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 1.0 Introduction ................................................................................................................................................................ 9 1.1 Background .......................................................................................................................................................... 10 1.2 Project Objectives .............................................................................................................................................. 11 1.3 Research Questions .......................................................................................................................................... 12 1.4 Outline of report ................................................................................................................................................ 13 2.0 Literature Review .................................................................................................................................................. 14 3.0 Computational 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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4.0 Results 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 5.0 Conclusions ............................................................................................................................................................... 45 References ........................................................................................................................................................................ 46 Appendix ........................................................................................................................................................................... 48
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Nomenclature
̅ ̅ ̅ ̅ ̅ ̅
Average Temperature of Wall Average Fluid Temperature Average Outlet Temperature Average Inlet Temperature Density of Fluid (water) Volumetric Flow Rate of Fluid Specific Heat Capacity of Fluid Heat gained by Coolant
Number of Channels
Area available for Heat Transfer
Average Heat Transfer Coefficient
Width of micro-channel Height of micro-channel Length of Heat Sink Rib height Rib width Rib length Height of Heat Sink Velocity in x-direction
Velocity in y-direction
Velocity in z-direction
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 (
) ..................................................................................... 20
Figure 3.5: Modelled domain of Case 3 (
)................................................................................... 20
Figure 3.6: Modelled domain of Case 5 (
) ..................................................................................... 21
Figure 3.7: Modelled domain of Case 6 (
)................................................................................... 21
Figure 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 4.13: Case 5, Contour of Pressure ............................................................................................................. 37 Figure 4.14: Case 5, Contour of Temperature .................................................................................................... 37 Figure 4.15: Case 5, Contour of Velocity .............................................................................................................. 37 Figure 4.16: Case 6, Contour of Pressure ............................................................................................................. 38 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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List of Tables Table 3.1: Dimensions of the micro-channel ...................................................................................................... 17 Table 4.1: Comparing Nusselt Number and Experimental Values from Lee et. Al. [7] ..................... 30 Table 4.2: Nusselt Number corresponding to the Mesh Used ........................................... ..................... ........................................... .......................... ..... 31 Table 4.3: Quantitative comparison of Heat Transfer and Pressure Loss for Single Rib ................. 42 42 Table 4.4: Quantitative comparison of Heat Transfer and Pressure Loss for Double Rib ............... 42
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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 inte gral 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 t he heat sink. Secondly by inducing i nducing 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.
Extended Ribs in a Micro 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.
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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. ii.
What are the best Numerical Methods available for this purpose? What are the limitations of Numerical Methods?
2. How to ensure that the Numerical Simulation is Correct? i. ii. iii.
What data is going to be used for Validation? What geometry is going to be employed? What simplifying assumptions can be applied to the system?
3. What sort of Extended Rib Profiles should be modelled? i. ii. iii.
What existing study of Ribs is available? What already has been deduced about Extended Rib Profiles? 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 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/cm 2, and chip temperatures were maintained below 110˚C. 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 and energy 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 classical correlations 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 al though 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 Computational Methodology
3.1 Numerical Methods Numerical Methods are a re employed to perform pe rform this study. s tudy. Using the numerical numeric al 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 easi ly obtained, that make the visualisation and understanding of the physical ph ysical 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 i nside 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 Domain for different Cases Cas es As this investigation is based on the Extended Rib Surface, the cases developed are just ‘Ribs’ added onto the ‘Bare Channel’ Heat Channel’ Heat 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 Rib – Rib – 2mm 2mm
Case 2.
Single Rib – Rib – 5mm 5mm
Case 3.
Single Rib – Rib – 15mm 15mm
Case 4.
Double Rib – Rib – 2mm 2mm
Case 5.
Double Rib – Rib – 5mm 5mm
Case 6.
Double Rib – Rib – 15mm 15mm
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As the name suggests the Single Rib case supports a ‘Single Rib’ rig right ht 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 the
’
inlet. The variable parameter for these cases will be the Rib Length‘ 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 (
Figure 7: Modelled domain of Case 3 (
)
)
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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 ‘
Figure 8: Modelled domain of Case 5 (
Figure 9: Modelled domain of Case 6 (
.
’
)
)
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3.3 Meshing The Computational Domain is meshed using a regular rectangular grid; which is composed of
elements. The Mesh is further refined and developed; the Refinement and
Development is discussed further in sections 4.2 and 4.3.
Figure 10: Front View of Mesh
Figure 11: Side View of the Mesh
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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. 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 the
coolant, 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 Average
Temperature 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. 25
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 temperature required. 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 the software 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 from FLUENT [12] and should yield different values of greater than 300k every test case.
̅
This is the average Wall Temperature; this is to be similarly extracted from 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 also extracted 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‘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
Symmetry: The side walls are set as ‘Symmetry’. o
This is where the Heat is transferred to the Heat Sink.
The side walls are set as Symmetry
Adiabatic 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.K 3. 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.
Computational Data
Experimental Data, Lee et. Al.
20 18 R E 16 B M U N14 T L E S 12 S U N E 10 G A R E V 8 A
6 4 0
500
1000
1500
2000
2500
REYNOLDS NUMBER
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.
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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 reali ty.
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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 be obtained. 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 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 Coarse
Mesh Size (elements)
1.9 1.9 x 10
Medium
1.6 1.6 x 10
Fine
3.6 3.6 x 10
Nusselt Number
9.50 9.71 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 don’t have over simplification and subsequent loss of data.
Figure 15: Resulting Mesh after Refinement
Figure 4.3 shows the Mesh obtained after the refinement 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 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 1.
Single Rib – Rib – 2mm 2mm
Case 2.
Single Rib – Rib – 5mm 5mm
Case 3.
Single Rib – Rib – 15mm 15mm
Case 4.
Double Rib – Rib – 2mm 2mm
Case 5.
Double Rib – Rib – 5mm 5mm
Case 6.
Double Rib – Rib – 15mm 15mm
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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Figure 19: Case 2, Contour of Pressure
Figure 20: Case 2, Contour of Temperature
Figure 21: Case 2, Contour of Velocity
Similar phenomenon for pressure and velocity can be seen in figure 4.7 and figure 4.9 for pressure and temperature respectively. There is a pressure rise in the rib region with the velocity being accelerated below the rib. However because the Rib Length was more - 5mm for this case, the turbulence caused by the disruption enables greater flow mixing and hence more heat transfer which can be seen from figure 4.8. From figure 4.8 it is observed the coolant temperature is cooler as compared to figure 4.5, hence more heat is transferred.
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Figure 22: Case 3, Contour of Pressure
Figure 23: Case 3, Contour of Temperature
Figure 24: Case 3, Contour of Velocity
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 it’s 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 t he rib.
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Figure 25: Case 5, Contour of Pressure
Figure 26: Case 5, Contour of Temperature
Figure 27: Case 5, Contour of Velocity
The pressure contour for the 5mm Double Rib case can be seen from figure 4.13, unlike the single Rib case the pressure is equally distributed past the ribs, and the velocity development as seen from the velocity contour in figure 4.15 is evenly developed throughout the channel, this results in even heat transfer throughout the channel. Figure 4.14, the temperature contour for the coolant shows how the temperature distribution is even and hence, better heat transfer. The 5mm is similar to the 2mm case; just the pressure developed is not much higher.
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Figure 28: Case 6, Contour of Pressure
Figure 29: Case 6, Contour of Temperature
Figure 30: Case 6, Contour of Velocity
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. respectivel y.
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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.
Bare Channel
2mm
5mm
15mm
16.00
14.00
R E B M U12.00 N T L E S 10.00 S U N E G A 8.00 R E V A
6.00 4.00
0
500
1000
1500
2000
2500
REYNOLDS NUMBER
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’. 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 Re ynolds 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 Rib – Rib – 15mm 15mm has a reduced heat transfer performance. Looking also at figure 4.21 we can see that the Single Rib – Rib – 15mm 15mm has the worst pressure loss; explaining even why the Heat Transfer performance is worse off.
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Bare Channel
2mm
5mm
15mm
16.00
14.00 R E B M12.00 U N T L E S 10.00 S U N E G A 8.00 R E V A
6.00
4.00 0
500
1000
1500
2000
2500
REYNOLDS NUMBER
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 f rom the pressure and velocity contours.
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4.4.3 Comparing Pressure Loss Single Rib (2mm)
Single Rib (5mm)
Single Rib (15mm)
Double Rib (2mm)
Double Rib (5mm)
Double Rib (15mm)
120.00
100.00 ) A 80.00 P K ( P O R D 60.00 E R U S S E R 40.00 P
20.00
0.00 0
500
1000
1500
2000
2500
REYNOLDS NUMBER
Figure 33: Pressure Loss for all Cases
Figure 4.21 is a graph of Pressure Loss for all the cases. The Pressure Loss in all the Rib configurations is compared. It is seen from the Graph that the Pressure Loss for the Single Rib cases is generally higher than their Double Rib counterparts. counterparts. As expected the worst worst pressure loss is for Case 3 (Double (Double Rib 15mm). As pressure loss happens happens the flow is greatly affected. The coolant is not as frequently being supplied, heat transfer reduces and hence overall temperature increases. The Best Heat Transfer case was Case 6 (Double Rib 15mm); the Pressure Loss was greater than the other Double Rib cases. We can also conclude that for these channel dimensions up till Pressure Loss of 80kPa the t he Heat Transfer performance continues to increase.
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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
Re 500 600 700 800 900 1000 1100 1200 1500 2000
Case 1 (2mm) 6.70 7.35 7.96 8.54 9.08 9.62 10.14 10.63 12.04 14.15
Nusselt Number Case 2 Case 3 (5mm) (15mm) 6.77 5.42 7.43 5.96 8.04 6.45 8.62 6.91 9.17 7.33 9.70 7.72 10.20 8.09 10.70 8.46 12.10 9.45 14.22 10.89
Pressure Drop (kPa) Bare Case 1 Case 2 Case 3 Channel (2mm) (5mm) (15mm) 6.72 11.43 15.34 22.11 7.35 13.38 18.75 27.21 7.95 18.94 22.25 32.47 8.51 21.96 25.83 37.86 9.04 25.05 29.50 43.37 9.55 28.26 33.25 48.99 10.04 31.47 37.08 54.78 10.52 34.79 40.99 60.50 11.86 45.20 53.20 78.66 13.86 63.99 75.12 110.67
Table 4.4: Quantitative comparison of Heat Transfer and Pressure Loss for Double Rib
Re 500 600 700 800 900 1000 1100 1200 1500 2000
Case 4 (2mm) 6.68 7.31 7.90 8.46 8.99 9.51 10.01 10.49 11.86 13.94
Nusselt Number Case 5 Case 6 (5mm) (15mm) 6.71 7.62 7.34 8.37 7.94 9.07 8.50 9.72 9.04 10.33 9.57 10.91 10.07 11.47 10.56 12.00 11.95 13.50 14.06 15.72
Bare Channel 6.72 7.35 7.95 8.51 9.04 9.55 10.04 10.52 11.86 13.86
Pressure Drop (kPa) Case 4 Case 5 Case 6 (2mm) (5mm) (15mm) 11.76 12.92 15.58 14.52 15.68 18.92 17.13 18.51 22.33 19.79 21.39 25.82 22.50 24.33 29.38 25.27 27.33 33.01 28.09 30.39 36.71 30.97 33.51 40.47 39.93 43.21 52.15 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 Transfer was 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. 43
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 these enhancements 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 accuratel y 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 and hence 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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11. Cui, J. and Fu, Y. (2012). A numerical study on pressure drop in microchannel flow with different bionic micro-grooved surfaces. Journal of Bionic Engineering , 9(1), pp.99--109. 12. ANSYS® FLUENT, Release 14.0, ANSYS, Inc. (2013) 13. Chai, L., Xia, G., Wang, L., Zhou, M. and Cui, Z. (2013). Heat transfer enhancement in microchannel heat sinks with periodic expansion--constriction cross-sections. International Journal of Heat and Mass Transfer , 62, pp.741--751. 14. Moradi, H. and Floryan, J. (2013). Maximization of heat transfer across microchannels. International channels. International Journal of Heat and Mass Transfer , 66, pp.517--530. 15. Xie, G., Liu, J., Ligrani, P. and Zhang, W. (2013). Numerical analysis of flow structure and heat transfer characteristics in square channels with different internal protruded dimple geometrics. International Journal of Heat and Mass Transfer , 67, pp.81--97. 16. Xia, G., Zhai, Y. and Cui, Z. (2013). Numerical investigation of thermal enhancement in a micro heat sink with fan-shaped reentrant cavities and internal ribs. Applied Thermal Engineering , 58(1), pp.52--60. 17. Ahmed, H., Mohammed, H. and Yusoff, M. (2012). An overview on heat transfer augmentation using vortex generators and nanofluids: Approaches and applications. Renewable and Sustainable Sustainable Energy Reviews, Reviews , 16(8), pp.5951--5993. 18. ANSYS® DesignModeller, Release 14.0, ANSYS, Inc. (2013) 19. Ip.sandia.gov, (2011). Sandia National Laboratories: The Sandia Cooler . Cooler . [online] Available at: https://ip.sandia.gov/technology https://i p.sandia.gov/technology.do/techID=66 .do/techID=66 [Accessed 25 Apr. 2014].
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Appendix
Appendix 1: Gantt chart used for Project Planning and Organization
Appendix 2: Validation using different turbulence models, k-3 a nd 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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Developed Simulation
Validated Simulation
Developed Test Cases Case s
Simulate Test Cases Ca ses
Evaluate Results
Appendix 6: Flow of work for this study
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