- 作 者：K·Vajravelu，K·V·Prasad
- 出 版 社：北京：高等教育出版社
- 出版年份：2014
- ISBN：9787040388916
- 标注页数：403 页
- PDF页数：411 页
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Chapter 0 Introduction 1
References 3
Chapter 1 Basics of the Finite Difference Approximations 5
1.1 Finite difference approximations 5
1.2 The initial value problem for ODEs 11
1.3 Some basic numerical methods 16
1.4 Some basic PDEs 26
1.5 Numerical solution to partial differential equations 32
References 38
Chapter 2 Principles of the Implicit Keller-box Method 41
2.1 Principles of implicit finite difference methods 41
2.2 Finite difference methods 53
2.3 Boundary value problems in ordinary differential equations 71
References 87
Chapter 3 Stability and Convergence of the Implicit Keller-box Method 89
3.1 Convergence of implicit difference methods for parabolic functional differential equations 90
3.1.1 Introduction 90
3.1.2 Discretization of mixed problems 91
3.1.3 Solvability of implicit difference functional problems 94
3.1.4 Approximate solutions of difference functional problems 96
3.1.5 Convergence of implicit difference methods 99
3.1.6 Numerical examples 103
3.2 Rate of convergence of finite difference scheme on uniform/non-uniform grids 105
3.2.1 Introduction 105
3.2.2 Analytical results 106
3.2.3 Numerical results 110
3.3 Stability and convergence of Crank-Nicholson method for fractional advection dispersion equation 112
3.3.1 Introduction 112
3.3.2 Problem formulation 113
3.3.3 Numerical formulation of the Crank-Nicholson method 114
3.3.4 Stability of the Crank-Nicholson method 115
3.3.5 Convergence 116
3.3.6 Radial flow problem 117
3.3.7 Conclusions 118
References 118
Chapter 4 Application of the Keller-box Method to Boundary Layer Problems 121
4.1 Flow of a power-law fluid over a stretching sheet 121
4.1.1 Introduction 121
4.1.2 Formulation of the problem 122
4.1.3 Numerical solution method 124
4.1.4 Results and discussion 125
4.1.5 Concluding remarks 126
4.2 Hydromagnetic flow of a power-law fluid over a stretching sheet 126
4.2.1 Introduction 126
4.2.2 Flow analysis 128
4.2.3 Numerical solution method 130
4.2.4 Results and discussion 130
4.3 MHD Power-law fluid flow and heat transfer over a non-isothermal stretching sheet 135
4.3.1 Introduction 135
4.3.2 Governing equations and similarity analysis 137
4.3.3 Heat transfer 139
4.3.4 Numerical procedure 141
4.3.5 Results and discussion 149
4.4 MHD flow and heat transfer of a Maxwell fluid over a non-isothermal stretching sheet 151
4.4.1 Introduction 151
4.4.2 Mathematical formulation 153
4.4.3 Heat transfer analysis 155
4.4.4 Numerical procedure 158
4.4.5 Results and discussion 159
4.4.6 Conclusions 165
4.5 MHD boundary layer flow of a micropolar fluid past a wedge with constant wall heat flux 166
4.5.1 Introduction 166
4.5.2 Flow analysis 167
4.5.3 Flat plate problem 170
4.5.4 Results and discussion 171
4.5.5 Conclusions 176
References 177
Chapter 5 Application of the Keller-box Method to Fluid Flow and Heat Transfer Problems 183
5.1 Hydromagnetic flow and heat transfer adjacent to a stretching vertical sheet 183
5.1.1 Introduction 183
5.1.2 Mathematical formulation 184
5.1.3 Solution of the problem 187
5.1.4 Results and discussion 188
5.1.5 Conclusions 194
5.2 Convection flow and heat transfer of a Maxwell fluid over a non-isothermal surface 194
5.2.1 Introduction 194
5.2.2 Mathematical formulation 196
5.2.3 Skin friction 199
5.2.4 Nusselt number 200
5.2.5 Results and discussion 200
5.2.6 Conclusion 206
5.3 The effects of variable fluid properties on the hydromagnetic flow and heat transfer over a nonlinearly stretching sheet 207
5.3.1 Introduction 207
5.3.2 Mathematical formulation 208
5.3.3 Numerical procedure 212
5.3.4 Results and discussion 213
5.3.5 Conclusions 223
5.4 Hydromagnetic flow and heat transfer of a non-Newtonian power law fluid over a vertical stretching sheet 223
5.4.1 Introduction 223
5.4.2 Mathematical formulation 225
5.4.3 Numerical procedure 229
5.4.4 Results and discussion 229
5.5 The effects of linear/nonlinear convection on the non-Darcian flow and heat transfer along a permeable vertical surface 238
5.5.1 Introduction 238
5.5.2 Mathematical formulation 240
5.5.3 Numerical procedure 243
5.5.4 Results and discussion 253
5.6 Unsteady flow and heat transfer in a thin film of Ostwald-de Waele liquid over a stretching surface 255
5.6.1 Introduction 255
5.6.2 Mathematical formulation 257
5.6.3 Numerical procedure 261
5.6.4 Results and discussion 262
5.6.5 Conclusions 272
References 272
Chapter 6 Application of the Keller-box Method to More Advanced Problems 279
6.1 Heat transfer phenomena in a moving nanofluid over a horizontal surface 279
6.1.1 Introduction 279
6.1.2 Mathematical formulation 281
6.1.3 Similarity equations 283
6.1.4 Numerical procedure 285
6.1.5 Results and discussion 286
6.1.6 Conclusion 297
6.2 Hydromagnetic fluid flow and heat transfer at a stretching sheet with fluid-particle suspension and variable fluid properties 298
6.2.1 Introduction 298
6.2.2 Mathematical formulation 300
6.2.3 Solution for special cases 303
6.2.4 Analytical solution by perturbation 303
6.2.5 Numerical procedure 305
6.2.6 Results and discussion 306
6.2.7 Conclusions 317
6.3 Radiation effects on mixed convection over a wedge embedded in a porous medium filled with a nanofluid 318
6.3.1 Introduction 318
6.3.2 Problem formulation 319
6.3.3 Numerical method and validation 322
6.3.4 Results and discussion 323
6.3.5 Conclusion 337
6.4 MHD mixed convection flow over a permeable non-isothermal wedge 337
6.4.1 Introduction 337
6.4.2 Mathematical formulation 339
6.4.3 Numerical procedure 342
6.4.4 Results and discussion 344
6.4.5 Concluding remarks 354
6.5 Mixed convection boundary layer flow about a solid sphere with Newtonian heating 355
6.5.1 Introduction 355
6.5.2 Mathematical formulation 357
6.5.3 Solution procedure 360
6.5.4 Results and discussion 360
6.5.5 Conclusions 366
6.6 Flow and heat transfer of a viscoelastic fluid over a flat plate with a magnetic field and a pressure gradient 371
6.6.1 Introduction 371
6.6.2 Governing equations 372
6.6.3 Results and discussion 375
6.6.4 Conclusions 382
References 382
Subject Index 391
Author Index 395