Mathematical models of convection:
Saved in:
| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Berlin [u.a.]
de Gruyter
2012
|
| Series: | De Gruyter studies in mathematical physics
5 |
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Item Description: | Literaturangaben |
| Physical Description: | XV, 417 S. graph. Darst. 25 cm |
| ISBN: | 3110258145 9783110258141 |
Staff View
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV040418819 | ||
| 003 | DE-604 | ||
| 005 | 20130314 | ||
| 007 | t | ||
| 008 | 120914s2012 gw d||| |||| 00||| eng d | ||
| 016 | 7 | |a 1020636106 |2 DE-101 | |
| 020 | |a 3110258145 |9 3-11-025814-5 | ||
| 020 | |a 9783110258141 |9 978-3-11-025814-1 | ||
| 035 | |a (OCoLC)809234348 | ||
| 035 | |a (DE-599)DNB1020636106 | ||
| 040 | |a DE-604 |b ger |e rakwb | ||
| 041 | 0 | |a eng | |
| 044 | |a gw |c XA-DE | ||
| 049 | |a DE-11 |a DE-384 |a DE-703 |a DE-19 | ||
| 082 | 0 | |a 536.25 |2 22/ger | |
| 084 | |a SK 950 |0 (DE-625)143273: |2 rvk | ||
| 084 | |a UF 4000 |0 (DE-625)145577: |2 rvk | ||
| 084 | |a UG 2700 |0 (DE-625)145620: |2 rvk | ||
| 084 | |a 530 |2 sdnb | ||
| 245 | 1 | 0 | |a Mathematical models of convection |c Victor K. Andreev ... |
| 264 | 1 | |a Berlin [u.a.] |b de Gruyter |c 2012 | |
| 300 | |a XV, 417 S. |b graph. Darst. |c 25 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a De Gruyter studies in mathematical physics |v 5 | |
| 500 | |a Literaturangaben | ||
| 650 | 0 | 7 | |a Konvektion |0 (DE-588)4117572-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Mathematisches Modell |0 (DE-588)4114528-8 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Konvektion |0 (DE-588)4117572-4 |D s |
| 689 | 0 | 1 | |a Mathematisches Modell |0 (DE-588)4114528-8 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Andreev, Viktor Konstantinovič |e Sonstige |0 (DE-588)1027094473 |4 oth | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-3-11-025859-2 |
| 830 | 0 | |a De Gruyter studies in mathematical physics |v 5 |w (DE-604)BV040141722 |9 5 | |
| 856 | 4 | 2 | |m X:MVB |q text/html |u http://deposit.dnb.de/cgi-bin/dokserv?id=3992613&prov=M&dok_var=1&dok_ext=htm |3 Inhaltstext |
| 856 | 4 | 2 | |m DNB Datenaustausch |q application/pdf |u 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 |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-025271609 | |
Record in the Search Index
| _version_ | 1807953690022117376 |
|---|---|
| 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 |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>00000nam a2200000 cb4500</leader><controlfield tag="001">BV040418819</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20130314</controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">120914s2012 gw d||| |||| 00||| eng d</controlfield><datafield tag="016" ind1="7" ind2=" "><subfield code="a">1020636106</subfield><subfield code="2">DE-101</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">3110258145</subfield><subfield code="9">3-11-025814-5</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783110258141</subfield><subfield code="9">978-3-11-025814-1</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)809234348</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)DNB1020636106</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">gw</subfield><subfield code="c">XA-DE</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-11</subfield><subfield code="a">DE-384</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-19</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">536.25</subfield><subfield code="2">22/ger</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 950</subfield><subfield code="0">(DE-625)143273:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">UF 4000</subfield><subfield code="0">(DE-625)145577:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">UG 2700</subfield><subfield code="0">(DE-625)145620:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">530</subfield><subfield code="2">sdnb</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Mathematical models of convection</subfield><subfield code="c">Victor K. Andreev ...</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Berlin [u.a.]</subfield><subfield code="b">de Gruyter</subfield><subfield code="c">2012</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XV, 417 S.</subfield><subfield code="b">graph. Darst.</subfield><subfield code="c">25 cm</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">De Gruyter studies in mathematical physics</subfield><subfield code="v">5</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Literaturangaben</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Konvektion</subfield><subfield code="0">(DE-588)4117572-4</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Mathematisches Modell</subfield><subfield code="0">(DE-588)4114528-8</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Konvektion</subfield><subfield code="0">(DE-588)4117572-4</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Mathematisches Modell</subfield><subfield code="0">(DE-588)4114528-8</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Andreev, Viktor Konstantinovič</subfield><subfield code="e">Sonstige</subfield><subfield code="0">(DE-588)1027094473</subfield><subfield code="4">oth</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Online-Ausgabe</subfield><subfield code="z">978-3-11-025859-2</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">De Gruyter studies in mathematical physics</subfield><subfield code="v">5</subfield><subfield code="w">(DE-604)BV040141722</subfield><subfield code="9">5</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">X:MVB</subfield><subfield code="q">text/html</subfield><subfield code="u">http://deposit.dnb.de/cgi-bin/dokserv?id=3992613&prov=M&dok_var=1&dok_ext=htm</subfield><subfield code="3">Inhaltstext</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">DNB Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">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</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-025271609</subfield></datafield></record></collection> |
| id | DE-604.BV040418819 |
| illustrated | Illustrated |
| indexdate | 2024-08-21T00:09:58Z |
| institution | BVB |
| isbn | 3110258145 9783110258141 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025271609 |
| oclc_num | 809234348 |
| open_access_boolean | |
| owner | DE-11 DE-384 DE-703 DE-19 DE-BY-UBM |
| owner_facet | DE-11 DE-384 DE-703 DE-19 DE-BY-UBM |
| 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 |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=3992613&prov=M&dok_var=1&dok_ext=htm 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 |
| volume_link | (DE-604)BV040141722 |
| work_keys_str_mv | AT andreevviktorkonstantinovic mathematicalmodelsofconvection |