Mathematical models of convection:
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
de Gruyter
2012
|
| Schriftenreihe: | De Gruyter studies in mathematical physics
5 |
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | Literaturangaben |
| Beschreibung: | XV, 417 S. graph. Darst. 25 cm |
| ISBN: | 3110258145 9783110258141 |
Internformat
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| 245 | 1 | 0 | |a Mathematical models of convection |c Victor K. Andreev ... |
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| 336 | |b txt |2 rdacontent | ||
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Datensatz im Suchindex
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| adam_text |
IMAGE 1
CONTENTS
PREFACE V
LIST O F CONTRIBUTING AUTHORS XI
1 EQUATIONS O F FLUID MOTION 1
1.1 BASIC HYPOTHESES O F CONTINUUM 1
1.2 TWO METHODS FOR THE CONTINUUM DESCRIPTION. TRANSLATION FORMULA . . .
. 4
1.3 INTEGRAL CONSERVATION LAWS. EQUATIONS O F CONTINUOUS MOTION 7
1.4 THERMODYNAMICS ASPECTS 13
1.5 CLASSICAL MODELS O F LIQUIDS AND GASES 16
2 CONDITIONS ON THE INTERFACE BETWEEN FLUIDS AND ON SOLID WALLS 24
2.1 NOTION O F THE INTERFACE 24
2.2 KINEMATIC CONDITION 25
2.3 DYNAMIC CONDITION 26
2.4 ELEMENTS O F THERMODYNAMICS O F THE INTERFACE 31
2.5 CONDITIONS O F CONTINUITY 33
2.6 ENERGY TRANSFER ACROSS THE INTERFACE 34
2.7 FREE SURFACES 39
2.8 ADDITIONAL CONDITIONS 4 1
3 MODELS O F CONVECTION O F AN ISOTHERMALLY INCOMPRESSIBLE FLUID 44
3.1 ISOTHERMALLY INCOMPRESSIBLE FLUID 4 4
3.2 EQUATIONS O F THERMAL CONVECTION O F AN ISOTHERMALLY INCOMPRESSIBLE
FLUID 46
3.3 MODEL O F LINEAR THERMAL EXPANSION 47
3.4 SOME SUBMODELS 49
3.5 ON BOUNDARY CONDITIONS 51
3.6 TWO PROBLEMS O F CONVECTION 53
HTTP://D-NB.INFO/1020636106
IMAGE 2
X I V
CONTENTS
4 HIERARCHY O F CONVECTION MODELS IN CLOSED VOLUMES 60
4.1 INITIAL RELATIONS 60
4.2 SIMILARITY CRITERIA 62
4.3 TRANSITION TO DIMENSIONAL VARIABLES 64
4.4 EXPANSION IN THE SMALL PARAMETER 67
4.5 EQUATIONS O F MICROCONVECTION O F AN ISOTHERMALLY INCOMPRESSIBLE
FLUID 71
4.6 OBERBECK-BOUSSINESQ EQUATIONS 74
4.7 LINEAR MODEL O F THE TRANSITIONAL PROCESS 75
4.8 SOME CONCLUSIONS 78
4.9 CONVECTION O F NONISOTHERMAL LIQUIDS AND GASES UNDER MICROGRAVITY
CONDITIONS 81
4.10 CONVECTION O F A THERMALLY INHOMOGENEOUS WEAKLY COMPRESSIBLE FLUID
88
4.11 EXACT SOLUTIONS IN AN INFINITE BAND 93
4.12 ANALYSIS O F WELL-POSEDNESS O F THE INITIAL-BOUNDARY PROBLEM FOR
EQUATIONS O F CONVECTION O F A WEAKLY COMPRESSIBLE FLUID 105
5 INVARIANT SUBMODELS O F MICROCONVECTION EQUATIONS 115
5.1 BASIC MODEL AND ITS GROUP PROPERTIES 115
5.2 OPTIMAL SUBSYSTEMS O F THE SUBALGEBRAS 0 I AND 0 2 , FACTOR-SYSTEMS,
AND SOME SOLUTIONS 118
5.3 ON ONE STEADY SOLUTION O F MICROCONVECTION EQUATIONS IN A VERTICAL
LAYER 126
5.4 SOLVABILITY O F A NONSTANDARD BOUNDARY-VALUE PROBLEM 137
5.5 UNSTEADY SOLUTION O F MICROCONVECTION EQUATIONS IN AN INFINITE BAND
. . 144
5.6 INVARIANT SOLUTIONS O F MICROCONVECTION EQUATIONS THAT DESCRIBE THE
MOTION WITH AN INTERFACE 150
6 GROUP PROPERTIES O F EQUATIONS O F THERMODIFFUSION MOTION 157
6.1 LIE GROUP O F THERMODIFFUSION EQUATIONS 157
6.2 GROUP PROPERTIES O F TWO-DIMENSIONAL EQUATIONS 174
6.3 INVARIANT SUBMODELS AND EXACT SOLUTIONS O F THERMODIFFUSION
EQUATIONS 182
IMAGE 3
CONTENTS XV
7 STABILITY O F EQUILIBRIUM STATES IN THE OBERBECK-BOUSSINESQ MODEL 1 98
7.1 CONVECTIVE INSTABILITY O F A HORIZONTAL LAYER WITH OSCILLATIONS OF
TEMPERATURE ON THE FREE BOUNDARY 198
7.2 INSTABILITY O F A LIQUID LAYERS WITH AN INTERFACE 208
7.3 CONVECTION IN A ROTATING FLUID LAYER UNDER MICROGRAVITY CONDITIONS .
. . 217
8 SMALL PERTURBATIONS AND STABILITY O F PLANE LAYERS IN THE
MICROCONVECTION MODEL 227
8.1 EQUATIONS O F SMALL PERTURBATIONS 227
8.2 STABILITY O F THE EQUILIBRIUM STATE O F A PLANE LAYER WITH SOLID
WALLS . . . . 231
8.3 EMERGENCE O F MICROCONVECTION IN A PLANE LAYER WITH A FREE BOUNDARY
241
8.4 STABILITY O F A STEADY FLOW IN A VERTICAL LAYER 252
9 NUMERICAL SIMULATION O F CONVECTIVE FLOWS UNDER MICROGRAVITY
CONDITIONS 263
9.1 NUMERICAL METHODS USED FOR CALCULATIONS 263
9.2 NUMERICAL STUDY O F UNSTEADY MICROCONVECTION IN CANONICAL DOMAINS
WITH SOLID BOUNDARIES 274
9.3 NUMERICAL STUDY O F STEADY MICROCONVECTION IN DOMAINS WITH FREE
BOUNDARIES 291
9.4 STUDY O F CONVECTION INDUCED BY VOLUME EXPANSION 307
9.5 CONVECTION IN MISCIBLE FLUIDS 327
10 CONVECTIVE FLOWS IN TUBES AND LAYERS 347
10.1 GROUP-THEORETICAL NATURE O F THE BIRIKH SOLUTION AND ITS
GENERALIZATIONS 347
10.2 AN AXIAL CONVECTIVE FLOW IN A ROTATING TUBE WITH A LONGITUDINAL
TEMPERATURE GRADIENT 355
10.3 UNSTEADY ANALOGS O F THE BIRIKH SOLUTIONS 363
10.4 MODEL O F VISCOUS LAYER DEFORMATION BY THERMOCAPILLARY FORCES 377
BIBLIOGRAPHY 401
INDEX 415 |
| any_adam_object | 1 |
| author_GND | (DE-588)1027094473 |
| building | Verbundindex |
| bvnumber | BV040418819 |
| classification_rvk | SK 950 UF 4000 UG 2700 |
| ctrlnum | (OCoLC)809234348 (DE-599)DNB1020636106 |
| dewey-full | 536.25 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 536 - Heat |
| dewey-raw | 536.25 |
| dewey-search | 536.25 |
| dewey-sort | 3536.25 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-08-21T00:09:58Z |
| institution | BVB |
| isbn | 3110258145 9783110258141 |
| language | English |
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| oclc_num | 809234348 |
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| physical | XV, 417 S. graph. Darst. 25 cm |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | de Gruyter |
| record_format | marc |
| series | De Gruyter studies in mathematical physics |
| series2 | De Gruyter studies in mathematical physics |
| spelling | Mathematical models of convection Victor K. Andreev ... Berlin [u.a.] de Gruyter 2012 XV, 417 S. graph. Darst. 25 cm txt rdacontent n rdamedia nc rdacarrier De Gruyter studies in mathematical physics 5 Literaturangaben Konvektion (DE-588)4117572-4 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Konvektion (DE-588)4117572-4 s Mathematisches Modell (DE-588)4114528-8 s DE-604 Andreev, Viktor Konstantinovič Sonstige (DE-588)1027094473 oth Erscheint auch als Online-Ausgabe 978-3-11-025859-2 De Gruyter studies in mathematical physics 5 (DE-604)BV040141722 5 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3992613&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=025271609&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mathematical models of convection De Gruyter studies in mathematical physics Konvektion (DE-588)4117572-4 gnd Mathematisches Modell (DE-588)4114528-8 gnd |
| subject_GND | (DE-588)4117572-4 (DE-588)4114528-8 |
| title | Mathematical models of convection |
| title_auth | Mathematical models of convection |
| title_exact_search | Mathematical models of convection |
| title_full | Mathematical models of convection Victor K. Andreev ... |
| title_fullStr | Mathematical models of convection Victor K. Andreev ... |
| title_full_unstemmed | Mathematical models of convection Victor K. Andreev ... |
| title_short | Mathematical models of convection |
| title_sort | mathematical models of convection |
| topic | Konvektion (DE-588)4117572-4 gnd Mathematisches Modell (DE-588)4114528-8 gnd |
| topic_facet | Konvektion Mathematisches Modell |
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