One-dimensional Stefan problems: an introduction
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Harlow
Longman Scientific & Technical
1987
|
| Schriftenreihe: | Pitman monographs and surveys in pure and applied mathematics
31. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVIII, 204 S. graph. Darst. |
| ISBN: | 0582988233 0470203889 |
Internformat
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| 100 | 1 | |a Hill, James M. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a One-dimensional Stefan problems |b an introduction |
| 264 | 1 | |a Harlow |b Longman Scientific & Technical |c 1987 | |
| 300 | |a XVIII, 204 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Pitman monographs and surveys in pure and applied mathematics |v 31. | |
| 650 | 4 | |a Approximation polynomiale | |
| 650 | 4 | |a Chaleur - Conduction | |
| 650 | 4 | |a Cinétique chimique | |
| 650 | 4 | |a Diffusion chaleur | |
| 650 | 4 | |a Equation intégrale | |
| 650 | 4 | |a Expérience numérique | |
| 650 | 4 | |a Fonction spéciale | |
| 650 | 4 | |a Problème Stefan | |
| 650 | 7 | |a Problème aux limites |2 ram | |
| 650 | 4 | |a Problèmes aux limites | |
| 650 | 7 | |a Thermocinétique |2 ram | |
| 650 | 4 | |a Boundary value problems | |
| 650 | 4 | |a Heat |x Conduction | |
| 650 | 0 | 7 | |a Randwertproblem |0 (DE-588)4048395-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Integralgleichung |0 (DE-588)4027229-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Näherungsverfahren |0 (DE-588)4206467-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Approximation |0 (DE-588)4002498-2 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1804120821413707776 |
|---|---|
| adam_text | Contents
Preface xi
Acknowledgements xv
List of symbols xvii
1 Heat diffusion moving boundary problems 1
1.1 Introduction 1
1.2 Formulation of classical Stefan problems 6
1.3 Neumann s exact solution 12
1.4 Pseudo steady state approximations 18
1.5 Review of other analytic methods 22
1.6 Numerical solution of classical Stefan problems 25
1.7 Additional symbols used 28
2 Large Stefan number expansion 30
2.1 Introduction 30
2.2 Derivation from general solutions 34
2.2.1 Plane freezing 34
2.2.2 Spherical freezing 36
2.2.3 Cylindrical freezing 38
2.3 Freezing an infinite slab 40
2.4 Freezing a liquid in a spherical container 44
2.5 Freezing an infinite circular cylinder 47
2.6 Review of subsequent developments 49
2.7 Additional symbols used 55
3 Integral formulation and bounds 57
3.1 Introduction 57
3.2 Integral formulation by integration 58
vii
viii CONTENTS
3.2.1 Spherical freezing 62
3.2.2 Cylindrical freezing 62
3.3 Integral formulation by Green s function 63
3.3.1 Spherical freezing 65
3.3.2 Cylindrical freezing 66
3.4 Bounds on the motion from 0 ^ T 1 67
3.5 Improved upper bound from T Tpss 69
3.6 Improved lower bounds by integration 73
3.6.1 Spherical freezing 75
3.6.2 Cylindrical freezing 76
3.7 Summary 77
3.8 Additional symbols used 81
4 Integral equations 82
4.1 Introduction 82
4.2 Formal series solutions 84
4.2.1 Spherical freezing 85
4.2.2 Cylindrical freezing 86
4.3 Unsolved integral equations for boundary motion 88
4.3.1 Spherical freezing 90
4.3.2 Cylindrical freezing 91
4.4 Integral iteration 92
4.4.1 Spherical freezing 94
4.4.2 Cylindrical freezing 98
4.5 Some general comments 100
4.6 Additional symbols used 104
5 Polynomial approximations 105
5.1 Introduction 105
5.2 Quadratic approximations 108
5.2.1 Megerlin s method 109
5.2.2 Integral formula method 109
5.2.3 Heat balance method 109
5.3 Planar solidification with surface cooling 112
5.3.1 Megerlin s method 112
5.3.2 Integral formula method 113
5.3.3 Heat balance method 113
5.4 Freezing a liquid in a spherical container 114
5.4.1 Megerlin s method 116
5.4.2 Integral formula method 117
5.4.3 Heat balance method for no surface cooling ()3 = 0) 118
CONTENTS ix
5.5 Freezing a liquid in a long circular cylindrical container 121
5.5.1 Megerlin s method 122
5.5.2 Integral formula method 123
5.5.3 Heat balance method for no surface cooling (/3 = 0) 123
5.6 Cubic approximations for no surface cooling 124
5.6.1 Megerlin s method 125
5.6.2 Integral formula method 125
5.6.3 Spherical freezing 126
5.6.4 Cylindrical freezing 128
5.7 Alternative temperature profile for cylindrical freezing 129
5.7.1 Megerlin s method 131
5.7.2 Integral formula method 131
5.8 Additional symbols used 132
6 Boundary fixing transformations and series solutions 134
6.1 Introduction 134
6.2 Planar solidification 137
6.2.1 Short time solution 138
6.2.2 Large time solution 141
6.3 Freezing a liquid in a spherical container 145
6.3.1 Solution for prescribed surface temperature (/? = 0) 145
6.3.2 Solution for surface heat loss (/3 * 0) 151
6.4 Freezing a liquid in a long circular cylindrical container 153
6.4.1 Solution for prescribed surface temperature (/J = 0) 155
6.4.2 Solution for surface heat loss (£ =£0) 157
6.5 Alternative solution for spherical freezing with no surface
cooling 160
6.6 Additional symbols used 162
7 Two simultaneous chemical reactions 164
7.1 Introduction 164
7.2 Large Stefan number expansion 166
7.3 Integral formulation by integration 170
7.4 Integral formulation by Green s function 172
7.5 Bounds for the motion of the boundary 176
7.6 Formal series solution and related integral equation 179
7.7 Additional symbols used 182
Appendix 1 Langford s cylinder functions cn(z, z0) and en(z, z0) 184
Al.l Additional symbols used 186
x CONTENTS
Appendix 2 Evaluating At(p), A2(p) and A ,(l) for spherical
solidification 188
A2.1 Solution for Ax(p) 188
A2.2 Solution for A2(p) 189
A2.3 Solution for ^(l) 191
A2.4 Additional symbols used 192
References 194
Citation index 203
|
| any_adam_object | 1 |
| author | Hill, James M. |
| author_facet | Hill, James M. |
| author_role | aut |
| author_sort | Hill, James M. |
| author_variant | j m h jm jmh |
| building | Verbundindex |
| bvnumber | BV006552064 |
| callnumber-first | Q - Science |
| callnumber-label | QA379 |
| callnumber-raw | QA379 QC321 |
| callnumber-search | QA379 QC321 |
| callnumber-sort | QA 3379 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 520 SK 950 |
| ctrlnum | (OCoLC)14133974 (DE-599)BVBBV006552064 |
| dewey-full | 536/.23 515/.62 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 536 - Heat 515 - Analysis |
| dewey-raw | 536/.23 515/.62 |
| dewey-search | 536/.23 515/.62 |
| dewey-sort | 3536 223 |
| dewey-tens | 530 - Physics 510 - Mathematics |
| discipline | Physik Mathematik |
| format | Book |
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| id | DE-604.BV006552064 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T16:48:11Z |
| institution | BVB |
| isbn | 0582988233 0470203889 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-004177353 |
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| owner | DE-739 DE-355 DE-BY-UBR |
| owner_facet | DE-739 DE-355 DE-BY-UBR |
| physical | XVIII, 204 S. graph. Darst. |
| publishDate | 1987 |
| publishDateSearch | 1987 |
| publishDateSort | 1987 |
| publisher | Longman Scientific & Technical |
| record_format | marc |
| series | Pitman monographs and surveys in pure and applied mathematics |
| series2 | Pitman monographs and surveys in pure and applied mathematics |
| spelling | Hill, James M. Verfasser aut One-dimensional Stefan problems an introduction Harlow Longman Scientific & Technical 1987 XVIII, 204 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Pitman monographs and surveys in pure and applied mathematics 31. Approximation polynomiale Chaleur - Conduction Cinétique chimique Diffusion chaleur Equation intégrale Expérience numérique Fonction spéciale Problème Stefan Problème aux limites ram Problèmes aux limites Thermocinétique ram Boundary value problems Heat Conduction Randwertproblem (DE-588)4048395-2 gnd rswk-swf Integralgleichung (DE-588)4027229-1 gnd rswk-swf Näherungsverfahren (DE-588)4206467-3 gnd rswk-swf Approximation (DE-588)4002498-2 gnd rswk-swf Stefan-Problem (DE-588)4183000-3 gnd rswk-swf Wärmeleitungsgleichung (DE-588)4188859-5 gnd rswk-swf Diffusion (DE-588)4012277-3 gnd rswk-swf Wärmeleitungsgleichung (DE-588)4188859-5 s Randwertproblem (DE-588)4048395-2 s Integralgleichung (DE-588)4027229-1 s 1\p DE-604 Approximation (DE-588)4002498-2 s 2\p DE-604 Näherungsverfahren (DE-588)4206467-3 s 3\p DE-604 Diffusion (DE-588)4012277-3 s 4\p DE-604 Stefan-Problem (DE-588)4183000-3 s 5\p DE-604 Pitman monographs and surveys in pure and applied mathematics 31. (DE-604)BV000022446 31 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004177353&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 5\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Hill, James M. One-dimensional Stefan problems an introduction Pitman monographs and surveys in pure and applied mathematics Approximation polynomiale Chaleur - Conduction Cinétique chimique Diffusion chaleur Equation intégrale Expérience numérique Fonction spéciale Problème Stefan Problème aux limites ram Problèmes aux limites Thermocinétique ram Boundary value problems Heat Conduction Randwertproblem (DE-588)4048395-2 gnd Integralgleichung (DE-588)4027229-1 gnd Näherungsverfahren (DE-588)4206467-3 gnd Approximation (DE-588)4002498-2 gnd Stefan-Problem (DE-588)4183000-3 gnd Wärmeleitungsgleichung (DE-588)4188859-5 gnd Diffusion (DE-588)4012277-3 gnd |
| subject_GND | (DE-588)4048395-2 (DE-588)4027229-1 (DE-588)4206467-3 (DE-588)4002498-2 (DE-588)4183000-3 (DE-588)4188859-5 (DE-588)4012277-3 |
| title | One-dimensional Stefan problems an introduction |
| title_auth | One-dimensional Stefan problems an introduction |
| title_exact_search | One-dimensional Stefan problems an introduction |
| title_full | One-dimensional Stefan problems an introduction |
| title_fullStr | One-dimensional Stefan problems an introduction |
| title_full_unstemmed | One-dimensional Stefan problems an introduction |
| title_short | One-dimensional Stefan problems |
| title_sort | one dimensional stefan problems an introduction |
| title_sub | an introduction |
| topic | Approximation polynomiale Chaleur - Conduction Cinétique chimique Diffusion chaleur Equation intégrale Expérience numérique Fonction spéciale Problème Stefan Problème aux limites ram Problèmes aux limites Thermocinétique ram Boundary value problems Heat Conduction Randwertproblem (DE-588)4048395-2 gnd Integralgleichung (DE-588)4027229-1 gnd Näherungsverfahren (DE-588)4206467-3 gnd Approximation (DE-588)4002498-2 gnd Stefan-Problem (DE-588)4183000-3 gnd Wärmeleitungsgleichung (DE-588)4188859-5 gnd Diffusion (DE-588)4012277-3 gnd |
| topic_facet | Approximation polynomiale Chaleur - Conduction Cinétique chimique Diffusion chaleur Equation intégrale Expérience numérique Fonction spéciale Problème Stefan Problème aux limites Problèmes aux limites Thermocinétique Boundary value problems Heat Conduction Randwertproblem Integralgleichung Näherungsverfahren Approximation Stefan-Problem Wärmeleitungsgleichung Diffusion |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004177353&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000022446 |
| work_keys_str_mv | AT hilljamesm onedimensionalstefanproblemsanintroduction |