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Heatsink CFD Analysis And Optimization

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 KOCAELİ UNIVERSITY

ENGINEERING FACULTY

MECHANICAL ENGINEERING DEPARTMENT

BACHELOR DEGREE FINAL PROJECT

HEATSINK CFD ANALYSIS AND

OPTIMIZATION

Consultant Professor: Prof.Dr.Hasan KARABAY

Prepared By;

Burak ASLAN

Eren YALÇINÖZ

KOCAELİ 2022
 T.C
KOCAELİ UNIVERSITY* ENGINEERING FACULTY
MECHANICAL ENGINEERING DEPARTMENT

HEATSINK CFD ANALYSIS AND

OPTIMIZATION

BACHELOR DEGREE FINAL PROJECT

Eren YALÇINÖZ
170218006

Burak ASLAN
170218038

The Department of Thermodynamics and Heat Technique

Consultant Professor: Prof. Dr. Hasan KARABAY

MAY 2022

1
ABSTRACT
Overheating of the components used in electronic systems due to heat generation during
operation may cause the performance of these components to decrease or to be damaged.
Especially today, with the developing technology, the increase in the power density of the
devices has made the overheating problems even more obvious. Therefore, effective cooling of
these components is of great importance for manufacturers. Fin geometry, dimensions and
arrangement of finned heat sinks are extremely important factors affecting the heat transfer rate
and pressure drop. In this study, aluminum coolers, which are offered as the cheapest and easiest
solution to the cooling problem, which is one of the most encountered problems in electronic
devices, were examined and compared according to their fin types and designs, and an
optimization study was carried out. In this study, designs were made with the SolidWorks
package program and numerical analyzes were performed using ANSYS Fluent computational
fluid dynamics. For experimental studies, tests were carried out on the Natural/Forced
Convection Heat Exchanger test device at the Materials Institute within the scope of TÜBİTAK
2247-C program. The sample with 6 fins was tested at 4 different speeds under the same
conditions, and the pressure drop and air duct outlet temperatures were determined. The
experiment was simulated in the ANSYS Fluent 2021 R2 Package program under the same
conditions. The simulation analysis results were compared with the experimental results. For
Finnish optimization, a total of 12 variations were made, 3 different cases. The sample width
and fin lengths were kept constant in each variation and the sample length was changed. In
addition, each variation group was examined in different fin thicknesses. The findings show
that fin integration has a positive effect on heat transfer and a negative effect on pressure drop.

Keywords: Heatsink, Fins, Heatsink Optimization, CFD Simulation, Design Optimization,

Experimentation

2
INDEX
ABSTRACT……………………………………………………………………………….…...2

INDEX…………………………………………………………………………………………3

ICONS AND ABBREVIATIONS………………………………………………...…...………5

INDEX OF FIGURES…………………………………………………………………………6
INDEX OF TABLES……………………………………………………………………..……8
ACKNOWLEDGEMENT…………………………………………………………....………..9
1.INTRODUCTION……………………………………………………………..….……..…10
1.1 Purpose Of The Study……………………………………………………………………11

2.LITERATURE RESEARCH………………………………………………………….……11

3. HEAT TRANSFER MECHANISM………………………………………………….……14

3.1 Conduction Heat Transfer………………………………………………..………….……15

3.2 Convection Heat Transfer……………………………………………………...…………16

3.2.1 Natural Convection…………………………………………………………………..…17

3.2.2 Forced Convection……………………………………………………….…………..…17

3.3 External Flow………………………………………………………………………….…19

3.4 Internal Flow………………………………………………………………………...……19

3.5 Radiation Heat Transfer……………………………………………………..……………19

3.6 Average Velocity Calculation………………………………………………….…………20

4. FLUID DYNAMICS……………………………………………….………………………20

4.1 Numerical Modeling…………………………………………………………...…………21

4.2 Using of Fins…………………………………………………………………….……..…22

5.COMPUTATIONAL FLUID DYNAMICS (CFD) …………………………………..……23

5.1 General CFD………………………………………………………………………...……24

5.2 Navier-Stokes Equations…………………………………………………………….……24

5.3 Continuity Equation……………………………………………………….…………...…24

6. ANSYS FLUENT HAD SOFTWARE PROGRAM………………………………………25

3
7.EXPERIMENTAL STUDIES………………………………………………………………26

7.1 NATURAL AND FORCED HEAT CONVECTION EXPERIMENT SETUP……….…26

7.1.1 Possible Experiments………………………………………………………….…..……26

7.1.2 Device Dimensions……………………..………………………………………………26

8. CFD EXPERIMENTAL STUDIES …………………………………………….…………29

8.1 Experimental Procedure………………………..…………………………………………29

8.2 Experiment Results………………………………………...…………………………..…30

8.2.1 Evaluation Of Experimental Results ………………………………………….…..……31

9. MODEL AND METHOD…………………………...………………………….….………31

9.1 Geometric Model……………………………………………….……………...…………31

10. SETTING THE OPTIMUM MESH FOR THE SOLUTION………………….…………33

10.1. Inflation……………………………………………………………..……………..……34

11. INSTALLATION AND SOLUTION (SETUP-SOLUTION) SETTINGS………………37

11.1 K-epsilon (k-є) Model……………………………………..…………………….………38

11.2 Material Used As Fin Material…………………………………………………….…….38

11.3 Boundary Conditions………………………………..………………………………..…39

12. COMPUTATIONAL FLUID DYNAMICS ANALYSIS RESULTS……………………39

13. FIN OPTIMIZATION……………………………………………..………………...……46

REFERANCES…………………………………………………………….…………………47

4
ICONS AND ABBREVIATIONS

Mem Safe Bending Moment

µ Dynamic Viscosity
C Drag Coefficient
Cf Coefficient of inertia
h Heat Convection Heat Transfer Coefficient
ṁ Mass Flow Rate
k Heat transfer coefficient
Nu Nusselt Number
Pr Prandtl Number
Re Reynolds Number
T Temperature (°C)
ρ Density (kg/m3)
Q Heat Transfer (watt )
A Area (m2)
ΔT Temperature Differance
Tw Surface Temperature (°C)
Tamb Ambient Temperature (°C)
Gr Grashof number
g Gravitational acceleration due to Earth
Ts Surface temperature (°C)
T Bulk temperature (°C)
L Vertical length (m)
D Diameter (m)
ν Kinematic viscosity

5
INDEX OF FIGURES
Fig.1. Types of heat dissipation

Fig.2. Mini-channel heatsink

Fig.3. Darcy-Weisbach and Colebrook Equations

Fig.4. Forced heat convection machine

Fig.5. Experimental setup representation picture

Fig.6. Experimental setup representation picture

Fig.7. Experimental setup representation picture

Fig.8. The heater with a power of 73.09 W gives heat uniformly

Fig.9. Examples of mini-channels fin

Fig.10. Heatsink specimen dimensions

Fig.11. Drawing the sample in solidworks program

Fig.12. Creating the experiment flow field

Fig.13. Establishment of flow volume

Fig.14. Heatsink experimental setup in the channel

Fig.15. Surface mesh structure in triangle structure

Fig.16. Surface mesh image

Fig.17. Recommended limit values for mesh quality.

Fig.18. Poly-hex mesh structure (Front view)

Fig.19. Poly-hex mesh structure (Top view)

Fig.20. Poly-hex mesh structure (Front view)

Fig.21. Poly-hex mesh structure (Top view)

Fig.22. Calculation of total heat transfer rate

Fig.23. Pressure drop convergence result

Fig.24. Outlet temperature

6
Fig.25. Convergence Result

Fig.26. Static temperature contour

Fig.27. Pressure drop convergence result

Fig.28. Outlet temperature

Fig.29. Convergence result

Fig.30. Static temperature contour

Fig.31. Pressure drop convergence result

Fig.32. Outlet temperature

Fig.33. Convergence result

Fig.34. Static temperature contour

Fig.35. Pressure drop convergence result

Fig.36. Outlet temperature

Fig.37. Convergence result

Fig.38. Static temperature contour

Fig.39.Velocity magnitude vectors image

Fig.40.Velocity magnitude vectors image

Fig.41. Velocity magnitude vectors image

Fig.42. Velocity magnitude vectors image

Fig.43. Total pressure contours image

7
INDEX OF TABLES

Table 1. Heat sink geometry used for simulation

Table 2. Experimental test results

Table 3. Material properties used in the experiment: Al 356 series

Table 4. Properties of the fluid (air) used in the experiment

Table 5. CFD-Fluent analysis results

Table 6. Fin optimization table and results

8
ACKNOWLEDGEMENT
We would like to thank our esteemed graduation project teacher Prof.Dr.Hasan KARABAY
who provided all kinds of guidance during the study period, encouraged us with his positive
attitudes, made us look at our work from different perspectives with her knowledge, and we are
proud to work with and to be his students.

The data of the experimental studies were obtained by performing the 2247-C Trainee Researcher
Scholarship Program at the TÜBİTAK Materials Institute Laboratory. We thank the Principal
Investigator Dr. Levent TURHAN and TÜBİTAK Materials Institute for their contributions.
Data were obtained within the scope of the project titled TUBITAK MAM 5215A02 Coded
Metal Foamed Heat Exchanger Development for Electronic Circuit/System Cooling with
internal support.

Burak ASLAN
İzmit, 2022

Eren YALÇINÖZ
İzmit, 2022

9
1.INTRODUCTION

In the modern world, people are using more and more new devices and electronic equipment
every day. These devices and electronic equipment used are a very important part of people's
lives, and even thinking about the failure of these devices to work properly creates a number of
problems for people. The heat generated by devices and electronic equipment is the main cause
of malfunctions. With the continuous development of electronic devices towards high
performance and miniaturization size, heat dissipation problem has become a major obstacle to
their development. In order for this heat generated by the devices not to damage the device
itself, the heat generated must be transferred to the environment. Appropriate heat transfer
methods should be used to protect the devices. The choice of the appropriate method depends
on the required performance, cost, application, production capability and efficiency. Two
popular methods of heat transfer are forced convection and natural convection. Forced
convection requires an external fan or blower to create and increase the flow movement. Adding
an external device requires an area for installing the device and an extra power to operate it,
which in many cases may be insufficient. Another very common method, natural convection
heat transfer, is caused by the lifting force of the flow as a result of a change in density in the
surrounding fluid caused by a temperature difference. This cooling method is noiseless and
trouble-free, and it is simple and low-cost, as it does not require extra power to operate any
circuitry or fan. However, natural convection generally has a low heat transfer capacity due to
its low heat transfer coefficient. Therefore, some innovative and efficient ways are needed to
improve heat transfer by convection.[1]
Today's rapid IT development like internet PC is capable of processing more data at tremendous
speed. This leads to higher heat density and increased heat dissipation, making CPU
temperature rise. CFD is gaining popularity especially as a decision support tool for the product
design process. Even a decade ago, commercial CFD software packages were rarely used for
heat transfer analysis, owing to lack of tools or a lack of details for heat transfer in them.
Especially, analyzing conduction and radiation together with convection was not possible.
Currently, all popula CFD software packages have tools for handling coupled conduction,
convection and radiation problems.[1]

10
1.1 Purpose Of The Study
The aim of this study is to investigate the temperature and pressure distributions of heat sink
models with different geometries at different speeds with a computational fluid dynamics and
heat sink optimization study.

In this study, a literature review was first conducted in order to better understand the subject
and shed light on the continuation of the study.

In the second part, heat transfer methods are defined and the topic of heatsink is discussed.

2.LITERATURE RESEARCH
A lot of research has been done for years to use aluminum coolers more efficiently. In 2010,
Dong-Kwon Kim (2010) made an optimization study by changing the fin width in plate fin
coolers. Kim used rectangular, triangular and inverted trapezoidal plate fins in his work. As a
result of the study, it was found that in natural convection, air-cooled aluminum coolers, when
the fin thickness is increased normal to the fluid direction, the thermal resistance decreases by
10 percent. However, it has been found that the difference between the thermal resistances of
coolers of equal thickness and coolers of variable thickness decreases as the height decreases.
As the heat flux decreases or the height of the cooler decreases, the rate of decrease in thermal
resistance will also decrease. Variable-thickness fin heatsinks with better thermal efficiency are
candidates for the next generation heatsink solution. [2]

According to the results obtained, the interface temperature decreases as the fin length
increases, but this is not desirable since the weight increases linearly. [2]

11
LiuYi-bing (2012) made an optimization study by changing the fin length, width and number
of plate fins. According to the results obtained, the interface temperature decreases as the fin
length increases, but this is not desirable since the weight increases linearly. As the fin width
increases, the air flow becomes more difficult as the gap between the fins decreases and this
reduces the thermal efficiency. Increasing the fin width also increases the weight. Increasing
the number of fins decreases the interface temperature as it increases the surface area. However,
after a certain number of times, since the space between is narrowed, resistance to air flow
occurs and the interface temperature increases.[3]

Shen et al. (2013) investigated the effect of steering in plate fins. The effects of orientation of
rectangular fins on airflow and heat transfer in natural convection were investigated numerically
and experimentally. These experiments were repeated in 8 directions. Denser fin arrays were
found to be more affected by steering. Besides, computer data showed that mismatch between
heat transfer areas and natural convection flow and obstruction of convection flow are the two
main factors reducing heat transfer in rectangular fins.[4]

12
Akram Jahanbakhshi, Afshin Ahmadi Nadooshan and Morteza Bayareh are studied a
combination of response surface method and genetic algorithm is used to provide an optimized
model for microchannel heatsink with wavy microtubes. Response surface in terms of total
flow, the ratio of the microchannel and microtube flow, as well as the location and diameter of
microtubes are used to estimate various performance parameters of micro heatsink such as
pressure drop, heatsink surface temperature, entropy generation, etc. by using genetic
algorithm. It is found that the response surfaces for estimating the maximum CPU surface
temperature in the worst-case conditions have approximately 5% error and the average
temperature estimation of this surface has a maximum error of 3%, which indicates the
acceptable accuracy of estimating response surfaces for the thermal parameters of the model.
Accuracy diagrams of estimation of entropy-related parameters also show that the estimation
of response surfaces for the total entropy generation in this geometry is accurate. It is concluded
that the pumping power behavior of the system in terms of average surface temperature in the
Pareto diagram is the same as the logarithm behavior of pumping power. It is found that
changing the height of the microtube from the bottom of the heatsink does not affect the
pumping power.[5]

13
3. HEAT TRANSFER MECHANISM
The design of the cooler is also important, and it needs to be optimized by selecting the optimal
fin parameters and selecting the required size, fan power or blower. For relatively low heat flux
applications, air cooling by natural convection is ideal. Due to the low heat transfer efficiency,
refrigerants are needed to expand the surface in order for the cooling performance to be
sufficient. However, the heat transfer coefficient is very sensitive to the design and direction of
the coolant.[6]

The molecules of the hot body are faster. Heat is the spontaneous transfer of energy from high
temperature to low temperature due to temperature difference. The reason for the energy
transfer here is the temperature difference. This phenomenon is called heat. This phenomenon
is called heat. Heat does not pass, it is energy that passes. The transition takes place by
momentum diffusion. Heat is a vector quantity. It is not heat that passes from one place to
another, but rather momentum diffusion. Momentum diffusion is not something that is owned,
and only occurs when there is a temperature difference. The higher the temperature difference,
the greater the momentum diffusion. As long as the temperature of the substance is not 0 Kelvin,
the atoms in the substance are always in motion. At 0 K, the movement in the substance ends.
Heat travels between the system and its surroundings in a one-dimensional analysis. Heat is
transferred not only between the system and its surroundings, but also within the system
itself.[7]

Heat transfer occurs in every area of our daily life. Heat transfer takes place from the windows
and walls of our warm house to the cold outside environment. In order to reduce heat loss,
people insulate the walls by covering them with a material with lower heat permeability. This
insulation reduces heat transfer and reduces the heat loss of the house. First of all, mankind
himself is a source of heat, and even human life depends on heat. Excessive heat loss will cause
human death.[8]

Heat transfer mechanism; It has three different forms as conduction, convection and radiation.

Conduction occurs at the molecular level, and when there is a temperature difference in a
medium (solid, liquid, gas), heat is transferred by conduction until the temperature is equalized.
Transfers some of its energy as a result of the interaction of the higher-energy object with the
lower-energy neighboring object next to it. The statement that there is conduction in solids and
convection in liquids is not true. It only happens more visibly in solids.[9]

14
 Fig.1. Types of heat dissipation

The transfer of heat by convection occurs with the movement of a fluid (solid, liquid, gas).
Convection occurs in the boundary layer on the solid surface with the fluid in motion at different
temperatures.[10]

Radiation is a form of energy emitted by infrared waves or photons emitted by matter in

electromagnetic form. This occurs as a result of changes in the electron structure of atoms and
molecules. [10]

Conduction and convection require the presence of a mediator, but do not feel radiation. Since
heat transfer with radiation takes place at the speed of light, it is the mechanism by which energy
is transported the fastest. Heat transport from the sun to the earth occurs by the mechanism of
radiation.[10]

3.1 Conduction Heat Transfer

The state of heat conduction is expressed in differential form by the Fourier law of heat
conduction and one-dimensionally,

𝚫𝐓
𝑸̇𝒄𝒐𝒏𝒅𝒖𝒄𝒕𝒊𝒐𝒏 = −𝒌𝑨 𝚫𝐱 [𝑾] (1)

is written as.

Here, k is the thermal conductivity coefficient, which is a measure of the material's ability to
𝒅𝑻
conduct heat and the temperature gradient, which is the slope of the temperature curve.[10]
𝒅𝒙

15
The thermal conductivity of materials generally varies depending on the temperature. Thermal
conductivity does not depend only on k. It also depends on diffusion, which we call heat
capacity. Diamond has the highest coefficient of thermal conductivity. Silver, aluminum,
copper, graphite are some materials with high thermal conductivity. More heat is transferred
with these materials. Generally, aluminum is used nowadays because it is cheap.[10]

Heat is conducted in the decreasing temperature direction and hence when heat is conducted in
the positive x direction, the temperature gradient is negative. Thus, the negative sign shown in
the formula (2) ensures that the heat transfer in the positive x-direction is a positive
quantity.[10]

𝚫𝐓
𝑸𝒄𝒐𝒏𝒅𝒖𝒄𝒕𝒊𝒐𝒏 = 𝒌𝑨 𝚫𝐱 , 𝚫𝐓 > 𝟎 (2)

It is the formula used to calculate the heat transfer in one dimension, independent of time, in
the x direction, in conduction heat transfer, which is one of the heat dissipation methods.

For the formula (formula 2) shown, the temperature difference must be positive.

3.2 Convection Heat Transfer

There are two types of transport; forced convection and natural convection. Natural convection
is heat convection that takes place without any external influence from the outside. In forced
convection, an external effect, force is applied and heat convection is increased. The basic
equation of heat transport between a solid surface and a fluid, known as Newton's law of
cooling, is:

𝑾
𝑸̇𝒄𝒐𝒏𝒗𝒆𝒄𝒕𝒊𝒐𝒏 = 𝒉𝑨𝒔 (𝑻𝒘 − 𝑻𝒂𝒎𝒃) [𝒎𝟐 ] (3)

is written as.

𝑾
h= Heat Convection Heat Transfer Coefficient, [𝒎𝟐 𝑲]

𝑨𝒔 =Heat Transfer Area [𝒎𝟐 ]

𝑻𝒘 = Surface Temperature [°C]

𝑻𝒂𝒎𝒃 = Ambient Temperature [°C]- fluid temperature far enough from the surface also that is
any temperature outside the thermal boundary.

The convection heat transfer coefficient characterizes the flow and the fluid.

16
h= function(fluid,flow) → In the engineering flow problem, first of all, where and how the flow
takes place should be looked at.

3.2.1 Natural Convection

Natural convection can be summarized as transferring heat from the surface with the circulation
of the fluid or transferring heat to a lower temperature surface. Heat convection occurs with the
principle of "hot fluid rises, cold fluid descends" which is called the buoyancy effect. The reason
for the rise of the heated fluid is the increase in the volume of the fluid and the decrease in the
density of the fluid with the temperature.[10]

Natural convection is symbolized by the numbers Pr and Gr.

𝒈 𝜷 (𝑻𝒔−𝑻∞)𝑫𝟑
Gr= 𝝂𝟐
(4)

g= Gravitational acceleration due to Earth

𝟏
β= Coefficient of thermal expansion (equal to approximately𝑻𝒆𝒎𝒑𝒆𝒓𝒂𝒕𝒖𝒓𝒆(𝑲), for ideal gases)
Ts= Surface temperature
T∞=Bulk temperature
L= Vertical length
D= Diameter
ν = Kinematic viscosity.

There is movement in the air due to flow. Force is needed for movement to occur. It is "g" that
causes this force. The "Gr" is related to the "g". The warming air is not actually rising, it is
being raised. There is no reason for the warming air to rise. Force is required for movement.
There are gravitational forces and they are always downwards.The cold fluid descends and
becomes dominant.[10]

3.2.2 Forced Convection

Forced convection is called heat transfer by forcing the fluid to flow through an external source.
Forcing the fluid to flow over a surface is called “outside flow”, and forcing it inside a pipe is
called “internal flow”.[10]

Forced convection is characterized by the number Re.

f(Nu)=h=f(Re,Pr) → Re gives information about flow, Pr is about fluid.

𝛒𝒗𝒔 𝑫 𝒗𝒔 𝑫 𝒊𝒏𝒆𝒓𝒕𝒊𝒂 𝒇𝒐𝒓𝒄𝒆𝒔

𝑹𝒆 = = = (5)
𝛍 𝛖 𝒗𝒊𝒔𝒄𝒐𝒔𝒊𝒕𝒚 𝒇𝒐𝒓𝒄𝒆𝒔

17
 𝒌𝒈
𝛒=density of fluid [𝒎𝟑 ]

𝒎
𝛖𝒔 =velocity of fluid [ 𝒔 ]

D= Hydraulic diameter of the pipe (channel)

μ - Dynamic viscosity of the fluid

𝛍
𝜐 - Kinematic viscosity of the fluid (𝜐= 𝛒)

𝟒𝑨𝒄
𝑫=
𝑷

𝑨𝒄 =Channel cross-sectional area [𝒎𝟐 ]

P= Wet circumference length [m]

a=channel width

b=channel height

In order to understand the state of the flow, it is necessary to compare the Re number of the
flow with the critical Re number. The flow conditions are given in the table below to understand
whether the external and work flow is turbulent. The critical value of Re number is 2300 in
inflow and 5x105 in outflow.

Re < (Re)c𝑟itical Laminar Flow

Re > (Re)c𝑟itical Turbulance Flow

In this study, Re calculation was made for the channel in the determined cross-section and a
constant velocity value.

𝟒∗𝟎,𝟎𝟒∗𝟎,𝟎𝟔𝟒
𝑫= = 𝟎, 𝟎𝟒𝟗𝟐𝟑 𝒎
𝟐(𝟎,𝟎𝟒+𝟎,𝟎𝟔𝟒)

𝟏,𝟐𝟐𝟓∗𝟑∗𝟎,𝟎𝟒𝟗𝟐𝟑 𝒎 𝒌𝒈
𝑹𝒆 = = 𝟗𝟕𝟎𝟑, 𝟓𝟕 (V=3 , 𝛒 = 𝟏, 𝟐𝟐𝟓 (𝒇𝒐𝒓 𝟐𝟐°𝑪 𝐜𝐨𝐧𝐝𝐢𝐭𝐢𝐨𝐧),
𝟏,𝟖𝟔𝟒𝟓𝐱𝟏𝟎−𝟓 𝒔 𝒎𝟑

𝒌𝒈
( 𝛍 = 𝟏, 𝟖𝟔𝟒𝟓𝐱𝟏𝟎−𝟓 𝒎𝒔 (𝒇𝒐𝒓 𝟐𝟐°𝑪 𝐜𝐨𝐧𝐝𝐢𝐭𝐢𝐨𝐧)

Reynolds number is greater than 2300, the flow is turbulent for the specified conditions.

18
3.3 External Flow

For external flow, we can say that the boundary layers develop without any restrictions. Outside
the boundary layer there is a flow region where velocity and temperature variables can be
ignored. In turbulent flow constant surface heat flux conditions, the Nusselt number is
calculated by equation 6 ;[10]

𝟒⁄ 𝟏
𝑵𝒖 = 𝟎. 𝟎𝟑𝟎𝟖𝑹𝒆 𝟓 𝑷𝒓 ⁄𝟑 (6)

3.4 Internal Flow

It is a common practice for cooling and heating in flow heat transfer through a channel and
tube. The movement of the fluid is provided by the pump or the fan to realize the heat transfer.
It is important to identify the difference between internal flow and external flow. In external
flow, the fluid boundary conditions have an independent surface that is free to expand, but in
internal flow, the fluid is bounded by the internal surface. Equation 7 is used to find the Nusselt
number for in-pipe internal flow.[10]

𝒇
( )𝑹𝒆 𝑷𝒓
𝟖
𝑵𝒖 = 𝟏 𝟐
(7)
𝒇 𝟐
𝟏.𝟎𝟕+𝟏𝟐.𝟕( ) (𝑷𝒓𝟑 −𝟏)
𝟖

3.5 Radiation Heat Transfer

Radiation heat transfer is the energy that is emitted by matter in the form of photons or
electromagnetic waves. Radiation can be important even in situations in which there is an
intervening medium. An example is the heat transfer that take place between a living entity with
its surrounding.[10]

19
3.6 Average Velocity Calculation

The average velocity value is calculated with the equation obtained from the law of
conservation of mass equation, leaving the velocity (V) value alone.

𝒌𝒈
𝒎̇ = 𝝆𝑽𝑨 [ 𝒔 ] (8)

When we leave V alone from 8, we get 9.

𝒎̇ 𝒎
𝑽 = 𝛒𝐀 [ 𝒔 ] (9)
𝒌𝒈
𝒎̇ [ 𝒔 ] = mass flow rate
𝒌𝒈
𝜌 [ 𝟑 ] = density of fluid
𝒎
𝐴𝑘 (𝑚2) = channel cross-sectional area
𝒎
V ([ 𝒔 ]) = average velocity

4. FLUID DYNAMICS
Fluid dynamics is related to the motion of the fluid in the gas and liquid phases in terms of
energy, momentum and mass. The software program solves the area knitted with cellular
networks using equations governing the finite element method. The first approach to describe
the fluid field is to describe incompressible and isothermal flow with the 3 laws of conservation
of mass. By making these assumptions, density and viscosity can be seen as constant when the
𝒎
velocity is less than Mach number 0.3 (ℳ𝒶=0.3≈100 [ 𝒔 ]), and the temperature is relatively

low during the simulation of the flow field.[11][12]

Conservation of mass = amount of mass entering and amount of mass leaving are equal to each
other.

𝛛𝐮 𝛛𝐯 𝛛𝐰
+ 𝛛𝐲 + =𝟎 (10)
𝛛𝐱 𝛛𝐳

The following set of formulas are referred to as the incompressible Navier-Stokes equations of
nonlinear partial differential equations.

(11)

(Navier-Stokes Equations)
20
Conservation of Energy (1st Law of Thermodynamics) = The total amount of energy in the
system always remains constant.

The first law for a thermodynamic process without transfer of matter is often formulated as;

𝜟𝑼 = 𝑸 − 𝑾 (1.1)

where denotes the change in the internal energy of a closed system (for which heat or work
through the system boundary are possible, but matter transfer is not possible), denotes the
quantity of energy supplied to the system as heat, and denotes the amount of thermodynamic
work done by the system on its surroundings[11]

4.1 Numerical Modeling

ANSYS Fluent 2021 R2, a CFD program, was used for numerical analysis. To facilitate the
analysis, the following assumptions have been made:[12]

- The flow is three-dimensional, incompressible and in steady state;

- Flow type turbulent;

- Fluid and solid material properties do not change with temperature.

Conservation equations used in numerical analysis are given in Equation 1-5 below:

Conservation of mass;

(12)
Momentum in the x direction;

(13)
Momentum in the y direction;

(14)
Momentum in the z direction;

(15)
21
Energy Equation;

(16)
𝒎
u, v, w are the velocities ( 𝒔 ) in the x, y and z directions, respectively, in the Cartesian coordinate
𝒌𝒈 𝑱
plane, ρ the density of the fluid (𝒎𝟑 ), cp the specific heat of the fluid (𝒌𝒈𝑲), and μ the dynamic
𝑵𝒔
viscosity of the fluid (𝒎𝟐 ) , T represents the temperature (K) and g the gravitational acceleration
𝒎
also (𝒔𝟐) S the source term.[12]

Fig.2. Mini-channel heatsink

A heat flux of 10773.6877 W/m2 is applied from the lower base (x-z plane) of the mini-channel
given in Figure 2. The adiabatic boundary condition was applied to the side walls and ceiling
of the modeled mini-channel.

4.2 Using of Fins

The biggest advantages of using finned structures are;

• Increase in heat transfer rate

• Used for cooling equipment

• It is an easy and inexpensive method

The fins attached to the surfaces where the heat transfer is desired to be increased, provide the
improvement of cooling by increasing the surface area and ensuring that the heat transfer is
from a wider area.

22
The heat transferred to the air in the duct causes the air to heat up gradually and the duct outlet
temperatures increase in direct proportion to the heatsink length. However, since the pressure
drop is directly proportional to the heatsink length, it will increase the pressure drop with the
increasing heatsink length.

Fig.3. Darcy-Weisbach and Colebrook Equations

5.COMPUTATIONAL FLUID DYNAMICS (CFD)

CFD is a numerical calculation and analysis method of fluid dynamics. The approach of CFD
simulation is to divide the physical space where the flow takes place into small finite volumetric
elements and make numerical calculations on these elements. HAD has a computer-based
design and analysis technique. It is possible to simulate in all phases (solid, liquid, gas). In
addition, the CFD method has the opportunity to perform advanced simulations such as the
simulation of moving parts and acoustics. The flow in the study is turbulent flow.[13]

23
5.1 General CFD

The Navier-Stokes equations used in all problems related to fluid mechanics and heat transfer
are solved numerically. In this study, the Navier-Stokes equations are 2D coupled partial
differential equations. There are 3 different equations used in fluid dynamics. These are the
continuity, momentum and energy equations that express the behavior of the flow. These
equations are derived from simple physical laws such as conservation of energy, mass, and
momentum. Since these equations are too complex to solve analytically, it is necessary to solve
them with numerical simulations. Differential equations are divided into large algebraic
equations in order to solve them numerically in CFD simulation.[14]

5.2 Navier-Stokes Equations

The Navier-Stokes equations are derived from Newton's 2nd Law and can also be viewed as
the equilibrium force of an element with an extremely small volume. The Navier-Stokes
equations are expressed as in equation (Navier-Stokes Equations) below. The 3 partial nonlinear
differential equations are expressed with a different equation for each velocity vector.[13]

(17)

Navier-Stokes Equations

5.3 Continuity Equation

The continuity equation is based on the principle that "mass cannot be destroyed" and is
expressed as in equation 18.[12]

𝛛𝛒 𝛛(𝛒𝐮) 𝛛(𝛒𝐯) 𝛛(𝛒𝐰)

+ + + =𝟎 (18)
𝛛𝐭 𝛛𝐱 𝛛𝐲 𝛛𝐳

Assuming the flow is incompressible, the continuity equation becomes as in equation 19

below.[12]

𝛛𝐮 𝛛𝐯 𝛛𝐰
𝛛𝐱
+ 𝛛𝐲 + 𝛛𝐳
=𝟎 (19)

24
6. ANSYS FLUENT CFD SOFTWARE PROGRAM
ANSYS Fluent is the software program we use to perform Had analysis in our study. ANSYS
is general purpose software used by engineers to simulate all interactions of physics, fluid,
turbulence, structure, vibration, fluid dynamics, heat transfer and electromagnetic disciplines.
It is used in many industrial areas, from the wing of a fighter jet with a very strong air flow over
it, to combustion in an oven, from air bubbles to oil platforms, from blood flow in vessels to
semiconductor production, from clean room design to wastewater treatment plants. ANSYS,
which enables to simulate tests or working conditions, enables testing in a virtual environment
before producing prototypes of products. In addition, it offers the opportunity to identify and
improve weak points, calculate reality and predict possible problems with 3D simulations in
the virtual environment.[15] [16]

With its modular structure, ANSYS software allows only the required features to be used.
ANSYS can work in harmony with CAD and FEA modules, which are programs used in
engineering.[15] [16]

ANSYS can receive and read the CAD file and also allows creating a geometry with
preprocessing possibilities. Just like in the preprocessor, the finite element model required for
computation is created. After defining the loads, conditions, data and performing the analysis,
the results can be seen numerically and graphically.[15] [16]

ANSYS can perform advanced engineering analyzes quickly, safely and practically with
various communication algorithms, time-based loading features and non-linear material
models.[15] [16]

ANSYS Workbench is a platform that integrates simulation technologies and parametric CAD
systems with unmatched automation and performance. The power of ANSYS Workbench
comes from years of experience and ANSYS solver algorithms. In addition, the purpose of
ANSYS Workbench is to test, audit and develop the product in a virtual environment.[15][16]

25
7.EXPERIMENTAL STUDIES
7.1 NATURAL AND FORCED HEAT CONVECTION EXPERIMENT SETUP

Fig.4. Forced heat convection machine

This experimental setup was used to examine natural and forced heat convection, which is one
of the heat transfer mechanisms. Flat plate type and rod type heaters are available.

7.1.1 Possible Experiments

1. Calculation of energy balance by natural and forced convection in different types of heat
exchangers
2. Variation of the total heat transmission coefficients depending on the speed in different
types of heat exchangers
3. Calculation of the surface thermal conductivity value at different speeds for different
types of heat exchangers
4. Calculation of thermal efficiency of different types of heaters in natural and forced
convection states

7.1.2 Device Dimensions

AxBxH=600x600x1790 mm

26
 Fig.5. Experimental setup representation picture
The device uses air as the fluid type. The flow rate of the fan can be controlled and the fan
speed can be measured. The necessary heat is provided by the resistance. The temperature
sensors work with direct air contact. At the same time, the fan and temperature values can be
displayed digitally.

Fig.6. Experimental setup representation picture

27
 Fig.7. Experimental setup representation picture
The air duct of the experimental setup is specially insulated. There is no heat transfer between
the inside of the air duct and its surroundings.

28
8. CFD EXPERIMENTAL STUDIES
8.1 Experimental Procedure
The experiment was carried out in a forced/natural convection heat exchanger test setup at 4
different speeds (1,2,3,4.5) (m/s). The fluid air entering the test setup was kept at a constant
room temperature of 22 °C throughout the experiment. A constant 73.09 W heat was given with
a resistor from the back of the sample. In the test setup, fluid air entered from the top of the
device and exited from the bottom. The test was continued until the sample surface temperature
remained constant. In the test device, air inlet and outlet temperatures and pressures are
measured instantaneously at the inlet and outlet of the air duct. The environment of the air duct
is completely isolated. With this test setup, the air inlet temperature and pressure are measured.
At the same time, when the air takes heat from the sample and comes to the outlet of the duct,
the outlet temperature and pressure of the air are measured.

Fig.8. The heater with a power of 73.09 W gives heat uniformly

Fig.9. Examples of mini-channels fin

29
 Table 1. Heat sink geometry used for simulation

The dimensional values of the tested sample are shown on the figüre (Fig.10) below.

Fig.10. Heatsink specimen dimensions

The desired test sample can be attached and removed from the test setup at any time. In the
experimental setup both static and dynamic pressure measurements are made.

8.2 Experiment Results

The test results performed at different speeds are given in the table below.

Velocity [m/s] Tinlet [K] Toutlet [K] Pressure Drop [Pa] Q [W]
1 297 306 -0.3 72
2 297 303.3 -5.7 72
3 297 301.3 -12 72
4.5 297 299.2 -29 72
Table 2. Experimental test results
Experimental studies in this section were carried out in the TÜBİTAK Materials Institute
Laboratory with the 2247-C Trainee Researcher Scholarship Program. We would like to express
our gratitude to Ph.D. Chief Researcher Dr.Levent TURHAN and TÜBİTAK Materials
Institute for their contributions.

30
8.2.1 Evaluation Of Experimental Results
As seen in the experiments, it is seen that at constant inlet temperature and constant heat source
conditions, the fluid outlet temperature gradually decreases with increasing speed, and the
pressure drop also increases with the speed.

Considering the data obtained from the test results, the study was continued in the ANSYS-
Fluent program using the computational fluid dynamics method, and the experimental results
and the analysis results were compared in terms of accuracy. As a result of the close results as
a result of the comparison, the fin optimization study was started.

9. MODEL AND METHOD

9.1 Geometric Model

In our study, air flow is provided between the fin blades in the channel. Fin analysis was
performed at different air velocities. The aim is to ensure that the air stays between the fin
blades as much as possible, stays in more interaction and ensures that more heat transfer is made
by convection, and that the maximum level of heat transfer that can be made from the fin to the
air in the channel. Thus, the cooling operation will be carried out.

As can be seen in the figure, the fin whose dimensions were determined was drawn in the
Solidworks program, and after the file was saved with the x.t parasolid extension, it was opened
in the geometry section of ANSYS-Workbench.

Fig.11. Drawing the sample in solidworks program

31
After the sample was saved with the x.t extension, the ANSYS-Workbench-Geometry section
opened with SpaceClaim, and the flow volume was created. As seen in the figure below, the
flow volume was assigned around the fin with the enclosure command and the appropriate flow
volume was created by taking into account the dimensions of the flow volume in the
experimental setup.

Fig.12. Creating the experiment flow field

Experimental dimensions were taken into account when creating the flow volume. The actual
duct dimensions, the distance of the air inlet region to the fin is greater than the outlet.
Therefore, the distance between the fin and the air intake zone is 1000 mm. Experiments were
carried out with a fin length of 100 mm and a total channel length of 1500 mm.

Fig.13. Establishment of flow volume

32
In order to determine the most suitable/efficient fin size in the study, studies were carried out
with fins at different speeds and the simulation results were transferred to the graphic. Based
on the graph obtained, it has been examined which fin size is more suitable and more suitable
for cooling efficiency.

Fig.14. Heatsink experimental setup in the channel

10. SETTING THE OPTIMUM MESH FOR THE SOLUTION

ANSYS Fluent 2021 R2 program was used in the analysis. This program uses the finite volume
method in its numerical calculations to realize the solution. Depending on the size of the
analysis, the mesh can be cast in two or three dimensions. To perform numerical simulation,
the geometry model is divided into simple parts by applying mesh.

As seen in Figure 18, poly-hexcore mesh structure is preferred in our geometry. Mosaic mesh
is a patent pending Ansys Fluent meshing technology for computational fluid dynamic
simulations. It accelerates the meshing process with a reduced face count, higher quality cells
and efficient parallel scalability. Mosaic meshing technology enables polyhedral connections
between disparate mesh types. Since the fin is rectangular in shape, poly-hexcore cell structure
is preferred as the mesh geometry. Dense mesh layers have been created around the fin to
achieve more realistic results and flow to provide clearer solutions. In other words, in order to
increase the precision of the solution, the mesh frequency should be increased as we approach
the walls we will analyze.

33
10.1. Inflation
It is a mesh technique that we should use mostly in flow analysis, where the fluid and the surface
come into contact. Since the fluid velocity will change in the regions close to the surface, the
mesh should be brought closer to the surface by layering and getting tighter in order for the
calculations to give more accurate results in these parts.

Fig.15. Surface mesh structure in triangle structure

Fig.16. Surface mesh image

There are various quality values that indicate the mesh quality. As seen in Figure 5.8 in the
ANSYS Fluent Program user manual, the limit values to be followed in order to determine the
mesh quality are given. Orthogonal value should be greater than 0.15 and Skewness value
should be less than 0.95. In our solution network structure studies, Orthogonal and Skewness
values were ensured to be in the desired range.

34
 Fig.17. Recommended limit values for mesh quality.

After the meshing process on the surface, boundary layer mesh was created with the scope
method in order to mesh the inner surfaces as well. Off-set method is made with aspect-ratio.
Even if there is no boundary layer in boundary layer solutions, the first 8 meshes are of great
importance. As seen in the figures, poly mesh is applied to the borders of the solid side and hex
mesh is applied to the inner sides. On the flow side, inflation layer, poly and hex mesh are used.
The biggest reason for using poly-hex mesh is to contribute to analytical convergence.

Fig.18. Poly-hex mesh structure (Front view)

35
Fig.19. Poly-hex mesh structure (Top view)

Fig.20. Poly-hex mesh structure (Front view)

Fig.21. Poly-hex mesh structure (Top view)

36
11. INSTALLATION AND SOLUTION (SETUP-SOLUTION) SETTINGS
After the preparations such as cellular networking and defining boundary conditions in the
Fluent Mesh module were completed, values related to the state in motion such as material
properties, boundary condition values, velocity-temperature values were entered in the Fluent
Setup module.

Since our fluid Re number is greater than 2300 in our study, the flow is turbulent. The most
suitable turbulence model for our study is the "k-epsilon (k-є) model- standard" model based
on the studies in the literature.

Turbulence is a fluid regime that is 3-dimensional and unstable in terms of time. Turbulence is
a term that allows you to understand the behavior of fluid movements, as it exhibits complex
and unpredictable behavior. Turbulent flow is eddy fluctuations randomly and rapidly.
Fluctuations require additional methods for momentum and heat transfer calculations. In this
case, a turbulence model consists of equations for determining unknown turbulent correlations
from the process. Turbulence models are simulated with the Navier-Stokes and continuity
equations.[17]

In this study, Fluent was used for CFD analysis, as we previously determined. Fluent program
offers the opportunity to use the turbulence models mentioned below.

1- Spalart-Allmaras

2- K-epsilon (k-є) model

3- K-omega (k-w) model

4- Reynolds stress model (RSM)

5- Big Eddy Simulation

Each of these models analyzes simulations in their respective fields. Among these studies, the
k-epsilon (k-є) turbulence model was preferred for our study.[17]

37
11.1 K-epsilon (k-є) Model

K-є is a two-equation and quasi-experimental model. It is true for almost all turbulent flows
over a wide area. More detailed definitions will be made in the subsections. This model; RNG
is divided into three parts as standard and realizable; Although all three have similarities, there
are differences in the method of calculating turbulent flow and viscosity. These features are
fundamental to all models, including turbulent generation, generation due to buoyancy,
calculation of compressibility effects, and modeling of heat and mass transfer.[17]

11.2 Material Used As Fin Material

The material of the cooler was chosen as aluminum. The reason for this is that aluminum is an
easily accessible, efficient, easily applicable, cost-effective material and is suitable for
experimental studies. The properties of aluminum used are given in Table 3. below.

Al 356 series was used in the study.

Property Value
Density (kg/m3) 2670
Thermal Conductivity (W/mK) 151
Specific Heat (J/kgK) 936
Table 3. Material properties used in the experiment: Al 356 series

In our study, aluminum was chosen as the fin body material. Air is selected and defined for the
fluid area. The properties of the air used in the simulation are given in Table 5.2 below.

Property Value
Density (kg/m3) 1.225
Thermal Conductivity (W/mK) 0.0242
Specific Heat (J/kgK) 1006.43
Table 4. Properties of the fluid (air) used in the experiment

38
11.3 Boundary Conditions
There are several cases for specifying inlet and outlet conditions (Table 5). We chose and
defined it as “velocity inlet” for input and “pressure outlet” for output. According to the speed
we have determined from the inlet, there is an air inlet and the air is expelled from the outlet
side. Other parts are defined as “Wall”. In addition, the value of 10773.6877 per square meter
of the heater with a heater power of 73.09 W was entered in the fin base region called heat_flux.

The fluid used in the work in all cases is air. The air temperature at the inlet is defined as 300K.
For velocity on solid surfaces, friction and kinetic energy are assumed to be zero and the channel
is assumed to be adiabatic.

The solution was made by making the energy equations open. In addition, the number of
iterations was determined as 500 and automatic stop was turned off from the residual settings
in order to ensure full convergence.

12. COMPUTATIONAL FLUID DYNAMICS ANALYSIS RESULTS

Outlet Heat Flux [W/m2]

Velocity [m/s] Temperature [K] Pressure Drop [Pa] (Uniform)
Q=73.09 W
1 316.952 3.336 10773.6877
2 305.981 11.818 10773.6877
3 302.319 24.950 10773.6877
4.5 299.886 50.427 10773.6877
Table 5. CFD-Fluent analysis results

It has been observed that, in response to increasing speeds, the outlet temperatures are gradually
decreasing among themselves, and the pressure drop values are also increasing at a certain rate
among themselves. However, 73.09 Watts of energy was given in the experiment with 1m/s
speed, but this value could not be kept constant during the experiments. Since 73.09 Watt
energy cannot be supplied, a heater power below this value is given. For this reason, there is a
difference in the values of 1m/s.

Controlling the residual part of the CFD analysis was carried out by controlling the fluxes, that
is, the energy balance in the system. According to the conservation of energy, which is the first
law of thermodynamics, the energies entering the system must be equal to the energies leaving.
The accuracy of the convergence is ensured by checking the balance of energy.

39
 Fig.22. Calculation of total heat transfer rate
𝒎
Inlet velocity 1 test conditions
𝒔

Pressure drop result; Outlet temperature result;

Fig.23. Pressure drop convergence result Fig.24. Outlet temperature

Convergence Graph;

Fig.25. Convergence Result

40
 Fig.26. Static temperature contour
𝒎
Inlet velocity 2 test conditions
𝒔

Pressure drop result; Outlet temperature result;

Fig.27. Pressure drop convergence result Fig.28. Outlet temperature

Convergence Graph;

Fig.29. Convergence result

41
 Fig.30. Static temperature contour
𝒎
Inlet velocity 3 test conditions
𝒔

Pressure drop result; Outlet temperature result;

Fig.31. Pressure drop convergence result Fig.32. Outlet temperature

Convergence Graph;

Fig.33. Convergence result

42
 Fig.34. Static temperature contour
𝒎
Inlet velocity 4.5 test conditions
𝒔

Pressure drop result; Outlet temperature result;

Fig.35. Pressure drop convergence result Fig.36. Outlet temperature

Convergence Graph;

Fig.37. Convergence result

43
 Fig.38. Static temperature contour

Velocity Magnitude Vectors;

Fig.39.Velocity magnitude vectors image

Fig.40. Velocity magnitude vectors image

44
 Fig.41. Velocity magnitude vectors image

Fig.42. Velocity magnitude vectors image

Total Pressure Contours;

Fig.43. Total pressure contours image

45
13. FIN OPTIMIZATION

Number Fin Fin Fin Outlet Pressure

Group Number Lenght Width
of Fins Height Thickness Distances Temperature(K) Drop (Pa)
1 6 80 64 40 0,8 11,84 301,00223 6,4293094
2 12 80 64 40 1 4,727273 300,91235 11,483572
A 3 15 80 64 40 1,2 3,285714 300,88907 18,365713
4 18 80 64 40 2 1,647059 300,86197 87,394836
5 6 100 64 40 0,8 11,84 302,38513 6,5490608
6 12 100 64 40 1 4,727273 302,38281 12,182092
B 7 15 100 64 40 1,2 3,285714 302,35172 19,427622
8 18 100 64 40 2,00 1,647059 302,3197 94,726540
9 6 120 64 40 0,8 11,84 303,93817 6,9899387
10 12 120 64 40 1 4,727273 303,86557 12,885309
C 11 15 120 64 40 1,2 3,285714 303,8208 20,950157
12 18 120 64 40 2 1,647059 303,78244 101,11758
Table 6. Fin optimization table and results
Information on geometries of different dimensions determined during the Finnish optimization
study was formed from three different groups as shown in Table 6.

Heatsink length, fin width and fin length were kept constant in geometries belonging to groups
A, B and C. Fin number and fin thickness were determined as variable. In response to these
determined parameters, the distance between the fins was also calculated.

According to the results of the CFD-Fluent analysis, it was observed that the outlet temperatures
were gradually decreasing, and the pressure drops were increasing according to the increasing
fin numbers, by looking at the increasing fin numbers as seen in each group.

If we compare the A and B groups, it has been determined that the outlet temperatures of the
samples with 80 mm heatsink length are lower than the samples with 100 mm heatsink length
of the B group. It is also seen that the pressure drops of group B are higher than group A.

The mentioned bet is also available for comparison of groups B and C.

Finally, as a result of increasing heatsink length and fin number, based on Newton's cooling
law, the outlet temperature of the air reaches higher degrees as a result of more heat transfer to
the air as a result of the increase in the heat transfer surface area of the heatsink. Since the
pressure drop is directly proportional to the increasing heatsink size. Pressure drop also
increases with the increasing length.[18]

46
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