vi
TABLE OF CONTENTS
CHAPTER
TITLE
PAGE
DECLARATION OF THESIS
SUPERVISOR’S DECLARATION
1
TITLE PAGE
i
DECLARATION PAGE
ii
ACKNOWLEDGEMENT
iii
ABSTRACT
iv
ABSTRAK
v
TABLE OF CONTENTS
vi
LIST OF TABLE
ix
LIST OF FIGURES
x
LIST OF SYMBOLS / NOTATIONS
xi
LIST OF APPENDIX
xiii
INTRODUCTION
1.1 Research background
1
1.2 Significance of research
2
1.3 Objectives of the study
3
1.4 Scope of the study
3
1.5 Thesis outline
3
vii
2
3
4
LITERATURE REVIEW
2.1 Introduction
5
2.2 Microgravity and g-jitter
5
2.3 G-jitter and its effects
7
2.4 The effect of g-jitter on heat transfer
9
THE EFFECT OF G-JITTER ON HEAT
TRANSFER FROM A SPHERE WITH
CONSTANT HEAT FLUX
3.1 Introduction
13
3.2 Basic equations
13
3.3 Solution Procedure
17
METHOD OF SOLUTION IN FINDING THE
NUMERICAL SOLUTION FOR G-JITTER
INDUCED FREE CONVECTION WITH
CONSTANT HEAT FLUX
4.1 Governing Equations in a First-Order System
21
4.2 Crank-Nicolson Scheme
23
4.3 MATLAB Programming in processing
elimination method
5
26
RESULTS AND DISCUSSIONS
5.1 Numerical solution for g-jitter induced free
convection with constant heat flux
5.2 Velocity and temperature profiles
27
31
viii
6
REFERENCES
Appendix A
CONCLUSION
6.1 Summary of research
36
6.2 Suggestions for Future Research
37
38
43 - 53
ix
LIST OF TABLE
TABLE NO.
5.1
TITLE
PAGE
 2 0 s 
Value of skin friction
a , 0  and
 2
wall temperature 0   a , 0  at different
position of  for Pr = 0.7, 1 and 7
s
28
x
LIST OF FIGURES
FIGURE NO.
TITLE
PAGE
3.1
Physical model and coordinate system
14
4.1
Net rectangle for difference approximations
23
4.2
MATLAB implementation of naïve Gaussian
elimination
26
Variations of the skin friction with  for different
values of Prandtl numbers, Pr
29
Variations of the wall temperature with  for
different values of Prandtl number, Pr
30
Profiles of the non-dimensional velocity for
different values of  a when Pr = 0.7
32
Profiles of the non-dimensional temperature for
different values of  a when Pr = 0.7
33
Profiles of the non-dimensional velocity for
different values of  a when Pr = 7
34
Profiles of the non-dimensional temperature for
different values of  a when Pr = 7
35
5.1
5.2
5.3
5.4
5.5
5.6
xi
LIST OF SYMBOLS / NOTATIONS
a
-
radius of a sphere
g t  -
g-jitter or residual gravity field
g0
-
magnitude of g-jitter
Gr
-
Grashof number
k
-
unit vector pointing vertically upward
p
-
non-dimensional pressure
Pr
-
Prandtl number
qw
-
wall heat flux
r
-
non-dimensional radial coordinate
Re
-
Reynolds number
t
-
time
T
-
non-dimensional fluid temperature
T0
-
mean temperature
Uc
-
characteristic velocity
u, v
-
velocity components along x and y axes

-
non-dimensional velocity vector
Greek symbols
T
-
thermal expansion coefficient

-
non-dimensional transformed independent variables
a
-
polar angle
c
-
thermal conductivity

-
dynamic viscosity

-
kinematic viscosity
xii

-
density

-
non-dimensional small quantity

-
non-dimensional concentration

-
non-dimensional stream function

-
frequency of g-jitter oscillation
Superscripts

-
dimensional variables
'
-
differentiation with respect to 
s
-
denotes steady part of the solution
u
-
denotes unsteady part of the solution
Subscripts
w
-
condition at the wall

-
ambient condition
xiii
LIST OF APPENDIX
APPENDIX
A
TITLE
MATLAB For Numerical Solution For
G-jitter Induced Free Convection With
Constant Heat Flux
PAGE
43