### A STUDY ON MAGNETOHYDRODYNAMIC NATURAL AND MIXED CONVECTION FLOWS IN VERTICAL CONCENTRIC ANNULI FILLED WITH POROUS MATERIAL

Title Page
Tables of Contents
Nomenclature and Greek Letters

CHAPTER ONE
GENERAL INTRODUCTION
1.1Introduction
1.2       Statement of the Problem
1.3       Aim and Objectives of the Study
1.4       Research Methodology
1.5       Organization of the Dissertation
1.6       Basic Definitions
1.7       Basic Hydrodynamic Equations

CHAPTER TWO
LITERATURE REVIEW
2.1       Introduction
2.2       Natural Convection
2.3       Magnetohydrodynamic (MHD)
2.4       Mixed Convection

CHAPTER THREE
MATHEMATICAL ANALYSIS AND SOLUTIONS
3.1       Introduction
3.2       Natural convection flow in vertical concentric annuli filled with porous material of variable porosity in presence of radial magnetic field
3.2.1    Mathematical Description
3.3       MHD Mixed Convection Flow in a Vertical Concentric Annuli Filled with Porous Material having Variable Porosity in Presence of Radial Magnetic Field
3.3.1    Mathematical Description
3.4       Non-Dimensionalization
3.5       Transformation for Linear Second Order Differential Equations
3.6       Solution to Problem 3.2
3.6.1    Skin Friction of Problem 3.2
3.7       Solution to Problem 3.3
3.7.1    Skin Friction of Problem 3.3
3.8       Validation of the Method

CHAPTER FOUR
RESULTS AND DISCUSSIONS
5.1       Introduction
5.2       Results and Discussion of problems 3.2
5.2       Results and Discussions of Problem 3.3

CHAPTER FIVE
SUMMARY, CONCLUSION AND RECOMMENDATIONS
5.1       Summary
5.2       Conclusion
5.3       Recommendation
REFERENCES
APPENDICE

ABSTRACT

This dissertationconsiders steady fully developed free and mixed convective flows of a viscous, incompressible, electrically conducting fluid in vertical concentric annuli, formed by two infinite and vertical concentric cylinders, filled with porous material having variable porosity in the presence of radial magnetic field. Unified exact solutions are derived by taking into account an isothermal or isoflux thermal boundary condition at the outer surface of inner cylinder. The solutions obtained are graphically represented and the effects of various controlling parameters such as Hartmann number, Darcy number, ratio of viscosity and the gap between the cylinders on the flow formation are discussed. The major results reveal that velocity of the fluid in the first problem is higher in case of isothermal heating of outer surface of inner cylinder compared to constant heat flux heating when the gap between cylinders is less or equal to radius of inner cylinders while reverse phenomena occur when the gap between cylinders is greater than radius of inner cylinder. In the second problem, velocity is approximately the same for both isothermal and isoflux thermal boundary conditions.

CHAPTER ONE

GENERAL INTRODUCTION

1.1  Introduction

To appreciate the importance of fluid dynamics in life demands little more than just a glance around us. In general, life as we know would not exist if there are no fluids and the behavior they exhibit. The water and air we respectively drink and breathe are fluids. In addition, our body fluids are mostly water based. Essential to our healthy living is the proper movement of these fluids within our bodies. In a more practical setting, like in our transportation systems, recreation, entertainment (sound from radio speakers for example) and our sleep (water beds), fluids greatly influence our comfort. It is clear to see from this that engineers need a clear knowledge of fluid behavior to handle many systems of their encounter. The study of electrically conducting fluid (e.g. liquid metals) called magnetohydrodynamics (MHD) flow is found in numerous pieces of literature. This is due to its many areas of industrial applications in geophysics and engineering to determine the desired convective flow in cases like the design of MHD power generators, cooling of nuclear reactors and changing of metals solidification processes. Natural convection flow in a vertical channel is vital in many transport processes both in nature and engineering applications. Examples of flow and heat transfer include natural circulation in geothermal reservoirs, porous insulators, solar power collectors, spreading of pollutants and so on. Similarly, combined natural and forced convection flow known as mixed convection flow in a vertical channel has many applications both in nature and engineering in many transport processes such as in cooling of electronic devices....

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