Simultaneous determination of two unknown thermal coefficients through a mushy zone model with an overspecified convective boundary condition

Autores
Ceretani, Andrea Noemí; Tarzia, Domingo Alberto
Año de publicación
2016
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We have considered the simultaneous determination of two unknown thermal coefficients for a semi-infinite material which was under a phase-change process with a mushy zone according to the model of Solomon, Wilson and Alexiades. It was assumed that the material was initially liquid at its melting temperature and that the solidification process began when a heat flux was imposed at the fixed face. The associated free boundary value problem was overspecified with a convective boundary condition aiming at the simultaneous determination of the temperature in the solid region, one of the two free boundaries of the mushy zone and two thermal coefficients. These were chosen among the latent heat by unit mass, the thermal conductivity, the mass density, the specific heat and the two coefficients that characterize the mushy zone. It was assumed that the other free boundary of the mushy zone, the bulk temperature, the heat flux and heat transfer coefficients at the fixed face were known. Depending on the choice of the unknown thermal coefficients, fifteen phase-change problems arose. In this paper, we present those fifteen problems and obtain necessary and sufficient conditions on data for each of them in order to obtain their solutions. We show that there are twelve cases in which it is possible to find a unique solution and that there are infinite solutions for the remaining three cases. Moreover, for each problem, we give explicit formulae for the temperature of the material, the unknown free boundary and the two unknown thermal coefficients.
Fil: Ceretani, Andrea Noemí. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Austral. Facultad de Ciencias Empresariales. Departamento de Matemáticas; Argentina. Universidad Nacional de Rosario; 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
LAMÉ-CLAPEYRON-STEFAN PROBLEM
MUSHY ZONE
PHASE-CHANGE
UNKNOWN THERMAL COEFFICIENTS
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/60875
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/60875
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Simultaneous determination of two unknown thermal coefficients through a mushy zone model with an overspecified convective boundary conditionCeretani, Andrea NoemíTarzia, Domingo AlbertoCONVECTIVE CONDITIONLAMÉ-CLAPEYRON-STEFAN PROBLEMMUSHY ZONEPHASE-CHANGEUNKNOWN THERMAL COEFFICIENTShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We have considered the simultaneous determination of two unknown thermal coefficients for a semi-infinite material which was under a phase-change process with a mushy zone according to the model of Solomon, Wilson and Alexiades. It was assumed that the material was initially liquid at its melting temperature and that the solidification process began when a heat flux was imposed at the fixed face. The associated free boundary value problem was overspecified with a convective boundary condition aiming at the simultaneous determination of the temperature in the solid region, one of the two free boundaries of the mushy zone and two thermal coefficients. These were chosen among the latent heat by unit mass, the thermal conductivity, the mass density, the specific heat and the two coefficients that characterize the mushy zone. It was assumed that the other free boundary of the mushy zone, the bulk temperature, the heat flux and heat transfer coefficients at the fixed face were known. Depending on the choice of the unknown thermal coefficients, fifteen phase-change problems arose. In this paper, we present those fifteen problems and obtain necessary and sufficient conditions on data for each of them in order to obtain their solutions. We show that there are twelve cases in which it is possible to find a unique solution and that there are infinite solutions for the remaining three cases. Moreover, for each problem, we give explicit formulae for the temperature of the material, the unknown free boundary and the two unknown thermal coefficients.Fil: Ceretani, Andrea Noemí. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Austral. Facultad de Ciencias Empresariales. Departamento de Matemáticas; Argentina. Universidad Nacional de Rosario; ArgentinaFil: Tarzia, Domingo Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Austral. Facultad de Ciencias Empresariales. Departamento de Matemáticas; ArgentinaPushpa Publishing House2016-05info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/60875Ceretani, Andrea Noemí; Tarzia, Domingo Alberto; Simultaneous determination of two unknown thermal coefficients through a mushy zone model with an overspecified convective boundary condition; Pushpa Publishing House; JP Journal of Heat and Mass Transfer; 13; 2; 5-2016; 277-3010973-5763CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.17654/HM013020277info:eu-repo/semantics/altIdentifier/url/http://www.pphmj.com/abstract/9816.htminfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:52:47Zoai:ri.conicet.gov.ar:11336/60875instacron: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 09:52:47.228CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Simultaneous determination of two unknown thermal coefficients through a mushy zone model with an overspecified convective boundary condition
title Simultaneous determination of two unknown thermal coefficients through a mushy zone model with an overspecified convective boundary condition
spellingShingle Simultaneous determination of two unknown thermal coefficients through a mushy zone model with an overspecified convective boundary condition
Ceretani, Andrea Noemí
CONVECTIVE CONDITION
LAMÉ-CLAPEYRON-STEFAN PROBLEM
MUSHY ZONE
PHASE-CHANGE
UNKNOWN THERMAL COEFFICIENTS
title_short Simultaneous determination of two unknown thermal coefficients through a mushy zone model with an overspecified convective boundary condition
title_full Simultaneous determination of two unknown thermal coefficients through a mushy zone model with an overspecified convective boundary condition
title_fullStr Simultaneous determination of two unknown thermal coefficients through a mushy zone model with an overspecified convective boundary condition
title_full_unstemmed Simultaneous determination of two unknown thermal coefficients through a mushy zone model with an overspecified convective boundary condition
title_sort Simultaneous determination of two unknown thermal coefficients through a mushy zone model with an overspecified convective boundary condition
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
LAMÉ-CLAPEYRON-STEFAN PROBLEM
MUSHY ZONE
PHASE-CHANGE
UNKNOWN THERMAL COEFFICIENTS
topic CONVECTIVE CONDITION
LAMÉ-CLAPEYRON-STEFAN PROBLEM
MUSHY ZONE
PHASE-CHANGE
UNKNOWN THERMAL COEFFICIENTS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We have considered the simultaneous determination of two unknown thermal coefficients for a semi-infinite material which was under a phase-change process with a mushy zone according to the model of Solomon, Wilson and Alexiades. It was assumed that the material was initially liquid at its melting temperature and that the solidification process began when a heat flux was imposed at the fixed face. The associated free boundary value problem was overspecified with a convective boundary condition aiming at the simultaneous determination of the temperature in the solid region, one of the two free boundaries of the mushy zone and two thermal coefficients. These were chosen among the latent heat by unit mass, the thermal conductivity, the mass density, the specific heat and the two coefficients that characterize the mushy zone. It was assumed that the other free boundary of the mushy zone, the bulk temperature, the heat flux and heat transfer coefficients at the fixed face were known. Depending on the choice of the unknown thermal coefficients, fifteen phase-change problems arose. In this paper, we present those fifteen problems and obtain necessary and sufficient conditions on data for each of them in order to obtain their solutions. We show that there are twelve cases in which it is possible to find a unique solution and that there are infinite solutions for the remaining three cases. Moreover, for each problem, we give explicit formulae for the temperature of the material, the unknown free boundary and the two unknown thermal coefficients.
Fil: Ceretani, Andrea Noemí. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Austral. Facultad de Ciencias Empresariales. Departamento de Matemáticas; Argentina. Universidad Nacional de Rosario; Argentina
Fil: Tarzia, Domingo Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Austral. Facultad de Ciencias Empresariales. Departamento de Matemáticas; Argentina
description We have considered the simultaneous determination of two unknown thermal coefficients for a semi-infinite material which was under a phase-change process with a mushy zone according to the model of Solomon, Wilson and Alexiades. It was assumed that the material was initially liquid at its melting temperature and that the solidification process began when a heat flux was imposed at the fixed face. The associated free boundary value problem was overspecified with a convective boundary condition aiming at the simultaneous determination of the temperature in the solid region, one of the two free boundaries of the mushy zone and two thermal coefficients. These were chosen among the latent heat by unit mass, the thermal conductivity, the mass density, the specific heat and the two coefficients that characterize the mushy zone. It was assumed that the other free boundary of the mushy zone, the bulk temperature, the heat flux and heat transfer coefficients at the fixed face were known. Depending on the choice of the unknown thermal coefficients, fifteen phase-change problems arose. In this paper, we present those fifteen problems and obtain necessary and sufficient conditions on data for each of them in order to obtain their solutions. We show that there are twelve cases in which it is possible to find a unique solution and that there are infinite solutions for the remaining three cases. Moreover, for each problem, we give explicit formulae for the temperature of the material, the unknown free boundary and the two unknown thermal coefficients.
publishDate 2016
dc.date.none.fl_str_mv 2016-05
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/11336/60875
Ceretani, Andrea Noemí; Tarzia, Domingo Alberto; Simultaneous determination of two unknown thermal coefficients through a mushy zone model with an overspecified convective boundary condition; Pushpa Publishing House; JP Journal of Heat and Mass Transfer; 13; 2; 5-2016; 277-301
0973-5763
CONICET Digital
CONICET
url http://hdl.handle.net/11336/60875
identifier_str_mv Ceretani, Andrea Noemí; Tarzia, Domingo Alberto; Simultaneous determination of two unknown thermal coefficients through a mushy zone model with an overspecified convective boundary condition; Pushpa Publishing House; JP Journal of Heat and Mass Transfer; 13; 2; 5-2016; 277-301
0973-5763
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.17654/HM013020277
info:eu-repo/semantics/altIdentifier/url/http://www.pphmj.com/abstract/9816.htm
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Pushpa Publishing House
publisher.none.fl_str_mv Pushpa Publishing House
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
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score 13.13397

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