundary conditions for substrate, both sides of the liquids are also assumed to

have a symmetric boundary condition (repetition of the model is assumed). Thus, the heat transfer at both sides is set

to zero (Eq. 14). In most of the practical cases the heat sinks manufactured in silicon will be sealed with glass plates

and the heat transfer from the top surface of the water to the ambient is negligible. So the heat loss from the top face

of the water is taken as zero in this study. This insulating condition for the top surface of the water is obtained using

the boundary condition in Eq.15. The heat that is being transferred from the liquid to the substrate and back from the

substrate to the liquid is assumed to be the same and this condition is represented using the boundary condition

given in Eq. 16, here Ω∂ represents the interface between the solid and liquid.

0,21,0,21,

=∂

∂=

∂

∂

=≤≤=≤≤ WzHyHx

F

zHyHx

F

z

T

z

T (14)

02,2,10,2,

=∂

∂=

∂

∂

≤≤=≤≤= WzWHyx

F

WzHyx

F

y

T

y

T (15)

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Ω∂Ω∂ ∂

∂=

∂

∂

n

Tk

n

Tk S

SF

F rr (16)

The maximum temperature of the substrate (which happens at the outlet of the substrate), the average inlet

temperature of the fluid, and the pressure drop across the devise is obtained from each of the above developed

models for further analysis. The thermal resistance and the pumping pressure is calculated from the above obtained

values using Eqs. 17 and 18. The thermal resistance is calculated as the ratio of the difference between the maximum

temperature of the substrate and the inlet temperature of the liquid to the heat input applied at the bottom of the

substrate (Eq. 17). Pumping pressure across the channel needed for the analysis is obtained by multiplying the

pressure drop with the flow rate of the liquid (Eq. 18).

q

TTR

inFoutS

th

,, −= (17)

VPPP &×∆= (18)

Another model of the heat sink with same dimensions as of the initial model but without the Pin-fin structures

were developed for nondimensionalizing the pumping power and the thermal resistance obtained from the models

under analysis. The method of nondimensionalizing the thermal resistance and pumping pressure are given using

Eqs. 19 and 20.

stuwithoutth

stuth

nonthR

RR

_,

,

, = (19)

stuwithout

stunon

PP

PPPP

_

= (20)

A weighted average scheme in which the weight of each quantities used in the term can be determined by the

design constrains used to develop the figure of merit (FOM) term. The equation to obtain the FOM term is given in

Eq. 21.

( ) ( )nonnonth PPnRnFOM

×××=

2,1

1 (21)

Where n1+ n2 =1, by varying the values of n1 and n2 the relative importance of each function in the equation for

calculating the FOM can be determined according to the objective of the design need. In normal situations, the value

of n1 and n2 is taken as 0.5, thus giving equal weight to each function in determining the FOM term.

III. Mesh Optimization and Grid Dependency

All the above governing equations are solved using commercially available software called

COVENTORWARE™, which uses the finite volume method to solve these equations, with the help of upwind

scheme. A convergence criterion was set for all the parameters while solving the governing equations. The

convergence criteria, that is the maximum relative change in the variable between two successive iterations, for the

three velocity components (X,Y and Z direction) was set as 10-4

and for the convergence of the temperature, the

criteria was set as 10-8

. The source term (mass residue term) had a convergence criteria being set at 10-4

and is

monitored throughout the simulation process.

Two type of meshing techniques are used in the development of the models studied in this paper. All the models

with square and rectangle Pin-fins are meshed using the Manhattan bricks (Fig. 2), and all other models are meshed

using the Extruded bricks (Fig. 3). For the Manhattan bricks the maximum element size used has a dimension of

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25µm, 15 µm and 10 µm along the x, y and z axes and the minimum element size used is 15µm, 10 µm and 8 µm

along the x, y and z axes. While meshing the other structures (except square and rectangle) Manhattan bricks cannot

be used, so Extruded brick meshing is used. When Extruded bricks are used for meshing, one of the faces of the

model (X-Y plane through Z = 0) will be meshed using the specified element size and then the mesh will be

extruded (in Z axis) into a 3D mesh. The element size in the extruded direction can be specified by the user, so that

the user has the flexibility of selecting the 3D element size of the mesh. In this study the maximum and the

minimum element size that is being specified on the face are 35 µm and 20 µm. The maximum value of the element

in the extruding direction is 12 µm and the minimum element size is 8 µm.

Figure 2. Manhattan Bricks Figure 3. Extruded bricks

One of the validation techniques used for checking the validity of the results obtained using a particular mesh is

the grid dependency. In this technique the size of the mesh used for each of the models are refined to such an extent

that further refining of the mesh size will not have much effect on the obtained results. The grid dependency check

for the Manhattan meshing scheme and extruded scheme is reported in Table 1and 2. As can be seen from these

tables, the results obtained by refining the mesh by increasing the number of nodes used for solving the equations,

there is not much change in the results obtained for both the maximum temperature of the substrate and the pressure

drop across the device. Another method used for the validation of the model and the mesh size that is being used for

the model is to monitor the liquid flow rate that is obtained from the outlet of the model. This result is compared

with the inlet flow rate (input parameter) and if the change in the flow rate between the two faces is negligible the

mesh is considered to be optimized.

Element size (µm) *umber of *odes Maximum temperature at

substrate (K)

Pressure drop (kPa)

25 × 15 ×10 559275 287.459 27.209

25 × 12 ×10 738243 287.472 26.447

25 × 10 ×10 917211 287.488 26.330

25 × 10 ×8 1112822 287.490 26.292

Table 1. Grid dependency of Manhattan bricks

Element size (µm) *umber of *odes Maximum temperature at

substrate (K)

Pressure drop (kPa)

35 × 12 239636 288.545 23.158

20 × 10 654635 288.290 21.889

20 × 8 821240 288.290 22.001

20 × 6 1077040 288.306 22.006

Table 2. Grid dependency of Extruded bricks

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8

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0 100 200 300 400 500 600

Rth

[K

/W]

Reynolds Number

Square Circle

Rectangle Ellipse

Rhombus Triangle

Figure 5. Thermal resistance of the six different models

with increasing Reynolds number

Figure 4. Temperature contour plot of a Pin-fin

heat sink with circular Pin-fins.

IV. Results

A contour plot of the micro pin-fin heat sink with circular pin fin is shown in Fig. 4. The dimensions of the

model shown in Fig. 4 are 1 cm in the X direction, 400 µm in Y direction and 500 µm in Z direction. The heat sink

has a Re of 300 at the entrance of the model, and a uniform heat flux of 250kW/m2 is applied to the bottom of the

structure. The temperature profile of the heat sink is shown in the picture, and as expected the temperature of the

liquid increases while moving from the inlet to the outlet and the maximum temperature of the substrate is obtained

towards the outlet of the substrate.

The plot of the thermal resistance of the six

different models with different shapes of Pin-fin

structures is given in the Fig. 5. The minimum area for

the liquid flow between the pin-fin structures in all the

six different models in the transverse direction is kept

constant at 100 µm. The Re at the entrance of all the

models is varied from 50 to 500 for the comparison

study of FOM between the heat sinks with pin-fin

structures of different shapes. The average liquid

temperature at the entrance of the channel and the

maximum temperature of the bottom of the substrate

are measured and the thermal resistance of each model

is calculated. As can be seen from the plot 5, at a Re of

50 the heat sink with square pin-fins is having the

maximum thermal resistance and the heat sink with

ellipse pin has the minimum thermal resistance. In the

case of ellipse and circle the continuously developing

flow occurring due to the Pin-fin structures is very

smooth. For the ellipse structures the reduction in

hydraulic diameter of the area available for liquid flow between the pins in the transverse direction remains for a

longer period compared to the circular pins causing a reduction in the overall thermal resistance. The thermal

resistance of the heat sinks with rectangle and square pin-fins remains the lowest for the intermediate values of Re

and the thermal resistance of the heat sink with triangle pin-fins attains the lowest value compared to other shapes at

Re of 500. The value of the thermal resistance for all the models reduces as the Re increases and the reduction of the

thermal resistance shows the same trend for all the six different models. The slight difference in the thermal

resistance in different model at the medium and the high flow rate is due to the difference in the flow pattern of the

liquid around the pin-fin structures inside the heat sink. The liquid flow pattern inside all the six models at Reynolds

number of 500 is shown in Fig. 6.

Figure 7 show the variation of the pressure drop

across the heat sink with the increase in the Re

values. At low Re the pressure drop across all the six

models remains almost the same because of the

creepy flow of the liquid around the pin-fin

structures and the liquid flow pattern inside all

models are similar to each other. But as the liquid

flow increase the flow pattern changes and as can be

seen from Fig. 6, the triangle and rhombus have the

maximum flow distribution and hence the maximum

pressure drop. The circle and the ellipse have a

similar flow pattern and the plot of the pressure drop

for these two structures is close to one another. But

when it comes to the rectangle and square pin-fins

the continuously developing flow inside the heat

sink around the pins at high Re is very poor. The

flow pattern of square and rectangular Pin-fin

models is almost the same and the pressure drop

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across them shows the same trend. An interesting point that can be noted from the plot of the pressure drop is the six

different shapes forms three pairs of similar structure and the pres

trend within the pairs.

A) Circle

C) Square

D) Rhombus

Figure 6 .The flow pattern for all the six models at a Reynolds number of 500 (contour plot taken from the

center of the liquid section in the XY plane) .

American Institute of Aeronautics and Astronautics

9

across them shows the same trend. An interesting point that can be noted from the plot of the pressure drop is the six

different shapes forms three pairs of similar structure and the pressure drop across these structures shows similar

B) Ellipse

D) Rectangle

F) Triangle

pattern for all the six models at a Reynolds number of 500 (contour plot taken from the

center of the liquid section in the XY plane) .

across them shows the same trend. An interesting point that can be noted from the plot of the pressure drop is the six

sure drop across these structures shows similar

pattern for all the six models at a Reynolds number of 500 (contour plot taken from the

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10

0

50

100

150

200

250

300

0 100 200 300 400 500 600

Pre

ssu

re D

rop

[kP

a]Reynolds Number

Square Circle

Rectangle Ellipse

Rhombus Triangle

Figure 7. Pressure drop across six different models at varying Re

The plot of the FOM term with the

increasing Reynolds number is shown in

Fig. 8. The FOM term which consists of

both thermal resistance and pumping

pressure terms is calculated using the Eq.

(21). Higher the FOM term, better the

overall performance of the heat sink. Here

the values of both n1 and n2 are taken as

0.5, that is equal weight is given to both

the terms. From the plot it can be seen that

the circle has the best performance

followed by ellipse at very low liquid flow

rate. Since the pressure drop across the

device is low at low flow rates the thermal

resistance is the major factor in

determining the FOM term. But as the

liquid flow rate increases with the increase

in the Reynolds number the pressure drop

becomes the major factor in the

determination of the FOM term and then the models with the lowest pressure drop will dominate the performance

criteria. The rectangle Pin-fin heat sinks has a poor performance at lower Reynolds number, but as the Reynolds

number reaches 200 its performance equals the performance of the ellipse Pin-fin heat sink and from there onwards

it show the best performance. The heat sinks with elliptical Pin-fins show a good overall performance throughout the

study and it falls just under the heat sinks with rectangular structures at high values of Re. Square Pin-fins also

shows a better performance towards the higher Reynolds number and it is due to the lower pressure drop across it at

higher Reynolds numbers compared to other structure except rectangle Pin-fins. Even though triangle has the lower

thermal resistance at a Re of 500 the overall performance is very bad because of the high pressure drop developing

across the model. Rhombus Pin-fins also have the same issue of high pressure drop but is slightly better than the

triangle Pin-fins at low Re but has the worst performance at high values of Re. The FOM term of all the models at

Reynolds number of 50 is very poor and hence not included in Fig. 8. The pressure drop across all the models is

very low at Re of 50 but the thermal resistance is very high so the FOM term is very low and remains almost the

same for all the six different models and hence is not included in the Fig. 8.

The FOM term is calculated and plotted in Fig. 9 by giving more weight to the thermal resistance. In this case

the n1 is kept as 0.75 and n2 is kept as 0.25. The overall magnitude of the FOM increased by giving more weight to

the thermal resistance term but the trend and the pattern of the FOM plot remains the same as that of the case with

equal weight for both thermal resistance and pumping power.

Figure 8. FOM term for six different models at

varying Reynolds number (n1 = n2 =0.5).

Figure 9. FOM term for six different models at varying

Reynolds number (n1 = 0.75, n2 = 0.25).

0.75

1.00

1.25

1.50

1.75

2.00

2.25

0 100 200 300 400 500 600

FO

M

Reynolds Number

Square Circle

Rectangle Ellipse

Rhombus Triangle

1.00

1.25

1.50

1.75

2.00

2.25

2.50

2.75

3.00

0 100 200 300 400 500 600

FO

M

Reynolds Number

Square Circle

Rectangle Ellipse

Rhombus Triangle

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V. Conclusion

The overall performance of the six different heat sinks with different shaped pin-fin structures arranged in a

staggered order was studied in this paper for different Reynolds number varying from 50 to 500. In order to identify

the optimal shape of the pin-fins of the micro heat sink, a figure of merit term was introduced in the paper. A

weighted average scheme was used for determining the FOM term from the thermal resistance and the pumping

power of the heat sinks. The conclusions on the optimal shape of the pin-fin structures for the heat sinks are:

1. At very low Re (Re < 125) the thermal resistance is the dominating factor in determining the FOM and the heat

sinks with circular pin-fins were observed to have the best performance followed by the elliptical pin (Fig. 8).

2. At medium Re (125 < Re < 200) both the thermal resistance and the pumping power are significant contributors

to FOM term and elliptical pin-fin heat sinks shows the best performance (Fig. 8).

3. At high Re (Re > 200) the pumping power will dominate the FOM term and this will lead to the better

performance of the rectangular pin-fin heat sinks over the other shaped structures (Fig. 7 and 8).

References 1Chen,H.-T., Chen, P.-L, Horng, J.-T., and Hung, Y-H., “Design optimization for pin-fin heat sinks,” Journal of Electronic

Packaging, Transactions of the ASME, Vol. 127, No. 4, 2005, pp. 397-406. 2Park, K., Choi, D.-H., and Lee, K.-S., “Numerical shape optimization for high performance of a heat sink with pin-fins,”

1umerical Heat Transfer; Part A: Applications, Vol. 46, No. 9, 2004, pp. 909-927. 3Park, K., Rew, K.-H., Kwon, J.-T., and Kim, B.-S., “Optimal solutions of pin-fin type heat sinks for different fin shapes,”

Journal of Enhanced Heat Transfer, Vol. 14, No. 2, 2007, pp. 93-104. 4Abdel-Rehim, Z. S., “Optimization and thermal performance assessment of pin-fin heat sinks,” Energy Sources, Part A:

Recovery, Utilization and Environmental Effects, Vol. 31, No. 1, 2009, pp. 51-65. 5Kosar, A., and Peles, Y., “TCPT-2006-096.R2: Micro scale pin fin heat sinks - Parametric performance evaluation study,”

IEEE Transactions on Components and Packaging Technologies, Vol. 30, No. 4, 2007, pp. 855-865. 6Peles, Y., Kosar, A., Mishra, C., Kuo, C.-J., and Schneidern, B., “Forced convective heat transfer across a pin fin micro heat

sink,” Journal of Electronic Packaging, Transactions of the ASME International Journal of Heat and Mass Transfer, Vol. 48,

No. 17, 2005, pp. 3615-3627. 7John, T. J., Mathew, B., and Hegab, H., “Characteristic Study on the Optimization of Pin-Fin Micro Heat Sink,” 2009 AMSE

International Mechanical Engineering Congress and Exposition, Lake Buena Vista, FL, 2009. 8Chintada, S., Ko, K.-H., and Anand, N. K., “Heat transfer in 3-D serpentine channels with right-angle turns,” 1umerical

Heat Transfer; Part A: Applications, vol. 36, no. 8, 1999, pp. 781-806.