About Book

Numerical analysis naturally finds application in all fields of engineering and the physical sciences, but in the 21st century also the life sciences, social sciences, medicine, business and even the arts have adopted elements of scientific computations. Numerical analysis is the study of algorithms that use numerical approximation for the problems of mathematical analysis. It emphasizes on the methods and applications of computing numerical data. It offers both new theories and their applications, showing bridge between theoretical investigations and possibility to apply them by researchers of different branches of science. It is used in the fields like system theory, science education, knowledge visualization and even in philosophy of science. The growth in computing power has revolutionized the use of realistic mathematical models in science and engineering, and subtle numerical analysis is required to implement these detailed models of the world. This book delves into the advanced concepts of MHD nanofluid flow, convective boundary, bifurcation scenarios, compressible flow and methods of structural fatigue, terahertz communications, incompressible fluid flow and heat transfer. It presents numerical analysis in the most comprehensible and easy to understand language. It includes topics, which are important for the holistic understanding of the subject matter. It studies, analyses and upholds the pillars of the subject and its utmost significance in modern times. Coherent flow of topics, student-friendly language and extensive use of examples make this book an invaluable source of knowledge. It will serve as a valuable source of reference for students and researchers.

Preface............................................................................................................v

Chapter 1 Numerical Analysis of the Liquid-Gas-Solid Three Phase Flow Inside AWJ Nozzle.....................................................................................1

Abstract ..................................................................................................1

1. Introduction............................................................................................2

2. Governing equations and numerical method..................................4

3. Results and discussion.......................................................................11

4. Conclusions..........................................................................................16

Acknowledgements.............................................................................17

Chapter 2 Numerical Analysis of Broadband Dipole-Loop Graphene Antenna for Applications in Terahertz Communications................................19

Abstract.................................................................................................19

1. Introduction..........................................................................................20

2. Antenna geometry..............................................................................21

3. Theoretical development....................................................................22

4. Numerical results................................................................................24

5. Conclusions..........................................................................................35

Acknowledgements.............................................................................35

Conflict of interest..............................................................................35

Chapter 3 Numerical Analysis of the Incompressible Fluid Flow and Heat Transfer.......................................................................................................38

Abstract.................................................................................................38

1. Introduction..........................................................................................38

2. Unsteady flow due to sudden movement of the plate...............40

3. Similarity solution for natural convection heated from a vertical

plate.......................................................................................................44

4. Linear stability of Taylor-Couette flow...........................................51

Chapter 4 Numerical Analysis of Hot Polymer-Coated Steel Pipeline Joints

in Bending..................................................................................................60

Abstract ...............................................................................................60

1. Introduction..........................................................................................61

2. Experimental investigation................................................................64

3. Numerical modelling.........................................................................67

4. Results and comparisons...................................................................76

5. Conclusions..........................................................................................83

Acknowledgements.............................................................................84

Chapter 5 Numerical Analysis Methods of Structural Fatigue and Fracture

Problems......................................................................................................86

Abstract.................................................................................................86

1. Introduction..........................................................................................86

2. Empirical models in fatigue problem.............................................88

3. Empirical models in fracture problem...........................................93

4. Finite element method.......................................................................99

5. Conclusion..........................................................................................102

Chapter 6 Numerical Analysis on the Simulated Heavy Rainfall Event of

Tropical Cyclone Fung-Wong..............................................................107

Abstract...............................................................................................107

1. Introduction........................................................................................108

2. Methodology......................................................................................110

3. Numerical experiments on TC landfall process and evolution of

rainfall.................................................................................................113

4. Numerical analysis on the multiscale systems associated with

the torrential rainfall........................................................................114

5. Summary and discussion................................................................120

Acknowledgements...........................................................................121

Chapter 7 Numerical Analysis of Laminar‐Turbulent Bifurcation Scenarios

in Kelvin‐Helmholtz and Rayleigh‐Taylor Instabilities for

Compressible Flow.................................................................................128

Abstract...............................................................................................128

1. Introduction and definitions...........................................................129

2. Governing equations and numerical methods............................135

3. Verification.........................................................................................137

4. Bifurcation analysis..........................................................................141

5. Discussion and conclusion..............................................................158

Chapter 8 Numerical Analysis of Three‐Dimensional MHD Nanofluid Flow

over a Stretching Sheet with Convective Boundary Conditions

through a Porous Medium...................................................................165

Abstract...............................................................................................165

1. Introduction........................................................................................165

2. Mathematical formulation...............................................................167

3. Similarity transformation.................................................................168

4. Method................................................................................................169

5. Results and discussion.....................................................................171

6. Conclusion..........................................................................................182

Nomenclature....................................................................................183

Greek symbols...................................................................................184

Citation......................................................................................................187

Index...........................................................................................................189

About Author

Russell Christopher holds Ph.D. in Applied Mathematics from Public University, Brewarrina. He is a Scholar of Numerical Analysis and Statistics based at Dunedin. His expertise and research interests lie in numerical analysis methods, numerical linear algebra, numerical integration and applications of principal component analysis in different fields such as engineering, finance, taxonomy, architecture, etc. He has contributed more than 150 articles and papers in leading international scientific journals. Christopher has also worked on large-scale scientific projects in various firms and companies.