Similarity solution for a two-phase one-dimensional Stefan problem with a convective boundary condition and a mushy zone model

Autores
Ceretani, Andrea Noemí; Tarzia, Domingo Alberto
Año de publicación
2018
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
A two-phase solidification process for a one-dimensional semi-infinite material is considered. It is assumed that it is ensued from a constant bulk temperature present in the vicinity of the fixed boundary, which it is modelled through a convective condition (Robin condition). The interface between the two phases is idealized as a mushy region and it is represented following the model of Solomon, Wilson, and Alexiades. An exact similarity solution is obtained when a restriction on data is verified, and it is analysed the relation between the problem considered here and the problem with a temperature condition at the fixed boundary. Moreover, it is proved that the solution to the problem with the convective boundary condition converges to the solution to a problem with a temperature condition when the heat transfer coefficient at the fixed boundary goes to infinity, and it is given an estimation of the difference between these two solutions.
Fil: Ceretani, Andrea Noemí. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Universidad Austral. Facultad de Ciencias Empresariales. Departamento de Matemáticas; Argentina
Fil: Tarzia, Domingo Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Austral. Facultad de Ciencias Empresariales. Departamento de Matemáticas; Argentina
Materia
CONVECTIVE CONDITION
EXPLICIT SOLUTIONS
PHASE-CHANGE PROCESS
SIMILARITY SOLUTIONS
STEFAN PROBLEMS
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/53174
Acceder
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network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Similarity solution for a two-phase one-dimensional Stefan problem with a convective boundary condition and a mushy zone modelCeretani, Andrea NoemíTarzia, Domingo AlbertoCONVECTIVE CONDITIONEXPLICIT SOLUTIONSPHASE-CHANGE PROCESSSIMILARITY SOLUTIONSSTEFAN PROBLEMShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1A two-phase solidification process for a one-dimensional semi-infinite material is considered. It is assumed that it is ensued from a constant bulk temperature present in the vicinity of the fixed boundary, which it is modelled through a convective condition (Robin condition). The interface between the two phases is idealized as a mushy region and it is represented following the model of Solomon, Wilson, and Alexiades. An exact similarity solution is obtained when a restriction on data is verified, and it is analysed the relation between the problem considered here and the problem with a temperature condition at the fixed boundary. Moreover, it is proved that the solution to the problem with the convective boundary condition converges to the solution to a problem with a temperature condition when the heat transfer coefficient at the fixed boundary goes to infinity, and it is given an estimation of the difference between these two solutions.Fil: Ceretani, Andrea Noemí. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Universidad Austral. Facultad de Ciencias Empresariales. Departamento de Matemáticas; ArgentinaFil: Tarzia, Domingo Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Austral. Facultad de Ciencias Empresariales. Departamento de Matemáticas; ArgentinaSociedade Brasileira de Matemática Aplicada e Computacional2018-05info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/53174Ceretani, Andrea Noemí; Tarzia, Domingo Alberto; Similarity solution for a two-phase one-dimensional Stefan problem with a convective boundary condition and a mushy zone model; Sociedade Brasileira de Matemática Aplicada e Computacional; Matematica Aplicada E Computacional; 37; 2; 5-2018; 2201-22170101-8205CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s40314-017-0442-0info:eu-repo/semantics/altIdentifier/doi/10.1007/s40314-017-0442-0info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1609.04690info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:51:46Zoai:ri.conicet.gov.ar:11336/53174instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-03 09:51:47.249CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Similarity solution for a two-phase one-dimensional Stefan problem with a convective boundary condition and a mushy zone model
title Similarity solution for a two-phase one-dimensional Stefan problem with a convective boundary condition and a mushy zone model
spellingShingle Similarity solution for a two-phase one-dimensional Stefan problem with a convective boundary condition and a mushy zone model
Ceretani, Andrea Noemí
CONVECTIVE CONDITION
EXPLICIT SOLUTIONS
PHASE-CHANGE PROCESS
SIMILARITY SOLUTIONS
STEFAN PROBLEMS
title_short Similarity solution for a two-phase one-dimensional Stefan problem with a convective boundary condition and a mushy zone model
title_full Similarity solution for a two-phase one-dimensional Stefan problem with a convective boundary condition and a mushy zone model
title_fullStr Similarity solution for a two-phase one-dimensional Stefan problem with a convective boundary condition and a mushy zone model
title_full_unstemmed Similarity solution for a two-phase one-dimensional Stefan problem with a convective boundary condition and a mushy zone model
title_sort Similarity solution for a two-phase one-dimensional Stefan problem with a convective boundary condition and a mushy zone model
dc.creator.none.fl_str_mv Ceretani, Andrea Noemí
Tarzia, Domingo Alberto
author Ceretani, Andrea Noemí
author_facet Ceretani, Andrea Noemí
Tarzia, Domingo Alberto
author_role author
author2 Tarzia, Domingo Alberto
author2_role author
dc.subject.none.fl_str_mv CONVECTIVE CONDITION
EXPLICIT SOLUTIONS
PHASE-CHANGE PROCESS
SIMILARITY SOLUTIONS
STEFAN PROBLEMS
topic CONVECTIVE CONDITION
EXPLICIT SOLUTIONS
PHASE-CHANGE PROCESS
SIMILARITY SOLUTIONS
STEFAN PROBLEMS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv A two-phase solidification process for a one-dimensional semi-infinite material is considered. It is assumed that it is ensued from a constant bulk temperature present in the vicinity of the fixed boundary, which it is modelled through a convective condition (Robin condition). The interface between the two phases is idealized as a mushy region and it is represented following the model of Solomon, Wilson, and Alexiades. An exact similarity solution is obtained when a restriction on data is verified, and it is analysed the relation between the problem considered here and the problem with a temperature condition at the fixed boundary. Moreover, it is proved that the solution to the problem with the convective boundary condition converges to the solution to a problem with a temperature condition when the heat transfer coefficient at the fixed boundary goes to infinity, and it is given an estimation of the difference between these two solutions.
Fil: Ceretani, Andrea Noemí. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Universidad Austral. Facultad de Ciencias Empresariales. Departamento de Matemáticas; Argentina
Fil: Tarzia, Domingo Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Austral. Facultad de Ciencias Empresariales. Departamento de Matemáticas; Argentina
description A two-phase solidification process for a one-dimensional semi-infinite material is considered. It is assumed that it is ensued from a constant bulk temperature present in the vicinity of the fixed boundary, which it is modelled through a convective condition (Robin condition). The interface between the two phases is idealized as a mushy region and it is represented following the model of Solomon, Wilson, and Alexiades. An exact similarity solution is obtained when a restriction on data is verified, and it is analysed the relation between the problem considered here and the problem with a temperature condition at the fixed boundary. Moreover, it is proved that the solution to the problem with the convective boundary condition converges to the solution to a problem with a temperature condition when the heat transfer coefficient at the fixed boundary goes to infinity, and it is given an estimation of the difference between these two solutions.
publishDate 2018
dc.date.none.fl_str_mv 2018-05
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/53174
Ceretani, Andrea Noemí; Tarzia, Domingo Alberto; Similarity solution for a two-phase one-dimensional Stefan problem with a convective boundary condition and a mushy zone model; Sociedade Brasileira de Matemática Aplicada e Computacional; Matematica Aplicada E Computacional; 37; 2; 5-2018; 2201-2217
0101-8205
CONICET Digital
CONICET
url http://hdl.handle.net/11336/53174
identifier_str_mv Ceretani, Andrea Noemí; Tarzia, Domingo Alberto; Similarity solution for a two-phase one-dimensional Stefan problem with a convective boundary condition and a mushy zone model; Sociedade Brasileira de Matemática Aplicada e Computacional; Matematica Aplicada E Computacional; 37; 2; 5-2018; 2201-2217
0101-8205
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s40314-017-0442-0
info:eu-repo/semantics/altIdentifier/doi/10.1007/s40314-017-0442-0
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1609.04690
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Sociedade Brasileira de Matemática Aplicada e Computacional
publisher.none.fl_str_mv Sociedade Brasileira de Matemática Aplicada e Computacional
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
_version_ 1842269116372615168
score 13.13397

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