Nonlinear flow phenomena and homotopy analysis: fluid flow and heat transfer
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Heidelberg [u.a.]
Springer [u.a.]
2012
|
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | XII, 190 S. graph. Darst. 235 mm x 155 mm |
| ISBN: | 3642321011 9783642321016 9787040354492 |
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Record in the Search Index
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CONTENTS
1 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 ANALYSIS METHOD 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
HTTP://D-NB.INFO/1023814625
X CONTENTS
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
4 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 ("FT-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
FOPPL-VON KARMAN 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,V
2
* 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 FT-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
CONTENTS XI
4.6.4 ON THE HOMOTOPY MULTIPLE-VARIABLE METHOD AND ITS
APPLICATIONS IN THE INTERACTIONS OF NONLINEAR GRAVITY
WAVES 98
REFERENCES 99
5 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
6 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
XII CONTENTS
6.2.2 FORMULATION OF THE THREE-PARAMETER PROBLEM 173
6.2.3 A RELATED FOUR-PARAMETER ILL-POSED PROBLEM 175
6.2.4 ANALYTICAL SOLUTION FOR /
(77
) VIA THE HOMOTOPY ANALYSIS
METHOD 178
6.2.5 RESULTS AND DISCUSSION 181
REFERENCES 184
SUBJECT INDEX 185
AUTHOR INDEX 187 |
| any_adam_object | 1 |
| author | Vajravelu, Kuppalapalle Van Gorder, Robert A. |
| author_GND | (DE-588)142196584 |
| author_facet | Vajravelu, Kuppalapalle Van Gorder, Robert A. |
| author_role | aut aut |
| author_sort | Vajravelu, Kuppalapalle |
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| dewey-full | 514.24 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514.24 |
| dewey-search | 514.24 |
| dewey-sort | 3514.24 |
| dewey-tens | 510 - Mathematics |
| discipline | Physik Mathematik |
| format | Book |
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| institution | BVB |
| isbn | 3642321011 9783642321016 9787040354492 |
| language | English |
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| physical | XII, 190 S. graph. Darst. 235 mm x 155 mm |
| publishDate | 2012 |
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| publisher | Springer [u.a.] |
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| spelling | Vajravelu, Kuppalapalle Verfasser aut Nonlinear flow phenomena and homotopy analysis fluid flow and heat transfer Kuppalapalle Vajravelu ; Robert A. Van Gorder Heidelberg [u.a.] Springer [u.a.] 2012 XII, 190 S. graph. Darst. 235 mm x 155 mm txt rdacontent n rdamedia nc rdacarrier Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd rswk-swf Analytische Lösung (DE-588)4313842-1 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Nichtlineare Differentialgleichung (DE-588)4205536-2 s Analytische Lösung (DE-588)4313842-1 s Numerisches Verfahren (DE-588)4128130-5 s DE-604 Van Gorder, Robert A. Verfasser (DE-588)142196584 aut Erscheint auch als Online-Ausgabe 978-3-642-32102-3 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=4068272&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025742619&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Vajravelu, Kuppalapalle Van Gorder, Robert A. Nonlinear flow phenomena and homotopy analysis fluid flow and heat transfer Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd Analytische Lösung (DE-588)4313842-1 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| subject_GND | (DE-588)4205536-2 (DE-588)4313842-1 (DE-588)4128130-5 |
| title | Nonlinear flow phenomena and homotopy analysis fluid flow and heat transfer |
| title_auth | Nonlinear flow phenomena and homotopy analysis fluid flow and heat transfer |
| title_exact_search | Nonlinear flow phenomena and homotopy analysis fluid flow and heat transfer |
| title_full | Nonlinear flow phenomena and homotopy analysis fluid flow and heat transfer Kuppalapalle Vajravelu ; Robert A. Van Gorder |
| title_fullStr | Nonlinear flow phenomena and homotopy analysis fluid flow and heat transfer Kuppalapalle Vajravelu ; Robert A. Van Gorder |
| title_full_unstemmed | Nonlinear flow phenomena and homotopy analysis fluid flow and heat transfer Kuppalapalle Vajravelu ; Robert A. Van Gorder |
| title_short | Nonlinear flow phenomena and homotopy analysis |
| title_sort | nonlinear flow phenomena and homotopy analysis fluid flow and heat transfer |
| title_sub | fluid flow and heat transfer |
| topic | Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd Analytische Lösung (DE-588)4313842-1 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| topic_facet | Nichtlineare Differentialgleichung Analytische Lösung Numerisches Verfahren |
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