FYP Thesis - Optimization of Cooling Performance of a Micro-Channel Heat Sink - Khawaja Aqib Aziz

8/11/2019 FYP Thesis - Optimization of Cooling Performance of a Micro-Channel Heat Sink - Khawaja Aqib Aziz

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The University of Nottingham, Malaysia Campus

Faculty of Engineering

Department of Mechanical, Materials and Manufacturing Engineering

PROJECT TITLE: OPTIMIZATION OF COOLING PERFORMACE BASED ON EXTENDED RIB SURFACE OF A

DIFFERENT RIB PROFILE IN A MICROCHANNEL HEAT SINK.

NAME : KHAWAJA AQIB AZIZ

STUDENT ID : 009973

SESSION : 2013/2014

SUPERVISOR : DR. WONG KOK CHEONG

Individual Project Report submitted for the degree of Bachelor of Engineering / Master of

Engineering in Mechanical Engineering.


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Summary

A Numerical Study is undertaken to optimize the Cooling performance of a micro-channel

heat sink, with application to the extended surface of a rib profile. The heat transfer

characteristics of the heat sink are investigated numerically using 3D conjugate heat transfer

modelling using ANSYS Fluent [12]. The model is validated with literature and is found in

good agreement with the experimental results of Lee et Al. [7]; also the computational

domain is based on the physical heat sink from this study.

Subsequently Ribs are added onto the validated heat sink and hence cases are generated to

optimize the cooling performance. Ribs are added inside the cooling channel to increase the

area available for transfer and to induce flow mixing. New cases are generalized in two

groups of Single Rib and Double Rib and results are presented. Number of Ribs and Length

of the Ribs are the parameters varied to check the best configuration of the Heat Sink.

The Double Rib (15mm) Heat Sink significantly improves in Heat Transfer performance for

all Reynolds Number tested (Re 500-2000). This proved to be the most successful

optimization case.

(Main Body word count: 6040 words)


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Acknowledgements

I would like to thank my final year project supervisor Dr. Wong Kok Cheong for his support

and guidance throughout the project. The support I have received has played an integral role

in me finishing this investigation successfully.


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Contents

Summary .............................................................................................................................................................................. 2

Acknowledgements ......................................................................................................................................................... 3

Contents ................................................................................................................................................................................ 4

Nomenclature ..................................................................................................................................................................... 6

List of Figures ..................................................................................................................................................................... 7

List of Tables ....................................................................................................................................................................... 8

1.0Introduction ................................................................................................................................................................ 9

1.1 Background .......................................................................................................................................................... 10

1.2 Project Objectives .............................................................................................................................................. 11

1.3 Research Questions .......................................................................................................................................... 12

1.4 Outline of report ................................................................................................................................................ 13

2.0Literature Review .................................................................................................................................................. 14

3.0Computational Methodology ............................................................................................................................. 16

3.1 Numerical Methods .......................................................................................................................................... 16

3.2 Setup ....................................................................................................................................................................... 17

3.2.1 Physical Model ........................................................................................................................................... 17

3.2.2 Computational Domain and Meshing ............................................................................................... 18

3.2.3 Computational Domain for different Cases .................................................................................... 19

3.3 Meshing ................................................................................................................................................................. 22

3.4 Governing Equations........................................................................................................................................ 23

3.7 Dimensionless Parameters ............................................................................................................................ 25

3.7.1 Deriving Dimensionless Parameters ................................................................................................ 25

3.7.2 Temperatures to Extract from ANSYS Fluent ............................................................................... 26

3.5 Boundary Conditions ....................................................................................................................................... 27

3.6 Assumptions and Other Properties ........................................................................................................... 28


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4.0Results and Discussion ........................................................................................................................................ 29

4.1 Validation.............................................................................................................................................................. 29

4.2 Grid Independence ........................................................................................................................................... 31

4.3 Mesh Refinement ............................................................................................................................................... 32

4.4 Case Studies ......................................................................................................................................................... 33

4.4.1 Contours of Pressure, Velocity and Temperature for all Cases ............................................. 33

4.4.2 Comparing Heat Transfer Performance .......................................................................................... 39

4.4.3 Comparing Pressure Loss ...................................................................................................................... 41

4.4.4 Quantitative Comparison for all Cases ............................................................................................. 42

4.4.5 Overall Discussion .................................................................................................................................... 43

4.4.6 Further Recommendations ................................................................................................................... 44

5.0Conclusions ............................................................................................................................................................... 45

References ........................................................................................................................................................................ 46

Appendix ........................................................................................................................................................................... 48


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Nomenclature

Average Temperature of Wall Width of micro-channel

Average Fluid Temperature

Height of micro-channel

Average Outlet Temperature Length of Heat Sink Average Inlet Temperature Rib height Density of Fluid (water) Rib width Volumetric Flow Rate of Fluid Rib length Specific Heat Capacity of Fluid Height of Heat Sink Heat gained by Coolant Velocity in x-direction Number of Channels Velocity in y-direction Area available for Heat Transfer Velocity in z-direction

Average Heat Transfer Coefficient Thermal Conductivity of Solid Hydraulic Diameter Thermal Conductivity of Fluid Average Nusselt Number

Reynolds Number

Velocity Dynamic Viscosity of Fluid


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List of Figures

Figure 1.1: Fan cooled Micro-Channel Heat Sink, by Fir0002/Flagstaffotos [1] ..................... ............... 9

Figure 1.2: Extended Ribs in a Micro Channel adapted from Gholami et Al. [3] ................................. 10

Figure 3.1 Schematic of the Physical Heat Sink................................................................................................. 17 Figure 3.2 Halved Single Unit of Micro-Channel ............................................................................................... 18

Figure 3.3: View of the domain geometry ........................................................................................................... 19

Figure 3.4: Modelled domain of Case 1 ( ) ..................................................................................... 20Figure 3.5: Modelled domain of Case 3 ()................................................................................... 20Figure 3.6: Modelled domain of Case 5 ( ) ..................................................................................... 21Figure 3.7: Modelled domain of Case 6 ()................................................................................... 21Figure 3.8: Front View of Mesh ................................................................................................................................ 22

Figure 3.9: Side View of the Mesh ........................................................................................................................... 22

Figure 3.10: Boundary Conditions for the Model Domain ............................................................................ 27

Figure 4.1: Comparison of results from Numerical study with experimental scatter ..................... . 29

Figure 4.2: Different Mesh Generated for Grid Independance ................................................................... 31

Figure 4.3: Resulting Mesh after Refinement..................................................................................................... 32

Figure 4.4: Case 1, Contour of Pressure ............................................................................................................... 33

Figure 4.5: Case 1, Contour of Temperature ...................................................................................................... 34

Figure 4.6: Case 1, Contour of Velocity ................................................................................................................. 34

Figure 4.7: Case 2, Contour of Pressure ............................................................................................................... 35

Figure 4.8: Case 2, Contour of Temperature ...................................................................................................... 35

Figure 4.9: Case 2, Contour of Velocity ................................................................................................................. 35

Figure 4.10: Case 3, Contour of Pressure ............................................................................................................. 36

Figure 4.11: Case 3, Contour of Temperature .................................................................................................... 36

Figure 4.12: Case 3, Contour of Velocity .............................................................................................................. 36


Figure 4.14: Case 5, Contour of Temperature .................................................................................................... 37Figure 4.15: Case 5, Contour of Velocity .............................................................................................................. 37


Figure 4.17: Case 6, Contour of Temperature .................................................................................................... 38

Figure 4.18: Case 6, Contour of Velocity .............................................................................................................. 38

Figure 4.19: Nusselt Number for Single Rib Cases........................................................................................... 39

Figure 4.20: Nusselt Number for Double Rib Cases ........................................................................................ 40

Figure 4.21: Pressure Loss for all Cases ............................................................................................................... 41


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1.0 Introduction

A Heat Sink is fitted to or is incorporated with systems to ensure that the operating

temperature does not exceed the maximum allowable limit. They are used with devices which

do not have the ability to cool themselves down; common examples include high power

semiconductors or Light Emitting Diodes (LEDs).

For effective operation, a Heat Sink is designed to maximize its area of contact with the

coolant (e.g. Surrounding Air or Water). Furthermore, Heat Sinks are either assembled onto

devices or are manufactured as an integral part of the device.

Figure 1: Fan cooled Micro-Channel Heat Sink, by Fir0002/Flagstaffotos [1]

Micro Channel Heat Sinks were initially suggested by Tuckerman & Pease [2]; they observed

improvements in the Heat Transfer by reducing the cooling channel to the micron scale.

These multiple cooling channels are machined into the back of the substrate of electronic

components, heat is transferred to the substrate by conduction and out from the substrate via

convection. Micro Channel Heat Sinks are compact, relatively simple and hence a very

feasible and worthwhile option to consider for Heat Removal applications.


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1.1 Background

This report is based on optimization of cooling performance, by testing different

configurations of extended ribs in the micro-channel. Extended Ribs as can be seen from

Figure 1.2 are protrusions in the micro-channel.

These protrusions improve heat transfer. Firstly due to the increased surface area for transfer

between the coolant and the heat sink. Secondly by inducing further flow mixing and thereby

giving better heat transfer. Also due to the decreased flow area and turbulence for the coolant,

flow resistance is induced.

Figure 2: Extended Ribs in a Micro Channel adapted from Gholami et Al. [3]

Whereas the extended ribs better the heat transfer, the flow resistance present is an unwanted

consequence. The flow resistance deters the flow of coolant through the channel adversely

affecting the heat transfer. Prompting the use of fans and pumps, which are used to force the

coolant through the micro-channel.

Due to this conflicting situation the reduction of flow resistance is very important and has

been studied with great interest.

Extended Ribs in a Micro


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1.2 Project Objectives

Aims:

To Optimize Heat Transfer by application to extended ribs in a micro-channel Heat

Sink.

Objectives:

To use Computational Methods to solve the given problem.

To Validate the Numerical Model with Experimental Literature.

To Generate Cases to optimize the Cooling Performance.

To understand the effect of Ribs on Heat Transfer and Fluid Flow.

To propose a feasible configurations of ribs in the micro-channel Heat Sink.


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1.3 Research Questions

The work required in this project puts forth the following research questions:

1. Can Numerical Methods be employed to accurately predict and observe the Heat

Transfer and Coolant Flow through the Micro-Channel?

i. What are the best Numerical Methods available for this purpose?

ii. What are the limitations of Numerical Methods?

2.

How to ensure that the Numerical Simulation is Correct?

i. What data is going to be used for Validation?

ii. What geometry is going to be employed?

iii.

What simplifying assumptions can be applied to the system?

3.

What sort of Extended Rib Profiles should be modelled?

i.

What existing study of Ribs is available?

ii. What already has been deduced about Extended Rib Profiles?

iii. Are the any recommendations for Rib Profile designs?


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1.4 Outline of report

The following text presents the sequential order of the report, and its encompassing sections.

2.0 Literature Review:

This section explains the past work done on micro channel heat sinks, discusses the

applicability of numerical techniques and their setup. Heat Transfer characteristics are

discussed as well as the best configurations to get maximised heat transfer.

3.0 Computational Methodology

This section presents the methodology put forth to solve the problem. Starting with

the model selection, to domain modelling, forth to the background governing

equations, domain meshing. The boundary conditions, properties and other

assumptions to solve the equations are discussed. Test cases are also discussed.

4.0 Results and Discussion

This section presents the results obtained by running the computation. Initially the

computation is validation with experimental results; then the best mesh is selected and

then refined.

The results of the test cases are presented and discussed; these discussions include

comments on the contours of pressure, velocity and temperature, graphs of Nusselt

Number against Reynolds Number and the comparison of pressure drop.

5.0 Conclusion

The main conclusions are drawn and put forth.


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2.0 Literature Review

Heat Transfer in Micro-channel Heat Sinks has been studied with great interest by a lot of

researchers. Some of the important and relevant works are summarised below.

The pioneers were Tuckerman and Pease [2], who initially put forth the idea of using micro

channels to remove heat, they decreased the cooling channel size to the micron scale that

subsequently increased the heat transfer rates. The heat sink was tested up to 790 W/cm2, and

chip temperatures were maintained below 110C.

Qu and Mudawar [4] investigated the pressure drop and the heat transfer for a micro channel

both numerically and experimentally. There results demonstrated a good correlation between

the numerical and the experimental analysis. The study concluded that the Navier-Stokes andenergy equations can reasonably accurately predict the fluid flow and heat transfer for a

Micro-channel Heat Sink.

Gunnasegaran et al. [5] numerically using the finite volume method investigated effect of

geometric parameters on the water flow and heat transfer characteristics. The journal

concluded that the Micro-channel Heat Sinks with the lowest Hydraulic Diameter had the

better heat transfer and was also better for Pressure Drop.

Mansoor et Al. [6] carried out a 3D conjugate numerical investigation for a rectangular

Micro-channel Heat Sink to predict the heat transfer. The model had simultaneously

developed single-phase flow regime and was compared with experimental and numerical

results from previous studies. Overall this study was in good agreement with previous results.

The study concluded that for increasing heat flux, the heat transfer coefficient increases.

Lee et Al. [7] carried out both experimental and numerical analysis for the micro-channel

heat sink for a range of dimensions. The experimental investigation validated the classicalcorrelations and was found to be in agreement with them. The analysis concluded that a

conventional numerical method can predict the heat transfer in micro channels but the

entrance and boundary conditions need to be carefully considered and set according to real

conditions.

Kamali and Binesh [8] carried out investigation of ribbed duct flow. A computer code was

developed to simulate turbulent flow past ribs of four different shape inside the duct. It was

seen that heat transfer coefficient and pressure loss is greatly affected by rib shapes. The


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trapezoidal shaped ribs provide the highest enhancement of both heat transfer and pressure

drop.

Liu et al. [9] studied forced convective heat transfer in Micro-channel Heat Sink using both

Computational Fluid Dynamics (CFD) and Lattice Boltzmann (LB) approaches. It is

concluded that both these methods are valid for predicting fluid flow and heat transfer in

micro channels. There were a few important observations from this study. Firstly it is found

that heat transfer efficiency is increased with an increase in Reynolds number. Secondly, the

shield shaped groove micro channel has the highest heat exchange performance.

Lee and Garimella [10] performed numerical simulations to investigate convective heat

transfer in micro channels of different aspect ratios. The study proposes optimization

correlations that show very good agreement with the experimental data.

Cui and Fu [11] relate to the bionic micro grooved surfaces on fish. It investigated whether a

bionic microgroove can reduce pressure loss in the channels of a MCHS. For that purpose

different types of bionic surfaces are tested. LB approach is used for the numerical analysis.

It is concluded that the ridge shaped grooved surface has the greatest drag reduction. It is also

seen that larger width to height ratio of ridge shaped groove are more suitable for larger

Reynolds number.

Lei et Al. [13] used criss cross configuration for cooling channels and found increase in heat

transfer above Re = 300. Moradi and Floryan [14] proposed and used grooves parallel to the

flow direction to improve heat transfer. Xie et Al. [15] used internal protruded dimples and

found the case where the difference between dimples is 16mm to have the best heat transfer

for least pressure loss.

Xia et Al. [16] fan-shaped re-entrant cavities and internal ribs and found the best performance

for the case where cavity and ribs both were used. Ahmed et Al. [17] used both vortex

generators and nano-fluids; they concluded that although heat transfer is improved greatly but

presents a pressure deficit.

As can be seen there is a lot of research material available on the MCHS. However there is a

research gap, not much study is done on the extended rib profile. Hence we will study the

effects on extended ribs.


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3.0 Computational Methodology

3.1 Numerical Methods

Numerical Methods are employed to perform this study. Using the numerical study there is a

greater flexibility to vary different parameters; more results are achieved in the same time

frame as compared to an experimental study. Also contours of Velocity, Temperature and

pressure can be easily obtained, that make the visualisation and understanding of the physical

phenomenon much simpler.

Numerical Methods usually employ Iterative techniques and computational tools to obtain

solutions where analytical solutions are not possible. For this study ANSYS Fluent [12] will

be used to obtain a 3D conjugate analysis accounting for both conduction inside the copper

substrate and for convection in the coolant flowing through the micro channel.

The computation setup is designed similar to the experimental work of Lee et Al. [7].


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3.2 Setup

3.2.1 Physical Model

The physical model and its dimensions are shown in the schematic in Figure 3.1. The coolant

inlet and outlet configuration is also illustrated.

Figure 3 Schematic of the Physical Heat Sink

The heat sink substrate walls are set to 0.15mm. This value is arbitrary as the copper heat

sink is assumed to have perfect heat conduction. The top wall and the side walls are specified

as adiabatic walls.

Table 3.1: Dimensions of the micro-channel

Dimensions of the micro-channel


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3.2.2 Computational Domain and Meshing

The computational domain is modelled using ANSYS Design Modeller [18]. Figure 3.2

shows the half micro-channel, on which the computational domain is based upon.

Figure 4 Halved Single Unit of Micro-Channel

The domain used for this simulation is half of a single Micro Channel; the simplification is

considered because of the apparent symmetry in the Heat Sink. Same behaviour will be

experienced from both inside walls of the micro-channel; hence having a symmetry boundary

condition will give us the same result, while halving the number of computational nodes and

the computational grid. This reduction of the Computational Grid and Number of Nodes will

reduce the computational power required without having to compromise on the accuracy of

our results.


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3.2.3 Computational Domain for different Cases

As this investigation is based on the Extended Rib Surface, the cases developed are just

Ribs added onto the Bare ChannelHeat Sink domain.

Figure 3.3 shows a bare channel computational domain; this will serve as the base model.

Ribs are added to the middle of this domain to generate cases.

Figure 5: View of the domain geometry

The cases developed either have Single Rib or Double Ribs. The Rib Length is going to be

varied (kept either 2mm or 5mm or 15mm) to see what effects Rib Length has on Heat

Transfer values and characteristics.

Apart from the bare channel, a total 6 cases are generated:

Case 1. Single Rib2mm



Case 4. Double Rib2mm




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As the name suggests the Single Rib case supports a Single Rib right down the middle of

the Heat Sink. The Rib Height is and the Rib width is . The Ribs for all the cases start from after a length of 10.4mm from theinlet. The variable parameter for these cases will be the Rib Length

.

Figure 3.4 below shows the modelled domain of case 1. Successively the following figures

show the modelled domain for different cases.

Figure 6: Modelled domain of Case 1 ( )



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The subsequent figures below show the Cases for Double Ribs. For these cases the Rib width

is and the Rib height is .




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3.4 Governing Equations

To model the solid and fluid behaviour differential equations are used. These equations

known as the governing equations are solved using computational methods. These

governing equations govern the phenomenon occurring both in solids and liquids.

Firstly for the fluid flow there are governing equations for the continuity (conservation of

mass) and momentum (conservation of momentum).

Secondly for the heat transfer modelling there are governing equations for Heat Transfer in

the Fluid and Heat Transfer in the Solid.

Equation 1: the Continuity Equation

Equation 2: the Momentum Equations

( )

(

)

( )


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Equation 3: the Energy Equation (Fluid)

(

)

[

]

[() ()

( )]

( ) ( )

Equation 4: the Energy Equation (Solid)

[

]

ANSYS Fluent [12] is used to iterate these equations to solve for the fluid and heat transfer

behaviour. These governing equations are discretised using the first order upward scheme.

The pressure-velocity coupling is done using the SIMPLE scheme. The convergence criteria

was kept for the residuals for the solution to converge. Dimensionless parameters are used to evaluate the Heat Transfer Characteristics.

These dimensionless numbers and their derivation are discussed in the next section.


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3.7 Dimensionless Parameters

To evaluate the Heat Transfer and Fluid Flow, Average Nusselt Number and Reynolds

number are derived respectively.

Nusselt number is the ratio of convective heat transfer to conductive heat transfer; a higher

Nusselt number implies greater convective heat transfer.

3.7.1 Deriving Dimensionless Parameters

The Heat Transferred to the coolant and is given by the following equation.

Equation 5: Heat Gain by Coolant

,

o Where the term indicate the average rise in temperature of thecoolant, from the inlet to the outlet.

Once the Heat Transferred to the coolant is obtained, the Average Heat Transfer Coefficient

can be derived using its formula, the following equation:

Equation 6: Average Heat Transfer Coefficient

In the above formula the N represents the number of channels, and in this case its value is 1.

A is the area available for transfer and is the Surface Area in contact with the Fluid. The

Average Temperature of the Wall is obtained using the software and the AverageTemperature of the Fluid is obtained using the following equation.Equation 7: Average Fluid Temperature

After the Average Heat Transfer Coefficient is obtained, the Average Nusselt Number is

calculated using the following equation.

Equation 8: Average Nusselt Number

o Where is the Hydraulic Diameter and is the thermal conductivity.


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The Nusselt Number obtained is dependent on the Reynolds number of the flow which is

calculated using the following equation.

Equation 9: Obtaining Reynolds Number

o Where the values of velocity v are varied in the ANSYS Fluent [12] software

to obtain the required Reynolds number.

3.7.2 Temperatures to Extract from ANSYS Fluent

As seen previously from the mathematical formulation there are 4 values of temperaturerequired. Table 2 below outlines where these values are extracted from.

Table 1: Temperature to Extract

Temperature Description

This is the average Inlet Temperature; this can be obtained from thesoftware from Reports. For our Study this is set and will always have a

value of 300k as it is specified in the software.

This is the average Outlet Temperature; this is to be extracted fromFLUENT [12] and should yield different values of greater than 300k

every test case.

This is the average Wall Temperature; this is to be similarly extractedfrom FLUENT [12]. As Copper (Heat Sink Material set) has high

thermal Conductivity this can be assumed to be accurate

This is the average Fluid Temperature; although this can be alsoextracted but for simplicity we use the inlet and outlet temperature and

equation 7 to calculate its value,


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3.5 Boundary Conditions

These boundary conditions set for this investigation are as follows:

Figure 12: Boundary Conditions for the Model Domain

The Inlet Boundary condition is velocity-inlet.

o This is set as the velocity inlet because as depending on our case (Reynolds

Number of Flow) the entrance velocity of the coolant fluid would vary.

Outlet Boundary Condition: The Outlet Boundary condition is pressure based outlet.

o This specifies the point from where the fluid would exit and hence develops

the flow.

Bottom Wall Heat Flux: Bottom of the Heat Sink is set as Heat Flux.

o This is where the Heat is transferred to the Heat Sink.

Symmetry: The side walls are set as Symmetry.

o The side walls are set as Symmetry

Adiabatic Walls: The Remaining walls are set as Adiabatic Walls.

o This is in line with the simplifying assumption put on the experiment that

negligible heat loss to the environment.


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3.6 Assumptions and Other Properties

The properties of the solid and fluid materials being used are very important. As properties of

the materials lie within a range at different operating conditions, it is important and

imperative that material properties are specified justified for their assumptions.

Hence firstly the assumptions for this study are specified and then the material properties are

specified.

The assumptions for this study are:

1. The Fluid Flow is laminar, steady and incompressible.

2. The Heat Loss to the environment is negligible.

3. Fluid properties are constant.

The Fluid for this study is Water and its properties are set as:

1.

Density = 996.69 kg/m3

2.

Specific Heat = 4187 J/kg.K3. Thermal Conductivity = 0.6 W/m.K

4. Viscosity = 0.000852 kg/m.s

The Solid for this study is Copper and its properties are set as:

1. Density = 8978 kg/m3

2.

Specific Heat = 381 j/kg.K

3.

Thermal Conductivity = 387.6 w/m.K


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4.0 Results and Discussion

4.1 Validation

Validation is performed to determine whether the computational simulation gives results

agreeing with the physical reality. To validate this simulation the results obtained are

compared with the experiment performed by Lee et Al. [7].

Figure 4.1 shows the comparison of our results with the results from experimental

investigation. These results are equated using the mathematical manipulation discussed in

section 3.7.1.

Figure 13: Comparison of results from Numerical study with experimental scatter

From figure 4.1 it is observed that Computational simulation accurately predicts the heat

transfer characteristics; similar to the experimental trend the Average Nusselt Number

increases as the Reynolds Number increases.

4

6

8

10

12

14

16

18

20

0 500 1000 1500 2000 2500

AVERAGEN

USSELTNUMBER

REYNOLDS NUMBER

Computational Data Experimental Data, Lee et. Al.


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To complement the comparison using the graph, values at specific Reynolds numbers are also

compared. It can is seen from table 4.1 that the deviation in the experimental and

computational results does not increase more than 10% (which is the acceptable norm).

Table 4.1: Comparing Nusselt Number and Experimental Values from Lee et. Al. [7]

Re Nu (this study) Nu (Lee et. Al.) Difference

900 9.04 8.6 5.1%

1000 9.55 9 6.1%

1100 10.04 9.7 3.5%

1200 10.52 10 5.2%

1500 11.86 11 7.8%

2000 13.86 14.3 -3.0%

From both figure 4.1 and table 4.1, it is concluded that the results from the computational

simulation are close to the experimental scatter, and therefore it is concluded that the

computational simulation accurately predicts the physical reality.


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4.2 Grid Independence

As the size of the mesh increases, the computational nodes also increase and consequently the

accuracy of the numerical study improves. This is observed because as the single mesh

element gets smaller it accounts for the smallest change, and overall better results will beobtained.

Nonetheless there is a point when after the mesh size is further increased, the results do not

change; the results become mesh independent (or grid independent). At this point a relatively

coarser mesh has a similar value to a finer mesh; hence the increase in computation size and

cost is unnecessary. To find that mesh size a Grid Independence Test is performed.

Figure 4.2 indicates the Meshes generated for the same computational domain and Table 3

has the results obtained for the Nusselt Number at (Re=1000) using the various mesh sizes.

Figure 14: Different Mesh Generated for Grid Independance

Table 4.2: Nusselt Number corresponding to the Mesh Used

Mesh Type Mesh Size (elements) Nusselt Number

Coarse 1.9 x 10 9.50

Medium1.6 x 10

9.71

Fine3.6 x 10

9.74

It is observed that there is a very small difference in the value of Nusselt Number between the

Medium Mesh and the Fine Mesh; hence Medium Mesh would be selected.


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4.3 Mesh Refinement

The mesh selected in section 4.2 is further modified at critical areas so phenomenon at those

critical areas in accounted for.

There are two critical areas identified in the domain where the mesh is then refined:

1. The Heat Flux at the bottom is a sensitive area, Energy rises from this point and

conduction starts. Any loss of data or oversimplification can make the results

inaccurate. Hence the Mesh Size here has to be increased.

2. The Solid-Fluid interface, where the coolant fluid is in contact with the solid heat

sink. Here the mesh on both the solid size and the liquid size has to be same size and

small enough so we dont have over simplification and subsequent loss of data.

Figure 15: Resulting Mesh after Refinement

Figure 4.3 shows the Mesh obtained after the refinement of critical areas. Medium Mesh from Figure

4.2 and the Refined Mesh from Figure 4.3 can be compared to see the refinement differences; at the

solid liquid interface and the bottom face.


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4.4 Case Studies

Cases are generated with two variable parameters. These parameters are changed across the

six cases developed. The two variable parameters are:

1.

Number of Ribs

2. Rib Length

The Resulting cases developed are:




Case 4.

Double Rib2mm



4.4.1 Contours of Pressure, Velocity and Temperature for all Cases

For the case of Single Rib (2mm), it is seen from figure 4.4 that the extended rib induced

flow mixing and hence therefore there is an area of high pressure developed right after the rib(the red region). The rib forms a bottleneck for the flow. The flow rapidly recovers to its

initial conditions further downstream.

Figure 16: Case 1, Contour of Pressure


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Figure 17: Case 1, Contour of Temperature

Figure 18: Case 1, Contour of Velocity

From the contours of velocity it is observe that the velocity under the rib accelerated. Once

the stream was obstructed the expectation was for the fluid to equally disperse. Rather, it is

interesting to see that even though the rib is placed in the middle of the channel cross section,

after obstruction the coolant fluid accelerated under the rib. This happens because the fluid

finds it easier to move below rather than above the rib, there is lesser flow resistance under

side of the rib.

It is observed from the temperature contour in figure 4.5 that the temperature is higher in the

above the rib region. As earlier discussed the local flow for that region has reduced, leading

to reduced heat transfer and a rise in local temperature.


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The 15mm Single Rib has a greater area available for convection. Also it has greater

obstruction for pressure loss. Figure 4.10 shows the pressure build-up in the channel and like

seen before its in the region under the rib. From figure 4.12 it can be seen there is a velocity

increase but not as quickly accelerated. The pressure loss in this channel is far too great to

benefit in heat transfer, and making it not feasible in application. Figure 4.11 shows heat

transfer taking place but slow adjacent to the rib.


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The 15mm Double Rib should in theory be similar to 15mm Single Rib case and because of

the increased flow blockage the heat transfer should be lesser than smaller rib counter parts. It

is seen from figure 4.17, the 15mm Double Rib has the best temperature distribution amongst

all the cases. Slow pressure development and velocity development can be seen from figure

4.16 and figure 4.18 respectively.


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4.4.2 Comparing Heat Transfer Performance

Heat Transfer Performance is described using Nusselt Number. These Nusselt Numbers are

derived using the equations from section 3.7.2. The Nusselt Number is plot corresponding to

the Reynolds Number of the Flow.

Figure 31: Nusselt Number for Single Rib Cases

Figure 4.19 compares the heat transfer performance of the newly generated cases with the

bare channel case. In figure 4.19 the lines for bare channel, 2mm and 5mm approximately

overlap each other and have negligible difference except for high Reynolds Number.

Therefore we can conclude that the newly generated cases do not improve the Heat Transfer

performance except for high Reynolds Number. For the Case 4 (Single Rib 15mm) the line is

below the bare channel line and hence it actually has a decrease in the Heat Transfer

Performance.

It can be seen that none of these cases give a noticeable Heat Transfer increase, hence it will

not be feasible to use any of them for application. Also we note that Case 3, which is the

Single Rib15mm has a reduced heat transfer performance. Looking also at figure 4.21 we

can see that the Single Rib15mm has the worst pressure loss; explaining even why the Heat

Transfer performance is worse off.

4.00

6.00

8.00

10.00

12.00

14.00

16.00

0 500 1000 1500 2000 2500

AVERAGENU

SSELTNUMBER

REYNOLDS NUMBER

Bare Channel 2mm 5mm 15mm


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Figure 32: Nusselt Number for Double Rib Cases

Figure 4.20 has graphs for Case 4, 5 and 6. Again from the figure it is seen that the Case 4

(2mm) and Case 5 (5mm) lines are overlapping hence negligible Heat Transfer performance

variation. For Case 6 (15mm) the line is over the bare channel line hence there is an

increase in the heat transfer performance. This improvement in the Heat Transfer can be

attributed to the increased surface area for Heat Transfer. It can also be attributed to the better

flow pattern for the coolant flow as seen from the pressure and velocity contours.

4.00

6.00

8.00

10.00

12.00

14.00

16.00

0 500 1000 1500 2000 2500

AVERAGENUSSELTNUMBER

REYNOLDS NUMBER

Bare Channel 2mm 5mm 15mm


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4.4.4 Quantitative Comparison for all Cases

Table 4.3: Quantitative comparison of Heat Transfer and Pressure Loss for Single Rib

Nusselt Number Pressure Drop (kPa)

Re

Case 1

(2mm)

Case 2

(5mm)

Case 3

(15mm)

Bare

Channel

Case 1

(2mm)

Case 2

(5mm)

Case 3

(15mm)

500 6.70 6.77 5.42 6.72 11.43 15.34 22.11

600 7.35 7.43 5.96 7.35 13.38 18.75 27.21

700 7.96 8.04 6.45 7.95 18.94 22.25 32.47

800 8.54 8.62 6.91 8.51 21.96 25.83 37.86

900 9.08 9.17 7.33 9.04 25.05 29.50 43.37

1000 9.62 9.70 7.72 9.55 28.26 33.25 48.99

1100 10.14 10.20 8.09 10.04 31.47 37.08 54.78

1200 10.63 10.70 8.46 10.52 34.79 40.99 60.501500 12.04 12.10 9.45 11.86 45.20 53.20 78.66

2000 14.15 14.22 10.89 13.86 63.99 75.12 110.67

Table 4.4: Quantitative comparison of Heat Transfer and Pressure Loss for Double Rib

Re

Nusselt Number Pressure Drop (kPa)

Case 4(2mm)

Case 5(5mm)

Case 6(15mm) Bare Channel

Case 4(2mm)

Case 5(5mm)

Case 6(15mm)

500 6.68 6.71 7.62 6.72 11.76 12.92 15.58

600 7.31 7.34 8.37 7.35 14.52 15.68 18.92

700 7.90 7.94 9.07 7.95 17.13 18.51 22.33

800 8.46 8.50 9.72 8.51 19.79 21.39 25.82

900 8.99 9.04 10.33 9.04 22.50 24.33 29.38

1000 9.51 9.57 10.91 9.55 25.27 27.33 33.01

1100 10.01 10.07 11.47 10.04 28.09 30.39 36.71

1200 10.49 10.56 12.00 10.52 30.97 33.51 40.47

1500 11.86 11.95 13.50 11.86 39.93 43.21 52.15

2000 13.94 14.06 15.72 13.86 51.67 60.54 72.83

Tables 4.3 and 4.4 summarize the Heat Transfer and Pressure Loss Values at certain flow

rates (fixed Reynolds Number). The values corresponding the best case are highlighted in

green and the values corresponding the worst case are highlighted in Red.


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4.4.5 Overall Discussion

By looking at the results thus far it is evident that better distribution of the flow yields better

heat transfer performance. Simply comparing the contours of the Single Rib cases and the

Double Rib Cases, it is observed that where the flow development was uniform Heat Transferwas better (also referring to their Temperature Contours).

In the case of Single Ribs it was seen from both the Velocity and Pressure Contours that

when the flow was obstructed by a Rib the flow becomes concentrated under the rib and the

region over the rib has lesser flow. This one sided flow results in a relatively large boundary

layer being created, which can be referred to as a dead layer (when speaking about heat

transfer). This dead layer hinders the heat transfer taking place.

Hence to disrupt the build-up of a dead layer we need to equally disrupt the flow in all

direction, by having a flow guiding rib, like a V-shape facing the flow. This phenomenon of

equally distributed flow is occurring in the Double Rib Cases. From the contours of Double

Ribs the evident pattern is seen and distribution is even. This distribution leads to the dead

layers being broken.

As spoken about earlier the flow obstruction helps because it breaks the dead layer, and when

the dead layer is continued to be replaced by new cooler fluid the heat transfer is enhanced.

Flow also has a better tendency to recover from an obstruction if the obstruction is parallel to

the line of the flow.

Although having a greater surface area for heat transfer improves the heat transfer, but the

flow regime is very important. From all the plots it is observed that at higher Reynolds

Number there is more Heat Transfer. This is owing to the quick replacement of the coolant

fluid.

By increasing the convective area flow blockages are included. Flow mixing occurs and

boundary layers are broken up, but the pressure loss has a greater negative effect than the

positives combined.

From the Double Rib cases it is seen that by dispersing the blockage into smaller parts

reducing the flow resistance significantly. Both the Single Rib and the Double Rib had the

same effective area for flow blockage. Their pressure loss and Heat Transfer should have

been similar. The blockage was divided into two parts (i.e. two smaller Ribs), and both Heat

Transfer was enhanced and Pressure Loss was reduced.


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4.4.6 Further Recommendations

Heat Sink configurations have been studied with great interest. Different Inlet & Outlet

configurations have been studied. Different Base shapes, channel shapes, have been studied.

Different studies have provided Cooling Performance enhancements. However if theseenhancements are feasible or not is another question?

The problems posed by conventional heat sinks can be reduced by using an innovative design

e.g. Sandia Cooler [19], which itself is a fan shaped heat sink. This Heat sink is rotating, and

as it rotates it dispenses hot air out from the sides while sucking in cool air from the top. This

design does not let the dead layer to accumulate. This is a big step in Heat Sinking

technology.


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5.0 Conclusions

There are a number of observations from the 6 test cases performed. The best Heat Transfer

performance was seen in case 6 (Double Rib-15mm), the worst heat transfer was seen in case

3 (Single Rib-15mm) and all the other cases did not significantly alter the heat transfer

performance as compared to bare channel heat sink.

The observations made from the study and the conclusions developed are listed below:

1. Heat Transfer is accurately predicted using ANSYS Fluent [12].

2.

Heat Transfer by increasing the area of convection is increased only if sufficient area

is increased.

3.

By increasing the blockage pressure loss occurs, which reduces coolant flow andhence reducing heat transfer.

4. Flow blockage forces flow to be concentrated in some regions therefore greater

pressure loss reducing heat transfer.

5. Ribs are desirable if they disperse the fluid into a pattern so fluid distribution is even,

not concentrated at some end.

6.

Boundary layer build up at walls, acts as a dead layer which if not disturbed or

removed will not let efficient heat transfer take place.


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References

1. Fir0002/Flagstaffotos, (2006). AMD Heat Sink and Fan. [image] Available at:

http://upload.wikimedia.org/wikipedia/commons/2/25/AMD_heatsink_and_fan.jpg

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2. Tuckerman, D. and Pease, R. (1981). High-performance heat sinking for VLSI.

Electron Device Letters, IEEE, 2(5), pp.126--129.

3. Gholami, H., Banaei, M. and Eskandari, A. (2013). Investigation of effect of

triangular rib in heat transfer of finned rectangular microchannel with extended

surfaces.Life Science Journal, 10(8s).

4. Qu, W. and Mudawar, I. (2002). Experimental and numerical study of pressure drop

and heat transfer in a single-phase micro-channel heat sink. International Journal of

Heat and Mass Transfer, 45(12), pp.2549--2565.

5. Gunnasegaran, P., Mohammed, H., Shuaib, N. and Saidur, R. (2010). The effect of

geometrical parameters on heat transfer characteristics of microchannels heat sink

with different shapes. International Communications in Heat and Mass Transfer,

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6. Mansoor, M., Wong, K. and Siddique, M. (2012). Numerical investigation of fluid

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Lee, P., Garimella, S. and Liu, D. (2005). Investigation of heat transfer in rectangular

microchannels. International Journal of Heat and Mass Transfer, 48(9), pp.1688--

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8. Kamali, R. and Binesh, A. (2008). The importance of rib shape effects on the local

heat transfer and flow friction characteristics of square ducts with ribbed internal

surfaces.International Communications in Heat and Mass Transfer, 35(8), pp.1032--

1040.

9. Liu, Y., Cui, J., Jiang, Y. and Li, W. (2011). A numerical study on heat transfer

performance of microchannels with different surface microstructures. Applied

Thermal Engineering, 31(5), pp.921--931.

10.Lee, P. and Garimella, S. (2006). Thermally developing flow and heat transfer in

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mass transfer, 49(17), pp.3060--3067.


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Appendix

Appendix 1: Gantt chart used for Project Planning and Organization

Appendix 2: Validation using different turbulence models, k-3 and LES


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Appendix 3: Calculating Velocity using Spreadsheet

Appendix 4: Calculating Heat Transferred using Spreadsheet

Appendix 5: Calculating Nusselt Number using Spreadsheet


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Appendix 6: Flow of work for this study

DevelopedSimulation

ValidatedSimulation

DevelopedTest Cases

SimulateTest Cases

EvaluateResults

FYP Thesis - Optimization of Cooling Performance of a Micro-Channel Heat Sink - Khawaja Aqib Aziz

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