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Format: 1 online resource (482 pages).

ISBN: 0-12-811759-1

Series Statement: Mathematics in Science and Engineering

Note: Includes index. , Front Cover -- Mathematics in Science and Engineering -- Mathematics in Science and Engineering -- Copyright -- Contents -- Preface -- 1 - Introduction -- 1.1 BASIC IDEALS OF ANALYTICAL METHODS -- 1.1.1 Analytical Methods -- 1.1.1.1 Taylor Series -- 1.1.1.2 Fourier Series -- 1.1.2 Padé Approximation -- 1.1.2.1 Weierstrass Approximation Theorem -- 1.1.2.2 Definition of Padé Approximants -- 1.1.2.3 Uniqueness Theorem of Padé Approximants -- 1.1.2.4 Table of Padé Approximants -- 1.2 REVIEW OF ANALYTICAL METHODS -- 1.2.1 Perturbation Method -- 1.2.1.1 Regular Perturbation and Singular Perturbation -- 1.2.1.2 Asymptotic Matching Method -- 1.2.1.3 Poincare-Lighthill-Kuo Method -- 1.2.1.4 Average Method -- 1.2.1.5 Multiple Scales Method -- 1.2.2 Adomian Decomposition Method -- 1.2.3 Homotopy Analysis Method -- 1.2.4 Differential Transformation Method -- 1.2.5 Variational Iteration Method and Homotopy Perturbation Method -- 1.3 FRACTAL THEORY AND FRACTIONAL VISCOELASTIC FLUID -- 1.3.1 The Concept of Fractals -- 1.3.2 Fractional Order Calculus -- 1.3.2.1 Definition of Fractional Order Derivatives -- 1.3.3 Fractional Integral Transformations and Their Properties -- 1.3.3.1 Fourier Transformation -- 1.3.3.2 Laplace Transformation -- 1.3.3.3 Mellin Transformation -- 1.3.4 Fractional Viscoelastic Fluid -- 1.4 NUMERICAL METHODS -- 1.5 MODELING AND ANALYSIS FOR MODERN FLUID PROBLEMS -- 1.6 OUTLINE -- REFERENCES -- 2 - Embedding-Parameters Perturbation Method -- 2.1 BASICS OF PERTURBATION THEORY -- 2.1.1 Perturbation Theory -- 2.1.2 Asymptotic Expansion of Solutions -- 2.1.3 Regular Perturbation and Singular Perturbation -- 2.2 EMBEDDING-PARAMETER PERTURBATION -- 2.2.1 Approximate Solution to Blasius Flow -- 2.2.2 Approximate Solutions to Sakidias Flow -- 2.3 MARANGONI CONVECTION -- 2.4 MARANGONI CONVECTION IN A POWER LAW NON-NEWTONIAN FLUID. , 2.4.1 Marangoni Convection Caused by Temperature Gradient -- 2.4.2 Mathematical Formulation -- 2.4.3 Embedding-Parameters Perturbation Method Solutions -- 2.4.4 Results and Discussion -- 2.5 MARANGONI CONVECTION IN FINITE THICKNESS -- 2.5.1 Background to the Problem -- 2.5.2 Mathematical Model for Three Types of Conditions -- 2.5.3 Embedding-Parameters Perturbation Method Solutions and Discussion -- 2.5.3.1 Solutions for Cases I and II -- 2.6 SUMMARY -- REFERENCES -- 3 - Adomian Decomposition Method -- 3.1 INTRODUCTION -- 3.2 NONLINEAR BOUNDARY LAYER OF POWER LAW FLUID -- 3.2.1 Physical Background -- 3.2.2 Mathematical Formulation -- 3.2.3 Similarity Transformation -- 3.2.4 Crocco Variable Transformation -- 3.2.5 Adomian Decomposition Method Solutions -- 3.2.6 Results and Discussion -- 3.2.6.1 Analysis of Velocity Field -- 3.2.6.2 Analysis of Temperature Field -- 3.3 POWER LAW MAGNETOHYDRODYNAMIC FLUID FLOW OVER A POWER LAW VELOCITY WALL -- 3.3.1 Physical Background -- 3.3.2 Basic Governing Equations -- 3.3.3 Lie Group of Transformation -- 3.3.4 Generalized Crocco Variables Transformation -- 3.3.5 Adomian Decomposition Method Solutions -- 3.3.6 Results and Discussion -- 3.4 MARANGONI CONVECTION OVER A VAPOR-LIQUID SURFACE -- 3.4.1 Boundary Layer Governing Equations -- 3.4.2 Adomian Decomposition Method Solutions -- 3.4.3 Results and Discussion -- 3.5 SUMMARY -- REFERENCES -- 4 - Homotopy Analytical Method -- 4.1 INTRODUCTION -- 4.2 FLOW AND RADIATIVE HEAT TRANSFER OF MAGNETOHYDRODYNAMIC FLUID OVER A STRETCHING SURFACE -- 4.2.1 Description of the Problem -- 4.2.2 Mathematical Formulation -- 4.2.3 Homotopy Analysis Method Solutions -- 4.2.3.1 Zero-Order Deformation Equations -- 4.2.3.2 Higher-Order Deformation Equations -- 4.2.4 Results and Discussion -- 4.3 FLOW AND HEAT TRANSFER OF NANOFLUIDS OVER A ROTATING DISK -- 4.3.1 Background of the Problem. , 4.3.2 Formulation of the Problem -- 4.3.3 Von Karman's Transformation -- 4.3.4 Homotopy Analysis Method Solutions -- 4.3.5 Results and Discussion -- 4.3.5.1 Effects of Velocity Slip Parameter -- 4.3.5.2 Effects of Temperature Jump Parameter -- 4.3.5.3 Effects of Porosity Parameter -- 4.3.5.4 Effects of Types of Nanoparticle -- 4.4 MIXED CONVECTION IN POWER LAW FLUIDS OVER MOVING CONVEYOR -- 4.4.1 Physical Background of the Problem -- 4.4.2 Mathematical Formulation -- 4.4.3 Nonlinear Boundary Value Problems -- 4.4.4 Homotopy Analysis Method Solutions -- 4.4.5 Results and Discussion -- 4.4.5.1 Effects of Power Law Exponent n -- 4.4.5.2 Effects of Incline Angle ϕ -- 4.4.5.3 Effects of Velocity Ratio Coefficient γu -- 4.5 MAGNETOHYDRODYNAMIC THERMOSOLUTAL MARANGONI CONVECTION IN POWER LAW FLUID -- 4.5.1 Background of the Problem -- 4.5.2 Mathematical Formulation -- 4.5.3 Homotopy Analysis Method Solutions -- 4.5.4 Results and Discussion -- 4.6 SUMMARY -- REFERENCES -- 5 - Differential Transform Method -- 5.1 INTRODUCTION -- 5.1.1 Ideas of Differential Transform-Padé and Differential Transform-Basic Function -- 5.1.2 Definition of Differential Transformation Method and Formula -- 5.1.2.1 Differential Transformation for Function of One Variable -- 5.1.2.2 Differential Transformation for Functions of Several Variables -- 5.1.2.3 Differential Transformation Formula -- 5.1.3 Magnetohydrodynamic Boundary Layer Problem -- 5.2 MAGNETOHYDRODYNAMICS FALKNER-SKAN BOUNDARY LAYER FLOW OVER PERMEABLE WALL -- 5.2.1 Mathematical Physical Description -- 5.2.2 Differential Transformation Method-Padé Solutions -- 5.2.3 Results and Discussion -- 5.3 UNSTEADY MAGNETOHYDRODYNAMICS MIXED FLOW AND HEAT TRANSFER ALONG A VERTICAL SHEET -- 5.3.1 Mathematical Physical Description -- 5.3.2 Differential Transformation Method-Basic Function Solutions -- 5.3.3 Results and Discussion. , 5.4 MAGNETOHYDRODYNAMICS MIXED CONVECTIVE HEAT TRANSFER WITH THERMAL RADIATION AND OHMIC HEATING -- 5.4.1 Mathematical and Physical Description -- 5.4.2 Formulation of the Problem -- 5.4.3 Differential Transformation Method-Basic Function Solutions -- 5.4.4 Numerical Solutions -- 5.4.5 Results and Discussion -- 5.5 MAGNETOHYDRODYNAMIC NANOFLUID RADIATION HEAT TRANSFER WITH VARIABLE HEAT FLUX AND CHEMICAL REACTION -- 5.5.1 Mathematical and Physical Description -- 5.5.2 Formulation of the Problem -- 5.5.3 Differential Transformation Method-Basic Function Solutions -- 5.5.4 Numerical Solutions -- 5.5.5 Results and Discussion -- 5.6 SUMMARY -- REFERENCES -- 6 - Variational Iteration Method and Homotopy Perturbation Method -- 6.1 REVIEW OF VARIATIONAL ITERATION METHOD -- 6.2 FRACTIONAL DIFFUSION PROBLEM -- 6.3 FRACTIONAL ADVECTION-DIFFUSION EQUATION -- 6.3.1 Formulation of the Problem -- 6.3.2 Variational Iteration Method Solutions -- 6.3.3 Examples -- 6.4 REVIEW OF HOMOTOPY PERTURBATION METHOD -- 6.5 UNSTEADY FLOW AND HEAT TRANSFER OF A POWER LAW FLUID OVER A STRETCHING SURFACE -- 6.5.1 Boundary Layer Governing Equations -- 6.5.2 Modified Homotopy Perturbation Method Solutions -- 6.5.3 Results and Discussion -- 6.6 SUMMARY -- REFERENCES -- 7 - Exact Analytical Solutions for Fractional Viscoelastic Fluids -- 7.1 INTRODUCTION -- 7.1.1 The Viscoelastic Non-Newtonian Fluids -- 7.1.2 The Fractional Calculus -- 7.2 FRACTIONAL MAXWELL FLUID FLOW DUE TO ACCELERATING PLATE -- 7.2.1 Governing Equations -- 7.2.2 Statement of the Problem -- 7.2.3 Calculation of the Velocity Field -- 7.2.4 Calculation of the Shear Stress -- 7.2.5 Limiting Cases -- 7.2.6 Analysis and Discussion -- 7.3 HELICAL FLOWS OF FRACTIONAL OLDROYD-B FLUID IN POROUS MEDIUM -- 7.3.1 Formulation of the Problem -- 7.3.2 Helical Flow Between Coaxial Cylinders. , 7.3.3 Calculation of the Velocity Field -- 7.3.4 Calculation of the Shear Stress -- 7.3.5 The Solution of Heat Transfer Equation -- 7.3.6 Results and Discussion -- 7.4 MAGNETOHYDRODYNAMIC FLOW AND HEAT TRANSFER OF GENERALIZED BURGERS' FLUID -- 7.4.1 Governing Equations -- 7.4.2 Formulation of the Problem -- 7.4.3 The Solution of Velocity Fields -- 7.4.4 The Solution of Temperature Fields -- 7.4.5 Results and Discussion -- 7.5 SLIP EFFECTS ON MAGNETOHYDRODYNAMIC FLOW OF FRACTIONAL OLDROYD-B FLUID -- 7.5.1 Governing Equations -- 7.5.2 Formulation of the Problem -- 7.5.3 Exact Solutions -- 7.5.4 Special Cases -- 7.5.5 Results and Discussion -- 7.6 THE 3D FLOW OF GENERALIZED OLDROYD-B FLUID -- 7.6.1 Governing Equation -- 7.6.2 Formulation of the Problem -- 7.6.3 Calculation of the Velocity Field -- 7.6.4 Calculation of the Shear Stress -- 7.6.5 Special Cases -- 7.6.6 Results and Discussion -- 7.7 SUMMARY -- REFERENCES -- 8 - Numerical Methods -- 8.1 REVIEW OF NUMERICAL METHODS -- 8.1.1 Numerical Methods for Linear System of Equations -- 8.1.2 Numerical Methods for Ordinary/Partial Differential Equations -- 8.1.2.1 Runge-Kutta Method -- 8.1.2.2 Shooting Method -- 8.1.2.3 Control Volume Method -- 8.1.3 Numerical Methods for Fractional Differential Equations -- 8.2 HEAT TRANSFER OF POWER LAW FLUID IN A TUBE WITH DIFFERENT FLUX MODELS -- 8.2.1 Background of the Problem -- 8.2.2 Formulation of the Problems and Numerical Algorithms -- 8.2.3 Results and Discussion -- 8.3 HEAT TRANSFER OF THE POWER LAW FLUID OVER A ROTATING DISK -- 8.3.1 Background of the Problem -- 8.3.2 Formulation of the Problem and Governing Equations -- 8.3.3 Generalized Karman Transformation -- 8.3.4 Multiple Shooting Method -- 8.3.5 Results and Discussion -- 8.4 MAXWELL FLUID WITH MODIFIED FRACTIONAL FOURIER'S LAW AND DARCY'S LAW -- 8.4.1 Background of the Problem. , 8.4.2 Mathematical Formulation and Governing Equations.

Additional Edition: ISBN 0-12-811753-2

Language: English

UID:

Format: 1 online resource (482 pages).

ISBN: 0-12-811759-1

Series Statement: Mathematics in Science and Engineering

Note: Includes index. , Front Cover -- Mathematics in Science and Engineering -- Mathematics in Science and Engineering -- Copyright -- Contents -- Preface -- 1 - Introduction -- 1.1 BASIC IDEALS OF ANALYTICAL METHODS -- 1.1.1 Analytical Methods -- 1.1.1.1 Taylor Series -- 1.1.1.2 Fourier Series -- 1.1.2 Padé Approximation -- 1.1.2.1 Weierstrass Approximation Theorem -- 1.1.2.2 Definition of Padé Approximants -- 1.1.2.3 Uniqueness Theorem of Padé Approximants -- 1.1.2.4 Table of Padé Approximants -- 1.2 REVIEW OF ANALYTICAL METHODS -- 1.2.1 Perturbation Method -- 1.2.1.1 Regular Perturbation and Singular Perturbation -- 1.2.1.2 Asymptotic Matching Method -- 1.2.1.3 Poincare-Lighthill-Kuo Method -- 1.2.1.4 Average Method -- 1.2.1.5 Multiple Scales Method -- 1.2.2 Adomian Decomposition Method -- 1.2.3 Homotopy Analysis Method -- 1.2.4 Differential Transformation Method -- 1.2.5 Variational Iteration Method and Homotopy Perturbation Method -- 1.3 FRACTAL THEORY AND FRACTIONAL VISCOELASTIC FLUID -- 1.3.1 The Concept of Fractals -- 1.3.2 Fractional Order Calculus -- 1.3.2.1 Definition of Fractional Order Derivatives -- 1.3.3 Fractional Integral Transformations and Their Properties -- 1.3.3.1 Fourier Transformation -- 1.3.3.2 Laplace Transformation -- 1.3.3.3 Mellin Transformation -- 1.3.4 Fractional Viscoelastic Fluid -- 1.4 NUMERICAL METHODS -- 1.5 MODELING AND ANALYSIS FOR MODERN FLUID PROBLEMS -- 1.6 OUTLINE -- REFERENCES -- 2 - Embedding-Parameters Perturbation Method -- 2.1 BASICS OF PERTURBATION THEORY -- 2.1.1 Perturbation Theory -- 2.1.2 Asymptotic Expansion of Solutions -- 2.1.3 Regular Perturbation and Singular Perturbation -- 2.2 EMBEDDING-PARAMETER PERTURBATION -- 2.2.1 Approximate Solution to Blasius Flow -- 2.2.2 Approximate Solutions to Sakidias Flow -- 2.3 MARANGONI CONVECTION -- 2.4 MARANGONI CONVECTION IN A POWER LAW NON-NEWTONIAN FLUID. , 2.4.1 Marangoni Convection Caused by Temperature Gradient -- 2.4.2 Mathematical Formulation -- 2.4.3 Embedding-Parameters Perturbation Method Solutions -- 2.4.4 Results and Discussion -- 2.5 MARANGONI CONVECTION IN FINITE THICKNESS -- 2.5.1 Background to the Problem -- 2.5.2 Mathematical Model for Three Types of Conditions -- 2.5.3 Embedding-Parameters Perturbation Method Solutions and Discussion -- 2.5.3.1 Solutions for Cases I and II -- 2.6 SUMMARY -- REFERENCES -- 3 - Adomian Decomposition Method -- 3.1 INTRODUCTION -- 3.2 NONLINEAR BOUNDARY LAYER OF POWER LAW FLUID -- 3.2.1 Physical Background -- 3.2.2 Mathematical Formulation -- 3.2.3 Similarity Transformation -- 3.2.4 Crocco Variable Transformation -- 3.2.5 Adomian Decomposition Method Solutions -- 3.2.6 Results and Discussion -- 3.2.6.1 Analysis of Velocity Field -- 3.2.6.2 Analysis of Temperature Field -- 3.3 POWER LAW MAGNETOHYDRODYNAMIC FLUID FLOW OVER A POWER LAW VELOCITY WALL -- 3.3.1 Physical Background -- 3.3.2 Basic Governing Equations -- 3.3.3 Lie Group of Transformation -- 3.3.4 Generalized Crocco Variables Transformation -- 3.3.5 Adomian Decomposition Method Solutions -- 3.3.6 Results and Discussion -- 3.4 MARANGONI CONVECTION OVER A VAPOR-LIQUID SURFACE -- 3.4.1 Boundary Layer Governing Equations -- 3.4.2 Adomian Decomposition Method Solutions -- 3.4.3 Results and Discussion -- 3.5 SUMMARY -- REFERENCES -- 4 - Homotopy Analytical Method -- 4.1 INTRODUCTION -- 4.2 FLOW AND RADIATIVE HEAT TRANSFER OF MAGNETOHYDRODYNAMIC FLUID OVER A STRETCHING SURFACE -- 4.2.1 Description of the Problem -- 4.2.2 Mathematical Formulation -- 4.2.3 Homotopy Analysis Method Solutions -- 4.2.3.1 Zero-Order Deformation Equations -- 4.2.3.2 Higher-Order Deformation Equations -- 4.2.4 Results and Discussion -- 4.3 FLOW AND HEAT TRANSFER OF NANOFLUIDS OVER A ROTATING DISK -- 4.3.1 Background of the Problem. , 4.3.2 Formulation of the Problem -- 4.3.3 Von Karman's Transformation -- 4.3.4 Homotopy Analysis Method Solutions -- 4.3.5 Results and Discussion -- 4.3.5.1 Effects of Velocity Slip Parameter -- 4.3.5.2 Effects of Temperature Jump Parameter -- 4.3.5.3 Effects of Porosity Parameter -- 4.3.5.4 Effects of Types of Nanoparticle -- 4.4 MIXED CONVECTION IN POWER LAW FLUIDS OVER MOVING CONVEYOR -- 4.4.1 Physical Background of the Problem -- 4.4.2 Mathematical Formulation -- 4.4.3 Nonlinear Boundary Value Problems -- 4.4.4 Homotopy Analysis Method Solutions -- 4.4.5 Results and Discussion -- 4.4.5.1 Effects of Power Law Exponent n -- 4.4.5.2 Effects of Incline Angle ϕ -- 4.4.5.3 Effects of Velocity Ratio Coefficient γu -- 4.5 MAGNETOHYDRODYNAMIC THERMOSOLUTAL MARANGONI CONVECTION IN POWER LAW FLUID -- 4.5.1 Background of the Problem -- 4.5.2 Mathematical Formulation -- 4.5.3 Homotopy Analysis Method Solutions -- 4.5.4 Results and Discussion -- 4.6 SUMMARY -- REFERENCES -- 5 - Differential Transform Method -- 5.1 INTRODUCTION -- 5.1.1 Ideas of Differential Transform-Padé and Differential Transform-Basic Function -- 5.1.2 Definition of Differential Transformation Method and Formula -- 5.1.2.1 Differential Transformation for Function of One Variable -- 5.1.2.2 Differential Transformation for Functions of Several Variables -- 5.1.2.3 Differential Transformation Formula -- 5.1.3 Magnetohydrodynamic Boundary Layer Problem -- 5.2 MAGNETOHYDRODYNAMICS FALKNER-SKAN BOUNDARY LAYER FLOW OVER PERMEABLE WALL -- 5.2.1 Mathematical Physical Description -- 5.2.2 Differential Transformation Method-Padé Solutions -- 5.2.3 Results and Discussion -- 5.3 UNSTEADY MAGNETOHYDRODYNAMICS MIXED FLOW AND HEAT TRANSFER ALONG A VERTICAL SHEET -- 5.3.1 Mathematical Physical Description -- 5.3.2 Differential Transformation Method-Basic Function Solutions -- 5.3.3 Results and Discussion. , 5.4 MAGNETOHYDRODYNAMICS MIXED CONVECTIVE HEAT TRANSFER WITH THERMAL RADIATION AND OHMIC HEATING -- 5.4.1 Mathematical and Physical Description -- 5.4.2 Formulation of the Problem -- 5.4.3 Differential Transformation Method-Basic Function Solutions -- 5.4.4 Numerical Solutions -- 5.4.5 Results and Discussion -- 5.5 MAGNETOHYDRODYNAMIC NANOFLUID RADIATION HEAT TRANSFER WITH VARIABLE HEAT FLUX AND CHEMICAL REACTION -- 5.5.1 Mathematical and Physical Description -- 5.5.2 Formulation of the Problem -- 5.5.3 Differential Transformation Method-Basic Function Solutions -- 5.5.4 Numerical Solutions -- 5.5.5 Results and Discussion -- 5.6 SUMMARY -- REFERENCES -- 6 - Variational Iteration Method and Homotopy Perturbation Method -- 6.1 REVIEW OF VARIATIONAL ITERATION METHOD -- 6.2 FRACTIONAL DIFFUSION PROBLEM -- 6.3 FRACTIONAL ADVECTION-DIFFUSION EQUATION -- 6.3.1 Formulation of the Problem -- 6.3.2 Variational Iteration Method Solutions -- 6.3.3 Examples -- 6.4 REVIEW OF HOMOTOPY PERTURBATION METHOD -- 6.5 UNSTEADY FLOW AND HEAT TRANSFER OF A POWER LAW FLUID OVER A STRETCHING SURFACE -- 6.5.1 Boundary Layer Governing Equations -- 6.5.2 Modified Homotopy Perturbation Method Solutions -- 6.5.3 Results and Discussion -- 6.6 SUMMARY -- REFERENCES -- 7 - Exact Analytical Solutions for Fractional Viscoelastic Fluids -- 7.1 INTRODUCTION -- 7.1.1 The Viscoelastic Non-Newtonian Fluids -- 7.1.2 The Fractional Calculus -- 7.2 FRACTIONAL MAXWELL FLUID FLOW DUE TO ACCELERATING PLATE -- 7.2.1 Governing Equations -- 7.2.2 Statement of the Problem -- 7.2.3 Calculation of the Velocity Field -- 7.2.4 Calculation of the Shear Stress -- 7.2.5 Limiting Cases -- 7.2.6 Analysis and Discussion -- 7.3 HELICAL FLOWS OF FRACTIONAL OLDROYD-B FLUID IN POROUS MEDIUM -- 7.3.1 Formulation of the Problem -- 7.3.2 Helical Flow Between Coaxial Cylinders. , 7.3.3 Calculation of the Velocity Field -- 7.3.4 Calculation of the Shear Stress -- 7.3.5 The Solution of Heat Transfer Equation -- 7.3.6 Results and Discussion -- 7.4 MAGNETOHYDRODYNAMIC FLOW AND HEAT TRANSFER OF GENERALIZED BURGERS' FLUID -- 7.4.1 Governing Equations -- 7.4.2 Formulation of the Problem -- 7.4.3 The Solution of Velocity Fields -- 7.4.4 The Solution of Temperature Fields -- 7.4.5 Results and Discussion -- 7.5 SLIP EFFECTS ON MAGNETOHYDRODYNAMIC FLOW OF FRACTIONAL OLDROYD-B FLUID -- 7.5.1 Governing Equations -- 7.5.2 Formulation of the Problem -- 7.5.3 Exact Solutions -- 7.5.4 Special Cases -- 7.5.5 Results and Discussion -- 7.6 THE 3D FLOW OF GENERALIZED OLDROYD-B FLUID -- 7.6.1 Governing Equation -- 7.6.2 Formulation of the Problem -- 7.6.3 Calculation of the Velocity Field -- 7.6.4 Calculation of the Shear Stress -- 7.6.5 Special Cases -- 7.6.6 Results and Discussion -- 7.7 SUMMARY -- REFERENCES -- 8 - Numerical Methods -- 8.1 REVIEW OF NUMERICAL METHODS -- 8.1.1 Numerical Methods for Linear System of Equations -- 8.1.2 Numerical Methods for Ordinary/Partial Differential Equations -- 8.1.2.1 Runge-Kutta Method -- 8.1.2.2 Shooting Method -- 8.1.2.3 Control Volume Method -- 8.1.3 Numerical Methods for Fractional Differential Equations -- 8.2 HEAT TRANSFER OF POWER LAW FLUID IN A TUBE WITH DIFFERENT FLUX MODELS -- 8.2.1 Background of the Problem -- 8.2.2 Formulation of the Problems and Numerical Algorithms -- 8.2.3 Results and Discussion -- 8.3 HEAT TRANSFER OF THE POWER LAW FLUID OVER A ROTATING DISK -- 8.3.1 Background of the Problem -- 8.3.2 Formulation of the Problem and Governing Equations -- 8.3.3 Generalized Karman Transformation -- 8.3.4 Multiple Shooting Method -- 8.3.5 Results and Discussion -- 8.4 MAXWELL FLUID WITH MODIFIED FRACTIONAL FOURIER'S LAW AND DARCY'S LAW -- 8.4.1 Background of the Problem. , 8.4.2 Mathematical Formulation and Governing Equations.

Additional Edition: ISBN 0-12-811753-2

Language: English

UID:

Format: 1 online resource (482 pages).

ISBN: 0-12-811759-1

Series Statement: Mathematics in Science and Engineering

Note: Includes index. , Front Cover -- Mathematics in Science and Engineering -- Mathematics in Science and Engineering -- Copyright -- Contents -- Preface -- 1 - Introduction -- 1.1 BASIC IDEALS OF ANALYTICAL METHODS -- 1.1.1 Analytical Methods -- 1.1.1.1 Taylor Series -- 1.1.1.2 Fourier Series -- 1.1.2 Padé Approximation -- 1.1.2.1 Weierstrass Approximation Theorem -- 1.1.2.2 Definition of Padé Approximants -- 1.1.2.3 Uniqueness Theorem of Padé Approximants -- 1.1.2.4 Table of Padé Approximants -- 1.2 REVIEW OF ANALYTICAL METHODS -- 1.2.1 Perturbation Method -- 1.2.1.1 Regular Perturbation and Singular Perturbation -- 1.2.1.2 Asymptotic Matching Method -- 1.2.1.3 Poincare-Lighthill-Kuo Method -- 1.2.1.4 Average Method -- 1.2.1.5 Multiple Scales Method -- 1.2.2 Adomian Decomposition Method -- 1.2.3 Homotopy Analysis Method -- 1.2.4 Differential Transformation Method -- 1.2.5 Variational Iteration Method and Homotopy Perturbation Method -- 1.3 FRACTAL THEORY AND FRACTIONAL VISCOELASTIC FLUID -- 1.3.1 The Concept of Fractals -- 1.3.2 Fractional Order Calculus -- 1.3.2.1 Definition of Fractional Order Derivatives -- 1.3.3 Fractional Integral Transformations and Their Properties -- 1.3.3.1 Fourier Transformation -- 1.3.3.2 Laplace Transformation -- 1.3.3.3 Mellin Transformation -- 1.3.4 Fractional Viscoelastic Fluid -- 1.4 NUMERICAL METHODS -- 1.5 MODELING AND ANALYSIS FOR MODERN FLUID PROBLEMS -- 1.6 OUTLINE -- REFERENCES -- 2 - Embedding-Parameters Perturbation Method -- 2.1 BASICS OF PERTURBATION THEORY -- 2.1.1 Perturbation Theory -- 2.1.2 Asymptotic Expansion of Solutions -- 2.1.3 Regular Perturbation and Singular Perturbation -- 2.2 EMBEDDING-PARAMETER PERTURBATION -- 2.2.1 Approximate Solution to Blasius Flow -- 2.2.2 Approximate Solutions to Sakidias Flow -- 2.3 MARANGONI CONVECTION -- 2.4 MARANGONI CONVECTION IN A POWER LAW NON-NEWTONIAN FLUID. , 2.4.1 Marangoni Convection Caused by Temperature Gradient -- 2.4.2 Mathematical Formulation -- 2.4.3 Embedding-Parameters Perturbation Method Solutions -- 2.4.4 Results and Discussion -- 2.5 MARANGONI CONVECTION IN FINITE THICKNESS -- 2.5.1 Background to the Problem -- 2.5.2 Mathematical Model for Three Types of Conditions -- 2.5.3 Embedding-Parameters Perturbation Method Solutions and Discussion -- 2.5.3.1 Solutions for Cases I and II -- 2.6 SUMMARY -- REFERENCES -- 3 - Adomian Decomposition Method -- 3.1 INTRODUCTION -- 3.2 NONLINEAR BOUNDARY LAYER OF POWER LAW FLUID -- 3.2.1 Physical Background -- 3.2.2 Mathematical Formulation -- 3.2.3 Similarity Transformation -- 3.2.4 Crocco Variable Transformation -- 3.2.5 Adomian Decomposition Method Solutions -- 3.2.6 Results and Discussion -- 3.2.6.1 Analysis of Velocity Field -- 3.2.6.2 Analysis of Temperature Field -- 3.3 POWER LAW MAGNETOHYDRODYNAMIC FLUID FLOW OVER A POWER LAW VELOCITY WALL -- 3.3.1 Physical Background -- 3.3.2 Basic Governing Equations -- 3.3.3 Lie Group of Transformation -- 3.3.4 Generalized Crocco Variables Transformation -- 3.3.5 Adomian Decomposition Method Solutions -- 3.3.6 Results and Discussion -- 3.4 MARANGONI CONVECTION OVER A VAPOR-LIQUID SURFACE -- 3.4.1 Boundary Layer Governing Equations -- 3.4.2 Adomian Decomposition Method Solutions -- 3.4.3 Results and Discussion -- 3.5 SUMMARY -- REFERENCES -- 4 - Homotopy Analytical Method -- 4.1 INTRODUCTION -- 4.2 FLOW AND RADIATIVE HEAT TRANSFER OF MAGNETOHYDRODYNAMIC FLUID OVER A STRETCHING SURFACE -- 4.2.1 Description of the Problem -- 4.2.2 Mathematical Formulation -- 4.2.3 Homotopy Analysis Method Solutions -- 4.2.3.1 Zero-Order Deformation Equations -- 4.2.3.2 Higher-Order Deformation Equations -- 4.2.4 Results and Discussion -- 4.3 FLOW AND HEAT TRANSFER OF NANOFLUIDS OVER A ROTATING DISK -- 4.3.1 Background of the Problem. , 4.3.2 Formulation of the Problem -- 4.3.3 Von Karman's Transformation -- 4.3.4 Homotopy Analysis Method Solutions -- 4.3.5 Results and Discussion -- 4.3.5.1 Effects of Velocity Slip Parameter -- 4.3.5.2 Effects of Temperature Jump Parameter -- 4.3.5.3 Effects of Porosity Parameter -- 4.3.5.4 Effects of Types of Nanoparticle -- 4.4 MIXED CONVECTION IN POWER LAW FLUIDS OVER MOVING CONVEYOR -- 4.4.1 Physical Background of the Problem -- 4.4.2 Mathematical Formulation -- 4.4.3 Nonlinear Boundary Value Problems -- 4.4.4 Homotopy Analysis Method Solutions -- 4.4.5 Results and Discussion -- 4.4.5.1 Effects of Power Law Exponent n -- 4.4.5.2 Effects of Incline Angle ϕ -- 4.4.5.3 Effects of Velocity Ratio Coefficient γu -- 4.5 MAGNETOHYDRODYNAMIC THERMOSOLUTAL MARANGONI CONVECTION IN POWER LAW FLUID -- 4.5.1 Background of the Problem -- 4.5.2 Mathematical Formulation -- 4.5.3 Homotopy Analysis Method Solutions -- 4.5.4 Results and Discussion -- 4.6 SUMMARY -- REFERENCES -- 5 - Differential Transform Method -- 5.1 INTRODUCTION -- 5.1.1 Ideas of Differential Transform-Padé and Differential Transform-Basic Function -- 5.1.2 Definition of Differential Transformation Method and Formula -- 5.1.2.1 Differential Transformation for Function of One Variable -- 5.1.2.2 Differential Transformation for Functions of Several Variables -- 5.1.2.3 Differential Transformation Formula -- 5.1.3 Magnetohydrodynamic Boundary Layer Problem -- 5.2 MAGNETOHYDRODYNAMICS FALKNER-SKAN BOUNDARY LAYER FLOW OVER PERMEABLE WALL -- 5.2.1 Mathematical Physical Description -- 5.2.2 Differential Transformation Method-Padé Solutions -- 5.2.3 Results and Discussion -- 5.3 UNSTEADY MAGNETOHYDRODYNAMICS MIXED FLOW AND HEAT TRANSFER ALONG A VERTICAL SHEET -- 5.3.1 Mathematical Physical Description -- 5.3.2 Differential Transformation Method-Basic Function Solutions -- 5.3.3 Results and Discussion. , 5.4 MAGNETOHYDRODYNAMICS MIXED CONVECTIVE HEAT TRANSFER WITH THERMAL RADIATION AND OHMIC HEATING -- 5.4.1 Mathematical and Physical Description -- 5.4.2 Formulation of the Problem -- 5.4.3 Differential Transformation Method-Basic Function Solutions -- 5.4.4 Numerical Solutions -- 5.4.5 Results and Discussion -- 5.5 MAGNETOHYDRODYNAMIC NANOFLUID RADIATION HEAT TRANSFER WITH VARIABLE HEAT FLUX AND CHEMICAL REACTION -- 5.5.1 Mathematical and Physical Description -- 5.5.2 Formulation of the Problem -- 5.5.3 Differential Transformation Method-Basic Function Solutions -- 5.5.4 Numerical Solutions -- 5.5.5 Results and Discussion -- 5.6 SUMMARY -- REFERENCES -- 6 - Variational Iteration Method and Homotopy Perturbation Method -- 6.1 REVIEW OF VARIATIONAL ITERATION METHOD -- 6.2 FRACTIONAL DIFFUSION PROBLEM -- 6.3 FRACTIONAL ADVECTION-DIFFUSION EQUATION -- 6.3.1 Formulation of the Problem -- 6.3.2 Variational Iteration Method Solutions -- 6.3.3 Examples -- 6.4 REVIEW OF HOMOTOPY PERTURBATION METHOD -- 6.5 UNSTEADY FLOW AND HEAT TRANSFER OF A POWER LAW FLUID OVER A STRETCHING SURFACE -- 6.5.1 Boundary Layer Governing Equations -- 6.5.2 Modified Homotopy Perturbation Method Solutions -- 6.5.3 Results and Discussion -- 6.6 SUMMARY -- REFERENCES -- 7 - Exact Analytical Solutions for Fractional Viscoelastic Fluids -- 7.1 INTRODUCTION -- 7.1.1 The Viscoelastic Non-Newtonian Fluids -- 7.1.2 The Fractional Calculus -- 7.2 FRACTIONAL MAXWELL FLUID FLOW DUE TO ACCELERATING PLATE -- 7.2.1 Governing Equations -- 7.2.2 Statement of the Problem -- 7.2.3 Calculation of the Velocity Field -- 7.2.4 Calculation of the Shear Stress -- 7.2.5 Limiting Cases -- 7.2.6 Analysis and Discussion -- 7.3 HELICAL FLOWS OF FRACTIONAL OLDROYD-B FLUID IN POROUS MEDIUM -- 7.3.1 Formulation of the Problem -- 7.3.2 Helical Flow Between Coaxial Cylinders. , 7.3.3 Calculation of the Velocity Field -- 7.3.4 Calculation of the Shear Stress -- 7.3.5 The Solution of Heat Transfer Equation -- 7.3.6 Results and Discussion -- 7.4 MAGNETOHYDRODYNAMIC FLOW AND HEAT TRANSFER OF GENERALIZED BURGERS' FLUID -- 7.4.1 Governing Equations -- 7.4.2 Formulation of the Problem -- 7.4.3 The Solution of Velocity Fields -- 7.4.4 The Solution of Temperature Fields -- 7.4.5 Results and Discussion -- 7.5 SLIP EFFECTS ON MAGNETOHYDRODYNAMIC FLOW OF FRACTIONAL OLDROYD-B FLUID -- 7.5.1 Governing Equations -- 7.5.2 Formulation of the Problem -- 7.5.3 Exact Solutions -- 7.5.4 Special Cases -- 7.5.5 Results and Discussion -- 7.6 THE 3D FLOW OF GENERALIZED OLDROYD-B FLUID -- 7.6.1 Governing Equation -- 7.6.2 Formulation of the Problem -- 7.6.3 Calculation of the Velocity Field -- 7.6.4 Calculation of the Shear Stress -- 7.6.5 Special Cases -- 7.6.6 Results and Discussion -- 7.7 SUMMARY -- REFERENCES -- 8 - Numerical Methods -- 8.1 REVIEW OF NUMERICAL METHODS -- 8.1.1 Numerical Methods for Linear System of Equations -- 8.1.2 Numerical Methods for Ordinary/Partial Differential Equations -- 8.1.2.1 Runge-Kutta Method -- 8.1.2.2 Shooting Method -- 8.1.2.3 Control Volume Method -- 8.1.3 Numerical Methods for Fractional Differential Equations -- 8.2 HEAT TRANSFER OF POWER LAW FLUID IN A TUBE WITH DIFFERENT FLUX MODELS -- 8.2.1 Background of the Problem -- 8.2.2 Formulation of the Problems and Numerical Algorithms -- 8.2.3 Results and Discussion -- 8.3 HEAT TRANSFER OF THE POWER LAW FLUID OVER A ROTATING DISK -- 8.3.1 Background of the Problem -- 8.3.2 Formulation of the Problem and Governing Equations -- 8.3.3 Generalized Karman Transformation -- 8.3.4 Multiple Shooting Method -- 8.3.5 Results and Discussion -- 8.4 MAXWELL FLUID WITH MODIFIED FRACTIONAL FOURIER'S LAW AND DARCY'S LAW -- 8.4.1 Background of the Problem. , 8.4.2 Mathematical Formulation and Governing Equations.

Additional Edition: ISBN 0-12-811753-2

Language: English