Thermal and Solutal Convection in Some Hydromagnetic Flows

Description

This book presents a theoretical analysis of several problems in thermal and solutal convections in magneto-hydrodynamic (MHD) flows. It provides a systemic discussion on the development of fluid dynamics, continuum hypothesis, Newton’s law of viscosity, heat transfer, mass transfer, thermal diffusion, diffusion-thermo-MHD, gray and non-gray gases, Fourier’s law of conduction, and Fick’s law of diffusion in such a way that readers with little knowledge in physics will find it easier to understand the contents. Some physical principles, such as those governing fluid motion, fluid temperature, and fluid concentration, are presented in vector form, allowing the corresponding form to be derived in any orthogonal curvilinear coordinate system. Laplace transform technique in closed form is used to obtain exact solutions to unsteady one-dimensional flow problems, an implicit finite difference method of Crank–Nicholson type is used to solve unsteady two-dimensional flow problems, and an asymptotic series expansion method is used to solve the governing equations of the steady three-dimensional flow problem analytically. Flow and transport phenomena are thoroughly treated in each chapter separately. This book emphasizes the influence of an induced magnetic field. The outcomes of the works are graphically depicted so that readers can gain a tangible understanding of the problems. It also includes a list of inverse Laplace transforms (ILTs) for several specific functions, some of which are not found in the existing literature. The ILTs of special functions are given in brief form and can further be utilized as standard formulae in finding those as special cases. Some new special functions are introduced in the book, along with appropriate definitions. As a result, the formulations for velocity, temperature, concentration, skin friction, Nusselt number, and Sherwood number have been appeared in brief and convenient forms that are uncommon in other literature. This book addresses numerous areas of contemporary magneto-fluid dynamics research that have major implications in engineering. It is primarily intended for researchers working in the field of heat and mass transfer in hydromagnetic flows. Preface Contents About the Author Symbols English Mathematical Notations Greek Symbols Subscripts 1 Introduction and Basic Concepts 1.1 Fluid Mechanics and Its Development 1.2 Continuum Hypothesis 1.3 Newton's Law of Viscosity 1.4 Heat Transfer 1.4.1 Conduction: Fourier's Law of Conduction 1.4.2 Convection: Newton's Law of Cooling 1.4.3 Radiation 1.5 Mass Transfer 1.5.1 Mass Transfer by Diffusion: Fick's Law of Diffusion 1.5.2 Mass Transfer by Convection 1.6 Thermal Diffusion or Soret Effect 1.7 Diffusion-thermo or Dufour Effect 1.8 MHD (Magnetohydrodynamics) 1.9 MHD Thermal and Solutal Convection and Its Development: A Literature Survey 1.10 Gray and Non-gray Gases: Some Definitions 1.11 Basic Equations 1.12 Some Physical Parameters 1.13 Remarks 1.14 Heaviside's Unit Step Function, Error Function, and Complementary Error Function 1.15 Some Properties of Error Function and Complementary Error Function 1.16 Laplace Transform Technique 1.17 Some Common Functions 1.18 Inverse Laplace Transforms of Some Special Functions 1.19 Bar Function and Delta Function References 2 MHD Transient Flow with Diffusion-Thermo and Radiation 2.1 Introduction 2.2 Mathematical Formulation of the Problem 2.3 Method of Solution 2.4 Rates of Transports 2.5 Analysis of the Results 2.6 Results Highlights Reference 3 MHD Flow with Diffusion—Thermo and Induced Magnetic Field 3.1 Introduction 3.2 Mathematical Formulation of the Problem 3.3 Method of Solution 3.4 Rates of Transports 3.5 Analysis of the Results 3.6 Results Highlights References 4 MHD Flow with Soret Effect and Induced Magnetic Field 4.1 Introduction 4.2 Mathematical Formulation of the Problem 4.3 Method of Solution 4.4 Rates of Transports 4.5 Analysis of the Results 4.6 Results Highlights 5 MHD Flow with Parabolic Conditions, and Diffusion-Thermo 5.1 Introduction 5.2 Mathematical Formulation of the Problem 5.3 Method of Solution 5.4 Rates of Transports 5.5 Analysis of the Results 5.6 Results Highlights 6 MHD Flow with Radiation, Chemical Reaction, and Diffusion-Thermo 6.1 Introduction 6.2 Mathematical Formulation of the Problem 6.3 Method of Solution 6.4 Rates of Transports 6.5 Analysis of the Results 6.6 Results Highlights 7 MHD Flow with Thermal Diffusion, Thermal Radiation, and Chemical Reaction 7.1 Introduction 7.2 Mathematical Formulation of the Problem 7.3 Method of Solution 7.4 Rates of Transports 7.5 Analysis of the Results 7.6 Results Highlights References 8 Natural Convection in Transient MHD Dissipative Flow 8.1 Introduction 8.2 Mathematical Formulation of the Problem 8.3 Method of Solution 8.4 Rates of the Transports 8.5 Analysis of the Results 8.6 Results Highlights Reference 9 MHD Radiating Flow with Thermal Diffusion, and Diffusion-Thermo 9.1 Introduction 9.2 Mathematical Formulation of the Problem 9.3 Method of Solutions 9.4 Zeroth-Order Equations 9.5 Cross-Flow Solutions 9.6 Solutions of First-Order Flow, Temperature, and Concentration Fields 9.7 Rate of Momentum Transfer 9.8 Plate Temperature 9.9 Plate Concentration 9.10 Analysis of the Results 9.11 Results Highlights References Appendix Future Scope