Travelling Waves Solutions for the Transesterification Reaction Kinetics of Biodiesel Production Using Tanh Method.

ABSTRACT A mathematical model consisting of a set of two coupled non-linear reaction diffusion equations has been developed. The model is based on the chemical kinetics of transesterification for biodiesel production using irreversible and non-catalytic conditions. Employing the hyperbolic tangent approach, an exact analytical solution for the travelling-waves of a finite series form was found. The wave number and the speed of the wave were determined. Furthermore,physical interpretations were deduced from the analysis of the model.

TABLE OF CONTENTS

Title Page ………………………………………………………………………………….i

Certification ……………………………………………………………………….............ii

Dedication …………………………………………………………………………………iii

Acknowledgement………………………………………………………………................iv

Table of Contents ………………………………………………………………………….v

Abstract …………………………………………………………………………………….vii

CHAPTER ONE

1.1 Introduction…………………………………………………………………………1

1.2 Aim of the Study…………………………………………………………................2

CHAPTER TWO

2.1 Literature Review………………………………….………………………………..3

CHAPTER THREE

3.0 Definition of Basic concepts…..…………………………………………...............8

3.1 The Concept of Biodiesel…………….…………………………………………….8

3.2 The Concept of Transesterification………………………………………………..8

3.3 The Concept of Kinetics of Transesterification……………………………………9

3.3.1 Variables for Transesterification………………………………………………….11

3.4 Concept of Reaction Diffusion……………………………………….……………11

3.5 Nonlinear Travelling waves Solutions…………………………………………….13

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CHAPTER FOUR

4.0 The Model……………………………………………………………………….14

4.1 Basic Assumptions………………………………………………………………15

4.2 Assumption for the model……………………………………………………….16

4.3 Non-dimensionalization………………………………………………………….17

4.4 Method of solution………………………………………………………………19

4.4 Solutions to the Model Using Tanh Method…………………………………….20

CHAPTER FIVE

5.0 Analysis of results………………………………………………………………28

5.1 Stability of the Fixed Points…………………………………………………….29

5.2 Discussion of Results……………………………………………………………30

5.3 Concluding remark………………………………………………….…………..31

5.4 Recommendation………………………………………………………………..31

REFERENCES…………………………………………………………………………32