《流動非線性及其同倫分析:流體力學和傳熱(英文版)》內容簡介：科學工程中的很多問題是非線性的，難以解決。傳統的解析近似方法只對弱非線性問題有效，但無法很好地解決強非線性問題。同倫分析方法是近20年發展起來的一種有效的求解強非線性問題的解析近似方法。《流動非線性及其同倫分析:流體力學和傳熱(英文版)》介紹了同倫分析方法的最新理論進展，但不局限於方法的理論架構，也給出了大量的流體力學和傳熱中的非線性問題實例，來體現同倫分析方法的套用性。
基本介紹
- 外文名：Nonlinear Flow Phenomena and Homotopy Analysis:Fluid Flow and Heat Transfer
- 書名：流動非線性及其同倫分析:流體力學和傳熱
- 作者：瓦捷拉維魯 (Kuppalapalle Vajravelu)
- 出版日期：2012年8月1日
- 語種：英語
- ISBN：9787040354492
- 出版社：高等教育出版社
- 頁數：190頁
- 開本：16
- 品牌：高教社
基本介紹,內容簡介,作者簡介,圖書目錄,
基本介紹
內容簡介
《流動非線性及其同倫分析:流體力學和傳熱(英文版)》適合於物理、套用數學、非線性力學、金融和工程等領域對強非線性問題解析近似解感興趣的科研人員和研究生。
作者簡介
作者：（美國）瓦捷拉維魯（ Kuppalapalle Vajravelu） （美國）隔德（Robert A.Van Gorder）
瓦捷拉維魯，為美國中佛羅里達大學數學系教授，機械、材料與航空和航天工程教授，Differential Equations and Nonlinear Mechanics的創刊主編。
隔德，任職於美國中佛羅里達大學。
瓦捷拉維魯，為美國中佛羅里達大學數學系教授，機械、材料與航空和航天工程教授，Differential Equations and Nonlinear Mechanics的創刊主編。
隔德，任職於美國中佛羅里達大學。
圖書目錄
Introduction 1
References 3
2 Principles of Homotopy Analysis 7
2.1 Principles of homotopy and the homotopy analysis method 7
2.2 Construction of the deformation equations 9
2.3 Construction of the series solution 11
2.4 Conditions for the convergence of the series solutions 12
2.5 Existence and uniqueness of solutions obtained by homotopy analysis 14
2.6 Relations between the homotopy analysis method and other analytical methods 14
2.7 Homotopy analysis method for the Swift-Hohenberg equation 14
2.7.1 Application of the homotopy analysismethod 16
2.7.2 Convergence of the series solution and discussion of results 17
2.8 Incompressible viscous conducting fluid approaching a permeable stretching surface 21
2.8.1 Exact solutions for some special cases 23
2.8.2 The case of G ≠ 0 25
2.8.3 The case of G = 0 29
2.8.4 Numerical solutions and discussion of the results 32
2.9 Hydromagnetic stagnation point flow of a second grade fluid over a stretching sheet 34
2.9.1 Formulation of the mathematical problem 38
2.9.2 Exact solutions 38
2.9.3 Constructing analytical solutions via homotopy analysis 40
References 46
3 Methods for the Control of Convergence in Obtained Solutions 53
3.1 Selection of the auxiliary linear operator and base function representation 53
3.1.1 Method of linear partition matching 56
3.1.2 Method of highest order differential matching 57
3.1.3 Method of complete differential matching 58
3.1.4 Initial versus boundary value problems 59
3.1.5 Additional options for the selection of an auxiliary linear operator 60
3.1.6 Remarks on the solution expression 60
3.2 The role of the auxiliary function 61
3.3 Selection of the convergence control parameter 63
3.4 Optimal convergence control parameter value and the Lane-Emden equation of the first kind 65
3.4.1 Physical background 65
3.4.2 Analytic solutions via Taylor series 66
3.4.3 Analytic solutions via homotopy analysis 69
References 75
Additional Techniques 77
4.1 Construction of multiple homotopies for coupled equations 77
4.2 Selection of an auxiliary nonlinear operator 79
4.3 Validation of the convergence control parameter 80
4.3.1 Convergence control parameter plots ("h-plots") 80
4.3.2 Minimized residual errors 80
4.3.3 Minimized approximate residual errors 82
4.4 Multiple homotopies and the construction of solutions to the F(o)ppl-von Kármán equations governing deflections of a thin flat plate 82
4.4.1 Physical background 82
4.4.2 Linearization and construction of perturbation solutions 84
4.4.3 Recursive solutions for the clamped edge boundary data 85
4.4.4 Special case: The thin plate limit h → 0,v2 → 1 87
4.4.5 Control of error and selection of the convergence control parameters 88
4.4.6 Results 90
4.5 Nonlinear auxiliary operators and local solutions to the Drinfel'd-Sokolov equations 91
4.6 Recent work on advanced techniques in HAM 97
4.6.1 Mathematical properties of h-curve in the frame work of the homotopy analysis method 97
4.6.2 Predictor homotopy analysis method and its application to some nonlinear problems 98
4.6.3 An optimal homotopy-analysis approach for strongly nonlinear differential equations 98
4.6.4 On the homotopy multiple-variable method and its applications in the interactions of nonlinear gravity waves 98
References 99
Application of the Homotopy Analysis Method to Fluid Flow Problems 101
5.1 Thin film flow of a Sisko fluid on a moving belt 102
5.1.1 Mathematical analysis of the problem 103
5.1.2 Application of the homotopy analysis method 106
5.1.3 Numerical results and discussion 108
5.2 Nano boundary layers over stretching surfaces 112
5.2.1 Formulation of the problem 113
5.2.2 Application of the homotopy analysis method 115
5.2.3 Analytical solutions via the homotopy analysis method 116
5.2.4 Numerical solutions 118
5.2.5 Discussion of the results 121
5.3 Rotating flow of a third grade fluid by homotopy analysis method 123
5.3.1 Mathematical formulation 124
5.3.2 Solution of the problem 126
5.3.3 Results and discussions 129
5.4 Homotopy analysis for boundary layer flow of a micropolar fluid through a porous channel 133
5.4.1 Description of the problem 134
5.4.2 HAM solutions for velocity and micro-rotation fields 136
5.4.3 Convergence of the solutions 139
5.4.4 Results and discussion 140
5.5 Solution of unsteady boundary-layer flow caused by an impulsively stretching plate 142
5.5.1 Mathematical description 143
5.5.2 Homotopy analytic solution 145
5.5.3 Results and discussion 147
References 151
Further Applications of the Homotopy Analysis Method 157
6.1 Series solutions of a nonlinear model of combined convective and radiative cooling of a spherical 157
6.1.1 Basic equations 157
6.1.2 Series solutions given by the HAM 159
6.1.3 Result analysis 164
6.1.4 Conclusions and discussions 169
6.2 An ill-posed problem related to the flow of a thin fluid film over a sheet 171
6.2.1 Introduction and physical motivation 171
Contents
6.2.2 Formulation of the three-parameterproblem 173
6.2.3 A related four-parameter ill-posed problem 175
6.2.4 Analytical solution for f (η) via the homotopy analysis method 178
6.2.5 Results and discussion 181
References 184
Subject Index 185
Author Index 187
References 3
2 Principles of Homotopy Analysis 7
2.1 Principles of homotopy and the homotopy analysis method 7
2.2 Construction of the deformation equations 9
2.3 Construction of the series solution 11
2.4 Conditions for the convergence of the series solutions 12
2.5 Existence and uniqueness of solutions obtained by homotopy analysis 14
2.6 Relations between the homotopy analysis method and other analytical methods 14
2.7 Homotopy analysis method for the Swift-Hohenberg equation 14
2.7.1 Application of the homotopy analysismethod 16
2.7.2 Convergence of the series solution and discussion of results 17
2.8 Incompressible viscous conducting fluid approaching a permeable stretching surface 21
2.8.1 Exact solutions for some special cases 23
2.8.2 The case of G ≠ 0 25
2.8.3 The case of G = 0 29
2.8.4 Numerical solutions and discussion of the results 32
2.9 Hydromagnetic stagnation point flow of a second grade fluid over a stretching sheet 34
2.9.1 Formulation of the mathematical problem 38
2.9.2 Exact solutions 38
2.9.3 Constructing analytical solutions via homotopy analysis 40
References 46
3 Methods for the Control of Convergence in Obtained Solutions 53
3.1 Selection of the auxiliary linear operator and base function representation 53
3.1.1 Method of linear partition matching 56
3.1.2 Method of highest order differential matching 57
3.1.3 Method of complete differential matching 58
3.1.4 Initial versus boundary value problems 59
3.1.5 Additional options for the selection of an auxiliary linear operator 60
3.1.6 Remarks on the solution expression 60
3.2 The role of the auxiliary function 61
3.3 Selection of the convergence control parameter 63
3.4 Optimal convergence control parameter value and the Lane-Emden equation of the first kind 65
3.4.1 Physical background 65
3.4.2 Analytic solutions via Taylor series 66
3.4.3 Analytic solutions via homotopy analysis 69
References 75
Additional Techniques 77
4.1 Construction of multiple homotopies for coupled equations 77
4.2 Selection of an auxiliary nonlinear operator 79
4.3 Validation of the convergence control parameter 80
4.3.1 Convergence control parameter plots ("h-plots") 80
4.3.2 Minimized residual errors 80
4.3.3 Minimized approximate residual errors 82
4.4 Multiple homotopies and the construction of solutions to the F(o)ppl-von Kármán equations governing deflections of a thin flat plate 82
4.4.1 Physical background 82
4.4.2 Linearization and construction of perturbation solutions 84
4.4.3 Recursive solutions for the clamped edge boundary data 85
4.4.4 Special case: The thin plate limit h → 0,v2 → 1 87
4.4.5 Control of error and selection of the convergence control parameters 88
4.4.6 Results 90
4.5 Nonlinear auxiliary operators and local solutions to the Drinfel'd-Sokolov equations 91
4.6 Recent work on advanced techniques in HAM 97
4.6.1 Mathematical properties of h-curve in the frame work of the homotopy analysis method 97
4.6.2 Predictor homotopy analysis method and its application to some nonlinear problems 98
4.6.3 An optimal homotopy-analysis approach for strongly nonlinear differential equations 98
4.6.4 On the homotopy multiple-variable method and its applications in the interactions of nonlinear gravity waves 98
References 99
Application of the Homotopy Analysis Method to Fluid Flow Problems 101
5.1 Thin film flow of a Sisko fluid on a moving belt 102
5.1.1 Mathematical analysis of the problem 103
5.1.2 Application of the homotopy analysis method 106
5.1.3 Numerical results and discussion 108
5.2 Nano boundary layers over stretching surfaces 112
5.2.1 Formulation of the problem 113
5.2.2 Application of the homotopy analysis method 115
5.2.3 Analytical solutions via the homotopy analysis method 116
5.2.4 Numerical solutions 118
5.2.5 Discussion of the results 121
5.3 Rotating flow of a third grade fluid by homotopy analysis method 123
5.3.1 Mathematical formulation 124
5.3.2 Solution of the problem 126
5.3.3 Results and discussions 129
5.4 Homotopy analysis for boundary layer flow of a micropolar fluid through a porous channel 133
5.4.1 Description of the problem 134
5.4.2 HAM solutions for velocity and micro-rotation fields 136
5.4.3 Convergence of the solutions 139
5.4.4 Results and discussion 140
5.5 Solution of unsteady boundary-layer flow caused by an impulsively stretching plate 142
5.5.1 Mathematical description 143
5.5.2 Homotopy analytic solution 145
5.5.3 Results and discussion 147
References 151
Further Applications of the Homotopy Analysis Method 157
6.1 Series solutions of a nonlinear model of combined convective and radiative cooling of a spherical 157
6.1.1 Basic equations 157
6.1.2 Series solutions given by the HAM 159
6.1.3 Result analysis 164
6.1.4 Conclusions and discussions 169
6.2 An ill-posed problem related to the flow of a thin fluid film over a sheet 171
6.2.1 Introduction and physical motivation 171
Contents
6.2.2 Formulation of the three-parameterproblem 173
6.2.3 A related four-parameter ill-posed problem 175
6.2.4 Analytical solution for f (η) via the homotopy analysis method 178
6.2.5 Results and discussion 181
References 184
Subject Index 185
Author Index 187
