Keller-Box方法及其应用 英文版PDF|Epub|txt|kindle电子书版本网盘下载

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Chapter 0 Introduction1

References3

Chapter 1 Basics of the Finite Difference Approximations5

1.1 Finite difference approximations5

1.2 The initial value problem for ODEs11

1.3 Some basic numerical methods16

1.4 Some basic PDEs26

1.5 Numerical solution to partial differential equations32

References38

Chapter 2 Principles of the Implicit Keller-box Method41

2.1 Principles of implicit finite difference methods41

2.2 Finite difference methods53

2.3 Boundary value problems in ordinary differential equations71

References87

Chapter 3 Stability and Convergence of the Implicit Keller-box Method89

3.1 Convergence of implicit difference methods for parabolic functional differential equations90

3.1.1 Introduction90

3.1.2 Discretization of mixed problems91

3.1.3 Solvability of implicit difference functional problems94

3.1.4 Approximate solutions of difference functional problems96

3.1.5 Convergence of implicit difference methods99

3.1.6 Numerical examples103

3.2 Rate of convergence of finite difference scheme on uniform/non-uniform grids105

3.2.1 Introduction105

3.2.2 Analytical results106

3.2.3 Numerical results110

3.3 Stability and convergence of Crank-Nicholson method for fractional advection dispersion equation112

3.3.1 Introduction112

3.3.2 Problem formulation113

3.3.3 Numerical formulation of the Crank-Nicholson method114

3.3.4 Stability of the Crank-Nicholson method115

3.3.5 Convergence116

3.3.6 Radial flow problem117

3.3.7 Conclusions118

References118

Chapter 4 Application of the Keller-box Method to Boundary Layer Problems121

4.1 Flow of a power-law fluid over a stretching sheet121

4.1.1 Introduction121

4.1.2 Formulation of the problem122

4.1.3 Numerical solution method124

4.1.4 Results and discussion125

4.1.5 Concluding remarks126

4.2 Hydromagnetic flow of a power-law fluid over a stretching sheet126

4.2.1 Introduction126

4.2.2 Flow analysis128

4.2.3 Numerical solution method130

4.2.4 Results and discussion130

4.3 MHD Power-law fluid flow and heat transfer over a non-isothermal stretching sheet135

4.3.1 Introduction135

4.3.2 Governing equations and similarity analysis137

4.3.3 Heat transfer139

4.3.4 Numerical procedure141

4.3.5 Results and discussion149

4.4 MHD flow and heat transfer of a Maxwell fluid over a non-isothermal stretching sheet151

4.4.1 Introduction151

4.4.2 Mathematical formulation153

4.4.3 Heat transfer analysis155

4.4.4 Numerical procedure158

4.4.5 Results and discussion159

4.4.6 Conclusions165

4.5 MHD boundary layer flow of a micropolar fluid past a wedge with constant wall heat flux166

4.5.1 Introduction166

4.5.2 Flow analysis167

4.5.3 Flat plate problem170

4.5.4 Results and discussion171

4.5.5 Conclusions176

References177

Chapter 5 Application of the Keller-box Method to Fluid Flow and Heat Transfer Problems183

5.1 Hydromagnetic flow and heat transfer adjacent to a stretching vertical sheet183

5.1.1 Introduction183

5.1.2 Mathematical formulation184

5.1.3 Solution of the problem187

5.1.4 Results and discussion188

5.1.5 Conclusions194

5.2 Convection flow and heat transfer of a Maxwell fluid over a non-isothermal surface194

5.2.1 Introduction194

5.2.2 Mathematical formulation196

5.2.3 Skin friction199

5.2.4 Nusselt number200

5.2.5 Results and discussion200

5.2.6 Conclusion206

5.3 The effects of variable fluid properties on the hydromagnetic flow and heat transfer over a nonlinearly stretching sheet207

5.3.1 Introduction207

5.3.2 Mathematical formulation208

5.3.3 Numerical procedure212

5.3.4 Results and discussion213

5.3.5 Conclusions223

5.4 Hydromagnetic flow and heat transfer of a non-Newtonian power law fluid over a vertical stretching sheet223

5.4.1 Introduction223

5.4.2 Mathematical formulation225

5.4.3 Numerical procedure229

5.4.4 Results and discussion229

5.5 The effects of linear/nonlinear convection on the non-Darcian flow and heat transfer along a permeable vertical surface238

5.5.1 Introduction238

5.5.2 Mathematical formulation240

5.5.3 Numerical procedure243

5.5.4 Results and discussion253

5.6 Unsteady flow and heat transfer in a thin film of Ostwald-de Waele liquid over a stretching surface255

5.6.1 Introduction255

5.6.2 Mathematical formulation257

5.6.3 Numerical procedure261

5.6.4 Results and discussion262

5.6.5 Conclusions272

References272

Chapter 6 Application of the Keller-box Method to More Advanced Problems279

6.1 Heat transfer phenomena in a moving nanofluid over a horizontal surface279

6.1.1 Introduction279

6.1.2 Mathematical formulation281

6.1.3 Similarity equations283

6.1.4 Numerical procedure285

6.1.5 Results and discussion286

6.1.6 Conclusion297

6.2 Hydromagnetic fluid flow and heat transfer at a stretching sheet with fluid-particle suspension and variable fluid properties298

6.2.1 Introduction298

6.2.2 Mathematical formulation300

6.2.3 Solution for special cases303

6.2.4 Analytical solution by perturbation303

6.2.5 Numerical procedure305

6.2.6 Results and discussion306

6.2.7 Conclusions317

6.3 Radiation effects on mixed convection over a wedge embedded in a porous medium filled with a nanofluid318

6.3.1 Introduction318

6.3.2 Problem formulation319

6.3.3 Numerical method and validation322

6.3.4 Results and discussion323

6.3.5 Conclusion337

6.4 MHD mixed convection flow over a permeable non-isothermal wedge337

6.4.1 Introduction337

6.4.2 Mathematical formulation339

6.4.3 Numerical procedure342

6.4.4 Results and discussion344

6.4.5 Concluding remarks354

6.5 Mixed convection boundary layer flow about a solid sphere with Newtonian heating355

6.5.1 Introduction355

6.5.2 Mathematical formulation357

6.5.3 Solution procedure360

6.5.4 Results and discussion360

6.5.5 Conclusions366

6.6 Flow and heat transfer of a viscoelastic fluid over a flat plate with a magnetic field and a pressure gradient371

6.6.1 Introduction371

6.6.2 Governing equations372

6.6.3 Results and discussion375

6.6.4 Conclusions382

References382

Subject Index391

Author Index395