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MICRO CHAEL HEAT SIK WITH EMBEDDED

PI-FI STRUCTURES T. J. John

1 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 dissipation of heat with the help of micro channel heat sink and micro pin-fin fin heat

sink has been a topic of interest for many researchers over a decade. The comparison between

these two heat sink and the advantage and disadvantages of one over the other has been studied

by researchers. In this paper, the authors are trying to study the effect of introducing pin-fin

structures inside the micro channel heat sink. A FOM term is introduced in the paper to

evaluate the overall performance of the ordinary micro channel heat sink and the micro channel

heat sink with pin-fin structures embedded in it. The effect of introducing different shapes of

pin-fin structures inside the micro channel is also studied in the paper. The study results showed

that there is a huge increase in the overall performance of the micro channel heat sink by

introducing pin-fin structures inside the channel, but the study also showed that the effect of

introducing different shapes of pin-fin structures inside the channel is negligible.

.

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 2010-4780

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

American Institute of Aeronautics and Astronautics

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out = outlet

wall = wall

th = thermal

non = non dimensional

stu = with structure

without_stu = without structure

I. Introduction

icro channel heat sinks are being used as an effective method for dissipation of heat from electronic devices

for many years. Many researchers have done extensive research on increasing the heat dissipation efficiency

of micro level heat sinks [1,2]. The micro channel heat sinks have the advantage of increased heat transfer

coefficient compared to the macro level heat sinks due to the thinner thermal boundary layer. The heat transfer

coefficient is inversely proportional to the thickness of the thermal boundary layer, and the micro channel heat sinks

have the advantage of having very thin thermal boundary layer hence, increasing the heat transfer coefficient. The

effort to come up with more and more effective designs of heat sinks lead to the development of the pin-fin heat

sinks which is one of the most promising heat sinks developed till date [1-7]. In the pin-fin heat sinks the liquid flow

will be continuously disturbed by the fin structures, thereby forming a continuously developing flow which

increases the heat transfer efficiency of the heat sink. In this paper an effort is put to study the overall thermal

performance of a micro channel heat sink with pin-fin (MCHSPF) structures embedded in it. The advantage of the

thin thermal boundary layer of micro channels combined with the advantage of continuously developing flow

created by the pin-fin structures make the thermal performance (MCHSPF) much higher than the ordinary micro

channel based heat sink.

Qu W. conducted a study to compare the thermal performance of a micro channel heat sink with a micro

pin-fin based heat sink having same hydraulic diameter for the liquid flow [3]. Micro pin-fin heat sinks with

rectangular fins where made of copper substrate and water was used as the cooling agent. A micro channel heat sink

with same hydraulic diameter was analytically modeled and the results obtained from both the heat sinks were

compared to each other. The study revealed that the pin-fin heat sinks has a lower convective thermal resistance at

high liquid flow rates but the pressure drop across the device was much higher than the micro channel heat sinks. Qu

w. and Mudawar I. studied the three dimensional fluid flow and heat transfer inside a micro channel heat sink

numerically, and solutions were obtained using simple algorithm [4]. Even though the study didn’t reveal any

exiting results the work provided a detailed discussion on the numerical analysis of the fluid flow and heat transfer

and provided a good understanding on the validation of the numerical analysis. Yavo Pleles et al. conducted a study

on the optimization of the micro pin-fin heat sink with silicon as the substrate and water as the cooling agent [5].

The study suggested the usage of low density pin-fins for a low Reynolds number (liquid flow) application and

higher density pin-fins for a higher Reynolds number application. The same group came up with another paper in

2007 studying the thermal resistance and the pressure drop of a micro pin-fin heat sink [6]. Four different shapes of

pin-fin structures (circle, hydrofoil, cone, and rectangle) were subjected to the analysis and once again silicon was

used as the substrate and water as the cooling agent. 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 conditions, 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.

In order to study the overall performance of the MCHSPF a figure of merit term (FOM) which consists of the

overall thermal resistance of the heat sink and the pumping power is used in this paper. The thermal resistance of the

MCHSPF is compared with the thermal resistance of the micro channel heat sink for a wide range of Reynolds

number ranging from 50 to 500. The computer simulations used for the entire study were generated using CFD

software COVENTORWARE™. The liquid flow rate through the heat sinks varies corresponding to the Reynolds

numbers at the entrance of the heat sinks. Both the heat sinks under study are of 1cm length and width, and a small

section of the heat sink consisting of a micro channel and half of the channel spacing on both side of the channel is

developed (assuming repeatability towards both sides) for the simplicity ease of the study (fig: 1). The studied

portion of the heat sink have 1cm length and 375 µm width so that 26 repeating units makes the entire heat sink. A

M

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uniform heat flux of 400kW/m2 is applied to the bottom of the heat sink. Silicon with 500 micrometer thickness is

used as the substrate and deionized water is used as the cooling agent. The liquid channels are 150 micrometer deep

and 225 micrometers wide. The pin-fin structures are 150 micrometer high and the cross sectional width at the

center of the pin-fin structures is kept constant as 75 micrometers, so the minimum area available for the liquid flow

around the pin-fin structures will remain the same for all the fins. Three shapes of the pin-fin structures are subjected

to the study in this paper, and their thermal performance while embedded inside the channel is compared. The

overall performance based on the FOM of the MCHSPF with circular pin-fin is compared with the ordinary micro

channel heat sinks by keeping the pressure drop across both the models same. The pressure drop across both the

models is varied from 25kPa to 250kPa and the FOM value obtained from both the models are compared and the

results are discussed in this paper.

II. Theory

All the models developed in this study are solved using the computer simulations generated using

COVENTORWARE™ by solving four governing equations: continuity equation, momentum equation and two

energy equations. Certain assumptions are made for the ease of solving the models:

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.

Figure 1: Cross sectional view of the micro channel with pin-fin structures in two different planes YZ (X is

through the center of a pin) and XY (Z at the middle of the total width))

W2

W1

H1

H

W

W3

W4

Substrate

Liquid Liquid

X

Y L

H1 H

Liquid

B.

A.

Y

Z

Pin-fin

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Figure 1 shows the cross sectional view in two different planes (YZ plane and XY plane) of the pin-fin model that is

studied in this paper. All the governing equations used for obtaining the solution of the models are given below.

0=⋅∇ Vr

(1)

VPVVrrr

2)( ∇+−∇=∇⋅ µρ (2)

FFFP TkTCV 2∇=⋅∇r

ρ (3)

02 =∇ SS Tk (4)

Equations 1 through 4 give the vector form representation of the governing equations used to obtain the model

solution. Equations 1 and 2 are the continuity and the momentum equations and equations 3 and 4 give the energy

equations for the liquid and substrate. The boundary conditions used for obtaining the solution of the governing

equations are discussed below.

vVin&& = (5)

0=outP (6)

0=wallV

r (7)

The flow rate at the entrance of the channel is calculated by multiplying the cross sectional area available for the

liquid flow times the velocity of the liquid flow. The liquid flow rate is one of the input parameter for the model and

is represent by Eq. 5. The pressure at the outlet of the channel is taken as zero, and the velocity at the walls of the

channel is kept at zero (non slip condition). In reality, the pressure at the outlet of the liquid channel is not zero, but

since in this study the concern is only about the pressure drop across the liquid channel this assumption will hold for

this particular case. The boundary conditions from 8 to 11 are used for solving the governing equations for the

substrate. A uniform heat flux is applied to the bottom of the substrate of the heat sink and this condition is given in

Eq. 8.

",0,

qy

Tk

zyx

SS =∂

∂−

=

(8)

0=∂

∂

Ω∂ T

y

TS (9)

Where T

Ω∂ represent the top surface of the pin-fin structures and top surface of the channel spacing. The heat loss

from the top of the pin-fin and from the top of the channel spacing is considered to be zero (Eq. 9).

0,,0,,

=∂

∂=

∂

∂

== zyx

S

zyLx

S

x

T

x

T (10)

0,0,0,0,

=∂

∂=

∂

∂

=≤≤=≤≤ WzHyx

S

zHyx

S

z

T

z

T (11)

The heat loss from the inlet and outlet side of the substrate is assumed to be zero (Eq. 10) and a symmetry condition

is assumed on both sides of the model (Eq. 11). The boundary conditions 12 to 15 are used for solving the energy

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equations for the liquid. The inlet temperature of the liquid is kept at 278.15 K (Eq. 12) and the heat loss from the

outlet section of the liquid channel to the ambient is considered to be zero (Eq.13).

inzyxF TT == ,,0

(12)

0,,

=∂

∂

= zyLx

F

x

T (13)

043,,21,,

=∂

∂=

∂

∂

≤≤=≤≤= WzWHyx

F

WzWHyx

F

y

T

y

T (14)

Ω∂Ω∂ ∂

∂=

∂

∂

n

Tk

n

Tk S

SF

F rr (15)

In most of the actual micro channel heat sinks made of silicon substrate the top surface of the channels will be

sealed using a glass plate, so the heat transfer from the top of the liquid to the ambient will be negligible. The same

condition is applied to the models in this study and is represented using Eq. 14. The heat transfer from the liquid to

the substrate is same as the heat transfer from the substrate to the liquid (Eq. 15). Here Ω∂ represents the interface

between the solid and liquid.

The thermal resistance and the pumping power are calculated using the values obtained from the solution of

the models. The pumping power and the thermal resistance obtained from the MCHSPF and the ordinary micro

channel heat sinks is non dimensionalized using the pumping power and thermal resistance values obtained from the

ordinary micro channel model itself. So the FOM term for the ordinary micro channel heat sink is always one and

this makes the comparison of the FOM term for each values of pressure drop across the both the models more easier

to interpret . The equations used for calculating the thermal resistance, pumping power and the FOM is given below

(Eqs. 16 to 20)

q

TTR

inFoutS

th

,, −= (16)

VPPP &×∆= (17)

stuwithoutth

stuth

nonthR

RR

_,

,

, = (18)

stuwithout

stunon

PP

PPPP

_

= (19)

( ) ( )nonnonth PPR

FOM×

=,

1 (20)

Since the FOM term is inverse of the thermal resistance multiplied by the pumping power, higher the value of the

FOM term better is the overall performance of the heat sink.

III. Mesh Optimization and Grid Dependency

All the above governing equations are solved using 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

of ordinary micro channel heat sink and micro channel heat sinks with square pin-fin structures 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 dimensions of 50 µm, 15 µm and 10 µm (for ordinary micro channels)

and 25 µm, 15 µm and 10 µm ( for micro channels with square pin-fins) along the x, y and z axes and the minimum

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element size used is 40µm, 6 µm and 6 µm (for ordinary micro channels) and 15µm, 10 µm and 8 µm for micro

channels with square pin-fins) along the x, y and z axes. While meshing the other micro channels with circle and

rhombus structures 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 6 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)

50 × 8 × 8 613264 307.112 12.083

50 × 8 × 6 808744 307.123 12.113

50 × 6 × 6 1096208 307.125 12.125

Table 1. Grid dependency of Manhattan bricks

Element size (µm) umber of odes Maximum temperature at

substrate (K)

Pressure drop (kPa)

35 × 12 239636 295.365 33.710

20 × 10 654635 295.359 33.868

20 × 8 821240 395.346 34.046

Table 2. Grid dependency of Extruded bricks

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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,

375 µm in y direction and 500 µm in z direction. The

heat sink (Fig. 4)has a liquid flow rate with a Re of

300 at the entrance of the model, and a uniform heat

flux of 400kW/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 maximum temperature of the substrate

and the average temperature of the liquid inlet is

obtained from the model results and the thermal

resistance is calculated. The pumping pressure is

calculated from the pressure drop across the device

(obtained from the model) multiplied to the liquid

flow rate thorough the channel.

The comparison of the thermal resistance and pressure drop of both the models (MCHSPF and the ordinary

micro channel) is given in Fig. 5 and Fig. 6

Figure 5 shows a decrease in the thermal resistance of the micro channel with the introduction of pin-fin

structures to the channel. The difference in the thermal resistance is dominant even at low Re (like 50) and retains

the reduction in thermal resistance at higher magnitude of Re. The decrease in the thermal resistance in the micro

channels with pin-fin structures is due to the continuously developing flow around the pin-fin structures inside the

channel. The flow through the micro channel with pin-fins is a continuously developing flow and this helps in the

increase of the heat transfer coefficient of the micro channel heat sink, which in turn reduces the thermal resistance

of the entire device. The flow distribution and the pattern of the continuously developing flow are shown in Fig. 7.

The decrease in the thermal resistance of the micro channel heat sink is an advantage of introducing the pin-fin

structures inside the channel, but this advantage comes along with the disadvantage of the increase in the pressure

drop across the device. The comparison of the pressure drop across both the devices is given in Fig .6. It can be

observed from the figure that as the Re of the liquid flow through both the devices increases the pressure drop across

the devices is also increasing. But for the model with the pin-fin structures introduced to the channel the increase in

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0 100 200 300 400 500 600

Rth

[K

/W]

Reynolds Number

Micro Channel

Channel with Pin-fin

0.0

50.0

100.0

150.0

200.0

250.0

0 100 200 300 400 500 600

Pre

ssu

re D

rop

[k

Pa]

Reynolds Number

Micro Channel

Channel with Pin-fin

Figure 4: Contour Plot of temperature profile in a

micro channel with Pin-fin structures.

Figure 5: Comparison of the thermal resistance

of both MCHSPF and the ordinary micro channel Figure 6: Comparison of pressure drop across

both MCHSPF and the ordinary micro channel

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pressure drop across the device with the increase in the Reynolds number is more predominant. Since the advantage

of reduction in the thermal resistance while using the pin-fin structures inside the micro channel is nullified by the

disadvantage of increase of pressure across the device, a comparison of the overall performance of the heat sink

cannot be concluded using the results shown in Fig 5 and 6. A comparison of both the models with constant pressure

drop applied across the devices and with the introduction of the FOM is given later in this section.

The pressure drop across the micro channel with pin-fin structure of three different shapes is shown in Fig. 9. At

low values of Re, the pressure drop across all the three micro channels with three different shapes of pin-fin

structures are close to one another, but as the magnitude of the Reynolds number increases the pressure drop across

all three models shows different values. The pressure drop across the micro channel with the square and circle pin-

fin structure show almost the same pressure drop for all values of the Re, but the pressure drop across the micro

channel with rhombus shaped pin-fin shows an increase in the pressure drop compared to the other two structures

predominantly at high values of Re. This increase in pressure drop is due to the well disturbed flow pattern of the

liquid around the rhombus structure at high values of Re. The liquid flow around the rhombus structure show a

higher disturbance when compared to the other two pin-fin shapes.

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

0 100 200 300 400 500 600

Rth

[K

/W]

Reynolds Number

Square Pin-finCircle Pin-finRhombus Pin-fin

0.0

50.0

100.0

150.0

200.0

250.0

0 100 200 300 400 500 600

Pre

ssu

re D

rop

[k

Pa]

Reynolds Number

Square Pin-finCircle Pin-finRhombus Pin-fin

The velocity profile of the liquid flow inside the

micro channel with the Pin-fin structure embedded

inside the channel is shown in Fig. 7. The continuously

developing flow inside the channel increases the heat

transfer coefficient of the device. But the introduction

of the Pin-fin structure inside the liquid channel will

increase the resistance to the liquid flow through the

channel increasing the pressure drop across the device.

The effect of different shapes of Pin fin structure inside

the micro channel on the thermal resistance and the

pressure drop across the device is plotted in Fig. 8and

9. From Fig. 8, it can be seen that the change in the

thermal resistance of the micro channel heat sink

device with the change in the shape of the Pin-fin

structure embedded inside the channel is not

predominant throughout the value of Re studied in this

paper. There is a slight change in the thermal

resistance at certain values of Re, but it cannot be

concluded that the change is due to the change in the

shape of the structure because of its negligible

magnitude

Figure 7: The velocity profile of the liquid flow

inside the micro channel with Pin-fin structure.

Figure 8: Plot of thermal resistance against the

change in the Reynolds number with different

shape of structures embedded inside the micro

channel

Figure 9: Plot of the pressure drop across the micro

channel against the change in the Reynolds number

with different shape of structures embedded inside

the micro channel

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In order to study the effect of introducing the pin-fin structure inside the ordinary micro channel heat sinks, two

model were developed 1) ordinary micro channel heat sink and 2) micro channel heat sink with circle shaped pin-fin

structures embedded inside the channel. Both the models were solved with constants pressure drop across the device

and the results are used to derive the FOM term. The comparison of the FOM terms for both the models are shown

in Fig 10.

It can be seen from the figure that the FOM for the MCHSPF is much higher than the FOM term for the ordinary

micro channel. This phenomenon occurs due to two reasons; first one is the decrease in the thermal resistance of the

micro heat exchange due to the introduction of the pin-fin structure inside the channel causing a flow disturbance

increasing the heat transfer coefficient of the heat sink (Fig. 11). The second reason is the decrease in the flow rate

of the liquid through the device. As the MCHSPF has a much higher pressure drop across the device the liquid flow

rate through the device with pin-fin structures will be much lesser than the ordinary micro channel heat sink (Fig.

12). The smaller liquid flow rate through the device will decrease the pumping power needed to attain the required

pressure drop. The decrease in the pumping pressure by a considerable amount increases the FOM term of the

device because the pumping pressure in inversely proportional to the FOM term.

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0 50 100 150 200 250 300

FO

M

Pressure Drop [kPa]

Micro Channel

Channel With Pin-fin

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 50 100 150 200 250 300

Rth

Pressure Drop [kPa]

Micro channel

Channel with Pin-fin0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 50 100 150 200 250 300

Pum

pin

g P

ow

er

Pressure Drop [kPa]

Micro channel

Channel with Pin-fin

Figure 10: Comparison of FOM term for both the models

(MCHSPF and ordinary micro channel)

Figure 11: Plot of non dimensional Rth against

different Pressure Drop across both models

MCHSPF and the ordinary micro channel

Figure 12: Plot of non dimensional Pumping

power against different Pressure Drop across

both models MCHSPF and the ordinary micro

channel

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Figure 11 shows the decrease in the nondimensionalized thermal resistance of the micro channel heat sink with the

introduction of the pin-fin structures inside the channel. The decrease in the thermal resistance in notable for all

values of pressure drops considered in this study. Figure 12 gives the decrease in the nondimensionalized pumping

power with the use of the pin-fin structures inside the micro channel. The huge decrease in the pumping power

(almost 1/3rd

of the pumping power for the ordinary micro channel heat sink) is responsible for the huge increase in

the FOM for the micro channels with pin-fin structures.

V. Conclusion

The effect of introducing the pin-fin structures inside a micro channel heat sink was studied in this paper for

different Reynolds number varying from 50 to 500. In order to prove the dominance of the MCHSPF over the

ordinary heat sink a FOM term was introduced in the paper, a MCHSPF and an ordinary micro channel heat sink was

developed and solved for constant pressure drop across both the devices. The effect of both the thermal resistance

and the pressure drop across the MCHSPF with three different shapes of pin-fins introduced into the micro channel is

studied for a range of Reynolds number from 50 to 500.The conclusions of all the studies done in this paper is

presented below:

1. The thermal resistance of the micro channel heat sink with pin-fin structures embedded inside the channel is

much lower than the thermal resistance of the micro channel without pin-fin structures.

2. The pressure drop across the micro channel heat sink with pin-fin structures embedded inside the channel is

very high than the pressure drop across the micro channel without pin-fin structures.

3. The change in the thermal resistance of the micro channel heat sink with different shapes of pin-fin structures

embedded inside the channel is negligible.

4. The change in the pressure drop across the micro channel heat sink with rhombus shaped pin-fin structures is

much higher than the channels with square and circle pin-fin structures.

5. Both the thermal resistance and pumping power reduces considerably when pin-fin structures are introduced

inside the channel causing an increase in the FOM term.

6. The FOM of the micro channel heat sink with pin-fin structures embedded inside the channel is significantly

larger (three times) than the FOM of the micro channel without pin-fin structures

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