CHAPTER ONE

INTRODUCTION

1.0     BACKGROUND TO THE STUDY

Oscillatory flows has known to result in higher rates of heat and mass transfer, many studies have been done to understand its characteristics in different systems such as reciprocating engines, pulse combustors and chemical reactors.

The applications of variable suction and chemical reaction play important role in the design of chemical processing equipments, formation and dispersion of fog, distribution of temperature and moisture over agricultural fields and groves of fruits damage of crops due to freezing, food processing and cooling of towers. Investigation of periodic flow through a porous medium is important from practical point of view because fluid oscillations maybe expected in many magneto hydrodynamic devices and natural phenomena, where fluid flow is generated due to oscillating pressure gradient or due to vibrating walls. Consequently, Ayuba et al (2015) studied the effect of variable suction on magneto hydrodynamic couette flow through porous medium in the slip flow regime.

Joseph et al (2015) examined the problem of unsteady MHD mixed convictive oscillatory flow of an electrically conducting optically thin fluid through a planer channel filled with saturated porous medium. The effect of buoyancy, heat source, thermal radiation and chemical reaction of the fluid were taken into considerations with slip boundary condition, varying temperature and concentration. The closed-form analytical solutions are obtained for the momentum, energy and concentration equations. Chamkha (2003) studied the MHD flow of a numerical of uniformly stretched vertical permeable surface in the presence of heat generation/absorption and chemical reaction. Idowu et al (2013) studied the effect of chemical reaction on MHD oscillatory flow through a vertical porous plate with heat generation. Hady et al (2006) researched on the problem of free convection flow along a vertical wavy surface embedded in electrically conducting fluid saturated porous media in the presence of internal heat generation.

1.1   STATEMENT OF THE PROBLEM

My work is an extension of Idowu et al (2013) in which they study the effect of chemical reaction on MHD oscillatory flow through a vertical porous plate with heat generation.

We modified their work to show the effect of variable suction and chemical reaction on MHD oscillatory flow through a vertical porous plate with heat generation.

1.2    AIM AND OBJECTIVES

The aim of this project is to solve the problem of MHD oscillatory flow through a vertical porous plate with heat generation and to analyse the effect of variable suction and chemical reaction.

To achieve this we have the following objectives

Ø  To find the corresponding analytical solution of velocity and temperature of the system.

Ø  To determine the effects of flow parameters on the flow field such as: Reynolds number Re, Rotation parameter Ω, Hartmann number M, e.t.c.

Ø  To determine the solution for the dimensionless velocity, temperature, concentration of the governing equations with the corresponding boundary condition using dimensionless variables.

1.3    SCOPE AND LIMITATION

This project work on the effect of variable suction and chemical reaction on MHD oscillatory flow through a vertical porous plate with heat generation.

The solution of the governing equations that is; the velocity, temperature and species concentration profile are obtained using a method called perturbation technique.

1.4SIGNIFICANCE OF THE STUDY

Ø  It gives you an idea about the solution of the dimensionless velocity U and dimensionless temperature obtained by the use of close form method.

Ø  This study has the potential application in oil recovery filtration systems.

1.5     THEORETICAL FRAME WORK

This project contained five chapters; chapter one start with introduction, statement of the problem, Nomenclature, Aim and objectives, Scope and Limitation, and Significant of the study. Chapter two contained Literature review. Chapter three discussed the formulation of the problem, method of solution/ solution of the problem.  The transformations of the governing equations are also showed from the dimensional to non-dimensional equations in this chapter, also the chapter contained formation and methodology used to solve the problem analytical and MATLAB was used to generate the graphs. In chapter 4, results and discussions was presented on the method employed. We gives a detail conclusion in chapter 5 together with the summary of research along side with some future recommendations. Also references are listed after chapter 5, then, the appendix showing the mathematical formulas for the solutions obtained in this project work.

1.6     DEFINITION OF BASIC TERMS

MAGNETOHYDRODYNAMIC (MHD): it is defined as the study of motion of electrically conducting fluid. Example of such fluids include plasma, salt, water, liquid metal e.t.c

 OSCILLATORY FLOW: a particle or rigid body performs oscillations if its travel to and fro in some way about a central position, usually a point of stable equilibrium.

SCHMIDT NUMBER (SC): is a measure of relative thickness of the velocity and concentration boundary layer.

PRESSURE: The force (p) per unit area (A) is called pressure.

GRASHOF NUMBER (GR): it is the measure of the relative magnitude of the buoyancy force and the opposing viscous force acting on the fluid.

REYNOLDS NUMBER (Re): is the ratio of initial force to viscous force in the fluid.

ECKERT NUMBER (Ec): is a dimensionless number used in continuum mechanics.

PRANDTL NUMBER (Pr): defined as the ratio of momentum diffusivity to thermal diffusivity.

KINEMATIC VISCOSITY: is the ratio of absolute (or dynamic) viscosity to density a quantity in which no force involved.

SPECIFIC HEAT CAPACITY: is the amount of heat per unit mass required to raise the temperature by one degree Celsius.

TEMPERATURE: is the degree of hotness or coldness of an object.

MATLAB: matlab is an integrated technique, computing environment that combines numeric computation advance graphics, visualization and high level programming language.

1.7   NOMENCLATURE

K         permeability parameter

Pr        prandtl number

Gr        Thermal Grashof number

Gm      modified Grashof number

Re        Reynolds number

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