Analytical solutions to the Stefan problem with internal heat generation
Autor(a) principal: | |
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Data de Publicação: | 2016 |
Outros Autores: | , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.1016/j.applthermaleng.2016.03.122 http://hdl.handle.net/11449/161711 |
Resumo: | A first-order, ordinary differential equation modeling the Stefan problem (solid-liquid phase change) with internal heat generation in a plane wall is derived and the solutions are compared to the results of a computational fluid dynamics analysis. The internal heat generation term makes the governing equations non-homogeneous so the principle of superposition is used to separate the transient from steady-state portions of the heat equation, which are then solved separately. There is excellent agreement between the solutions to the differential equation and the CFD results for the movement of both the solidification and melting fronts. The solid and liquid temperature profiles show a distinct difference in slope along the interface early in the phase change process. As time increases, the changes in slope decrease and the temperature profiles become parabolic. The system reaches steady-state faster for larger Stefan numbers and inversely, the time to steady-state increases as the Stefan number decreases. (C) 2016 Published by Elsevier Ltd. |
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Repositório Institucional da UNESP |
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Analytical solutions to the Stefan problem with internal heat generationStefan problemInternal heat generationSolidificationMeltingA first-order, ordinary differential equation modeling the Stefan problem (solid-liquid phase change) with internal heat generation in a plane wall is derived and the solutions are compared to the results of a computational fluid dynamics analysis. The internal heat generation term makes the governing equations non-homogeneous so the principle of superposition is used to separate the transient from steady-state portions of the heat equation, which are then solved separately. There is excellent agreement between the solutions to the differential equation and the CFD results for the movement of both the solidification and melting fronts. The solid and liquid temperature profiles show a distinct difference in slope along the interface early in the phase change process. As time increases, the changes in slope decrease and the temperature profiles become parabolic. The system reaches steady-state faster for larger Stefan numbers and inversely, the time to steady-state increases as the Stefan number decreases. (C) 2016 Published by Elsevier Ltd.Univ Idaho, Dept Mech Engn, 875 Perimeter Dr,MS 0902, Moscow, ID 83844 USASouthern Utah Univ, Dept Integrated Engn, 351 W Univ Blvd, Cedar City, UT 84720 USASao Paulo State Univ, Dept Engn Mecan, BR-15385000 Ilha Solteira, SP, BrazilSao Paulo State Univ, Dept Engn Mecan, BR-15385000 Ilha Solteira, SP, BrazilElsevier B.V.Univ IdahoSouthern Utah UnivUniversidade Estadual Paulista (Unesp)McCord, DavidCrepeau, JohnSiahpush, AliFerres Brogin, Joao Angelo [UNESP]2018-11-26T16:48:20Z2018-11-26T16:48:20Z2016-06-25info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article443-451application/pdfhttp://dx.doi.org/10.1016/j.applthermaleng.2016.03.122Applied Thermal Engineering. Oxford: Pergamon-elsevier Science Ltd, v. 103, p. 443-451, 2016.1359-4311http://hdl.handle.net/11449/16171110.1016/j.applthermaleng.2016.03.122WOS:000379560500045WOS000379560500045.pdfWeb of Sciencereponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengApplied Thermal Engineering1,505info:eu-repo/semantics/openAccess2024-07-04T20:06:14Zoai:repositorio.unesp.br:11449/161711Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T17:46:30.619956Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Analytical solutions to the Stefan problem with internal heat generation |
title |
Analytical solutions to the Stefan problem with internal heat generation |
spellingShingle |
Analytical solutions to the Stefan problem with internal heat generation McCord, David Stefan problem Internal heat generation Solidification Melting |
title_short |
Analytical solutions to the Stefan problem with internal heat generation |
title_full |
Analytical solutions to the Stefan problem with internal heat generation |
title_fullStr |
Analytical solutions to the Stefan problem with internal heat generation |
title_full_unstemmed |
Analytical solutions to the Stefan problem with internal heat generation |
title_sort |
Analytical solutions to the Stefan problem with internal heat generation |
author |
McCord, David |
author_facet |
McCord, David Crepeau, John Siahpush, Ali Ferres Brogin, Joao Angelo [UNESP] |
author_role |
author |
author2 |
Crepeau, John Siahpush, Ali Ferres Brogin, Joao Angelo [UNESP] |
author2_role |
author author author |
dc.contributor.none.fl_str_mv |
Univ Idaho Southern Utah Univ Universidade Estadual Paulista (Unesp) |
dc.contributor.author.fl_str_mv |
McCord, David Crepeau, John Siahpush, Ali Ferres Brogin, Joao Angelo [UNESP] |
dc.subject.por.fl_str_mv |
Stefan problem Internal heat generation Solidification Melting |
topic |
Stefan problem Internal heat generation Solidification Melting |
description |
A first-order, ordinary differential equation modeling the Stefan problem (solid-liquid phase change) with internal heat generation in a plane wall is derived and the solutions are compared to the results of a computational fluid dynamics analysis. The internal heat generation term makes the governing equations non-homogeneous so the principle of superposition is used to separate the transient from steady-state portions of the heat equation, which are then solved separately. There is excellent agreement between the solutions to the differential equation and the CFD results for the movement of both the solidification and melting fronts. The solid and liquid temperature profiles show a distinct difference in slope along the interface early in the phase change process. As time increases, the changes in slope decrease and the temperature profiles become parabolic. The system reaches steady-state faster for larger Stefan numbers and inversely, the time to steady-state increases as the Stefan number decreases. (C) 2016 Published by Elsevier Ltd. |
publishDate |
2016 |
dc.date.none.fl_str_mv |
2016-06-25 2018-11-26T16:48:20Z 2018-11-26T16:48:20Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://dx.doi.org/10.1016/j.applthermaleng.2016.03.122 Applied Thermal Engineering. Oxford: Pergamon-elsevier Science Ltd, v. 103, p. 443-451, 2016. 1359-4311 http://hdl.handle.net/11449/161711 10.1016/j.applthermaleng.2016.03.122 WOS:000379560500045 WOS000379560500045.pdf |
url |
http://dx.doi.org/10.1016/j.applthermaleng.2016.03.122 http://hdl.handle.net/11449/161711 |
identifier_str_mv |
Applied Thermal Engineering. Oxford: Pergamon-elsevier Science Ltd, v. 103, p. 443-451, 2016. 1359-4311 10.1016/j.applthermaleng.2016.03.122 WOS:000379560500045 WOS000379560500045.pdf |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Applied Thermal Engineering 1,505 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
443-451 application/pdf |
dc.publisher.none.fl_str_mv |
Elsevier B.V. |
publisher.none.fl_str_mv |
Elsevier B.V. |
dc.source.none.fl_str_mv |
Web of Science reponame:Repositório Institucional da UNESP instname:Universidade Estadual Paulista (UNESP) instacron:UNESP |
instname_str |
Universidade Estadual Paulista (UNESP) |
instacron_str |
UNESP |
institution |
UNESP |
reponame_str |
Repositório Institucional da UNESP |
collection |
Repositório Institucional da UNESP |
repository.name.fl_str_mv |
Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP) |
repository.mail.fl_str_mv |
|
_version_ |
1808128855134699520 |