MAGNETOHYDRODYNAMIC UNSTEADY FREE CONVECTION FLOW PAST VERTICAL POROUS PLATES WITH SUCTION AND OSCILLATING BOUNDARIES

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ABSTRACT

In this dissertation, the problems of Magnetohydrodynamic unsteady free convection flow

past vertical porous plates with suction and oscillating boundaries are studied. The linear

and nonlinear partial differential equations governing the flow problems and boundary

conditions were transformed into dimensionless form, and the perturbation techniques

applied in getting analytical solutions for the velocity, temperature, the skin friction

coefficient and Nusselt number. It was observed that an increase in the values of thermal

Grashof number, Eckert number and heat source increases velocity profile, while an

increase in Darcy term retards the velocity profile. An increase in heat source and Grashof

number, also increases the Heat transfer coefficient. The effects of various parameters on

the flow fields have been presented with the help of graphs and tables.



TABLE OF CONTENTS

LIST OF FIGURES
LIST OF TABLES
DIMENSIONLESS NUMBERS
GREEK SYMBOLS
NOMENCLATURE
ABSTRACT

CHAPTER ONE
INTRODUCTION
1.1       Background of the study
1.2       Statement of the Problems
1.3       Aim and Objectives of the Study
1.4       Significance of the Study
1.5       Definitions of Basic Concepts
1.6       Structure of the Dissertation

CHAPTER TWO
LITERATURE REVIEW
2.1       Introduction
2.2       Some Related Literature Review

CHAPTER THREE
METHODOLOGY
3.2       Regular perturbation expansions
3.3       Problem Formulation
3.3.1    Magnetohydrodynamic Unsteady Free Convection Flow Past Vertical Porous Plates with Heat Deposition
3.3.2    Magnetohydrodynamic Unsteady Free Convection Flow Past an Infinite Vertical Porous Plates with Heat Deposition
3.3.3    Darcy Forchcheimer Magnetohydrodynamic Unsteady Free Convection Flow Past Vertical Porous Plates with Heat Deposition

CHAPTER FOUR
RESULTS AND DISCUSSION
4.1       Introduction
4.2       Magnetohydrodynamic Unsteady Free Convection Flow Past Vertical Porous Plates with Heat Deposition
            4.2.1    Velocity field
            4.2.2    Temperature field
            4.2.3    Skin friction coefficient and Nusselt number
4.3       Magnetohydrodynamic Unsteady Free Convection Flow Past an Infinite Vertical Porous Plates with Heat Deposition
            4.3.1    Velocity field
            4.3.2    Temperature field
            4.3.3    Skin friction coefficient and Heat transfer coefficient
4.4       Darcy Forchcheimer Magnetohydrodynamic Unsteady Free Convection Flow Past Vertical Porous Plates with Heat Deposition
            4.4.1    Velocity field
            4.4.2    Temperature field
            4.4.3    Skin friction coefficient and Heat transfer coefficient

CHAPTER FIVE
SUMMARY, CONCLUSION AND RECOMMENDATIONS
5.1       Introduction
5.2       Summary
5.3       Conclusion
5.3.1    Magnetohydrodynamic Unsteady Free Convection Flow Past Vertical Porous Plates with Heat Deposition
5.3.2    Magnetohydrodynamic Unsteady Free Convection Flow Past an Infinite Vertical Porous Plates with Heat Deposition
5.3.3    Darcy Forchcheimer Magnetohydrodynamic Unsteady Free Convection Flow Past Vertical Porous Plates with Heat Deposition
5.4       Recommendations
5.5       Contributions
5.6       Limitations of the Study
REFERENCES
APPENDICES


CHAPTER ONE

INTRODUCTION

1.1  Background of the study

As understanding of the natural world has grown, human civilization and communities

have consistently been established at locations that feature a viable source of fluid flowing.

Throughout history, people have continuously attempted to manipulate the natural fluid

flow, in order to effect an improvement in such areas as agricultural stability, living

environment, and transportation.

The Magnetohydrodynamic (MHD) channel flow, was first described theoretically by

Hartmann (1937), who considered plane Poiseuille flow with a transverse magnetic field.

Since then, the study of MHD has been an active area of research because of its geophysical

and astrophysical applications.  Ahmed and Batin (2013), investigated the effects of

conduction-radiation and porosity of the porous medium on laminar convective heat transfer

flow of an incompressible, viscous, electrically conducting fluid over an impulsively started

vertical plate embedded in a porous medium in presence of transverse magnetic field.

Modern technologies have emerged, and we have become increasingly reliant on the

fundamental principles of fluid flow. Humanity has come to depend upon the development

and design of modern transport, such as cars, ships and air-crafts, which are rooted in an

essential understanding and knowledge of fluid flows and this knowledge area, is an integral

area for solving aerodynamic problems. The area also provides a plethora of engineering

problems concerning energy conservation and transmission. Time past methodological

engineering, and even biomedical studies, have proven the universally accepted tenant that

understanding fluid flow is critical to the development of applied knowledge.

The effect of radiation, chemical reaction and variable viscosity on hydromagnetic heat and


mass transfer in the presence of magnetic field are studied by Seddeek and Almushigeh.....


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