TABLE OF CONTENTS
CHAPTER
1
2
TITLE
PAGE
DECLARATION
ii
DEDICATION
iv
ACKNOWLEDGEMENTS
vi
ABSTRACT
vii
ABSTRAK
viii
TABLE OF CONTENT
ix
LIST OF TABLES
xii
LIST OF FIGURES
xiii
LIST OF SYMBOLES
xv
INTRODUCTION
1
1.1 Background of the study
1
1.2 Statement of problem
4
1.3 Objectives
4
1.4 Scope of the study
5
LITERATURE REVIEW
6
2.1
How to simulate a fluid by CFD methods
6
2.2
Kinetic Theory
9
2.3
Lattice Boltzmann method
2.3.1 History
10
2.3.2 The Boltzmann equation
2.3.3 Distribution Function
11
2.3.4
14
Boltzmann Distribution
2.3.5 The BGKW Approximation
2.3.6 Two Dimensional Structure in LBM
10
12
15
17
2
2.3.6.1 D2Q5 and D2Q4 Arrangements
2.3.6.2 D2Q9 Arrangement
17
18
2.3.7 Boundary Condition
2.3.8 Advantages of Lattice Boltzmann Method
19
20
2.4 NanoFluids
2.4.1 History
21
21
2.4.2 Model description
22
2.4.2.1 Single phase
22
2.4.2.2 Two-phase model
23
2.4.3 Thermal conductivities of nanofluids
2.4.4 Application of nanofluids
24
26
2.4.4.1 Heat Transfer Applications
26
2.4.4.2 Automotive Applications
27
2.4.4.3
Electronic
Applications
(Cooling
Microchips)
2.4.4.4 Biomedical Applications
2.5
3
4
4
REFRENCES
Lattice Boltzmann model for nanofluids
of
30
30
31
RESEARCH METHODOLOGY
40
3.1
Introduction
3.2 Algorithm of Lattice Boltzmann Method (LBM)
40
3.3
42
Flow Chart for LBM algorithm
40
3.4 Geometry
43
ANALYSIS, FINDINGS AND DISCUSSION
44
4.1
44
Introduction
4.2 Grid Dependency Test
44
4.3 Effect of volume fraction
46
4.4 Effect of Rayleigh number
53
CONCLUSIONS
55
57
3
61
APPENDIX
LIST OF TABLES
4
TABLE NO.
1.1
TITLE
Development from the Boltzmann equation to the
PAGE
16
lattice Boltzmann
1.2
Various viscosity models for nanofluids
33
1.3
Various thermal conductivity models for nanofluids
34
4.1
Grid size for Rayleigh numbers
45
LIST OF FIGURES
5
FIGURE NO.
TITLE
PAGE
2.1
Fraction of molecules in different speeds
13
2.2
Lattice arrangements for 2D problems, D2Q4 and D2Q5
18
2.3
Lattice arrangements for 2D problems, D2Q9
18
2.4
Bounce back scheme one
19
2.5
Bounce back scheme two
20
3.1
Geometry of this study
43
4.1
Grid dependency test for different Rayleigh numbers
45
4.2
Changing nusselt average with volume fraction for CuO
46
nanoparticles
4.3
Changing nusselt average with volume fraction for Al2O3
47
nanoparticles
4.4
Streamlines of CuO nanoparticles in phi=5% for a)Ra=103
48
b)Ra=104 c)Ra=105
4.5
Effect of volume fraction on streamlines of Al2O3 nanofluid
49
with aspect ratio 1.0 for Rayleigh of a)103 b)104 c)105
4.6
Isotherms of different volume fraction of a)CuO b)Al2O3
nanofluid in Ra=10
4.7
50
3
Isotherms of different volume fraction of a)CuO b)Al2O3
50
nanofluid in Ra=104
4.8
Effect of volume fraction on locale Nusselt number across
51
heated wall
4.9
Variation of y-component of velocity at the horizontal
52
centerline at a)Ra=104 & b)Ra=105 for Al2O3
4.10
Changing of Nusselt number by increasing Rayleigh number
53
4.11
Comparison of isotherms by changing Rayleigh number for
54
CuO, =5% for all the aspect ratios a)103 b)104 c)105
6
LIST OF SYMBOLES
7
cp
-
Specific heat capacity (J/kg K)
C
-
Lattice streaming speed (m/s)
Ar
-
Aspect ratio
fi
-
Density distribution function
fieq
-
Equilibrium distribution function
gi
-
Energy distribution function
gieq
-
Equilibrium distribution function
lx
-
Length of channel
ly
-
Height of channel
k
-
Thermal conductivity (W/m K)
Nu
-
Nusselt number=−(knf/kf)×(∂θ/∂Y)
Nuave
-
Average Nusselt number=∫Nu⋅dx
Pr
-
Prandtl number=υ/α
Ra
-
Rayleigh number
T
-
Temperature (K)
u
-
Velocity in x direction
v
-
Velocity in y direction
H
-
Enclosure height
W
-
Enclosure weight
BGK
-
Bhatnagar-Gross-Krook
CFD
-
Computational Fluid Dynamics
D2Q9
-
Three
FEM
-
FDM
-
Finite Difference Method
FVM
-
Finite Volume Method
LB
-
Lattice Boltzmann
Abbreviayions
Dimensions nineteen
Boltzmann
method
Finite
Element Method
velocities lattice
8
LBE
-
Lattice Boltzmann Equation
LBM
-
Lattice Boltzmann Method
LGA
-
Lattice Gas Approach
PDE
-
Partial Differential Equations
MRT
-
Multi-Relaxation Time
SRT
-
Single Relaxation Time
Greek symbols
α
-
Thermal diffusivity (m2/s)
ε
-
Internal energy (J/kg)
ϕ
-
Particle volume fraction
μ
-
Dynamic viscosity (kg/m s)
ρ
-
Density (kg/m3)
τ
-
Relaxation time for fi
τc
-
Relaxation time for gi
υ
-
Kinematic viscosity (m2/s)
avg
-
average
C
-
Cold
F
-
Fluid
H
-
Hot
nf
-
Nanofluid
subscripts