### A STUDY OF TIME DEPENDENT NATURAL CONVECTION FLOW IN A VERTICAL POROUS CHANNEL

Title page
Abstract
Nomenclature and Greek letters

CHAPTER ONE
1          GENERAL INTRODUCTION
1.1       Introduction
1.2       Motivation
1.3       Aim and Objectives of the study
1.4       Methodology
1.5       De nition of Basic terms
1.6       Basic Equations
1.7       Organisation of the thesis

CHAPTER TWO
2.0       LITERATURE REVIEW
2.1       Heat Generation/Absorption
2.2       Suction/Injection

CHAPTER THREE
3.0       THE PROBLEMS UNDER CONSIDERATION
3.1       The e ect of transpiration and heat generation on transient natural convection in a vertical channel
3.2       E ect of transpiration on natural convection ow of heat generating uid in a vertical channel with isothermal and adiabatic conditions
3.3       Riemann-sum inversion of Laplace transform functions

CHAPTER FOUR
4.0       DISCUSSION OF THE RESULTS
4.1       Discussion of problem 3.1
4.2       Discussion of problem 3.2
4.3       Validation

CHAPTER FIVE
5          SUMMARY AND CONCLUSION
5.1       Summary
5.2       Conclusion
REFERENCES
Appendices

Abstract

The transient motion of a viscous incompressible uid in vertical porous channel is rst anal-ysed considering the e ect of transpiration and heat generation in the channel. In the second part of the problem, natural convection ow of an incompressible viscous uid in a vertical channel is analysed when the porous plates are subjected to isothermal and adiabatic condi-tions. The governing equations are solved using the Laplace transform method. Due to the di culties that are associated with the analytical inversion of the obtained results from the Laplace to the time domain, the Riemann-Sum approach is employed to do the inversion, thus obtaining the temperature, velocity, skin-friction and rate of heat transfer. To validate the Riemann-sum approach used, the steady state solution for velocity and temperature are obtained analytically. An excellent agreement is found between the steady state solutions and the transient solutions at large values of time. From the course of investigation, it is revealed that heat generation leads to an increase in heat transfer on the cold plate while it decreases it on the heated plate.

CHAPTER 1

GENERAL INTRODUCTION

1.1         Introduction

Fluid ows are of vital interest in almost every sphere of life. This is completely attributed to its wide applications in various elds. These applications are found in the eld of Engineer-ing, Geophysical, environmental dynamics, architectural designs and Biological Sciences for better understanding of researches and applications. Fluid through vertical channel is of great importance in many technological ows. Examples of these are found in the design of nuclear reactors, cooling of electronic equipment, heating of building through Trombe walls,ventilating systems, cooling and distillation towers, solar energy systems and many chemical processes. Others are found in the area of solid matrix heat exchanger, nuclear waste disposal and ther-mal insulations.

In other instances, the natural convection ow driven by internal heat generation/absorption has been of great interest. This interest stems from various possible applications of this type of ow in many process. These include cooling of nuclear reactors and convection in the earth mantle-Mckenzie et al. [1974]. Furthermore, perhaps the most wide spread application is in the eld of nuclear energy such as in nuclear-reactor core and in post-accident heat removal......

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