Heat transfer process with solid-solid interface: Analytical and numerical solutions

Autores
Rubio, Aurora Diana; Tarzia, Domingo Alberto; Umbricht, Guillermo Federico
Año de publicación
2021
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
This work is aimed at the study and analysis of the heat transport on a metal bar of length L with a solid-solid interface. The process is assumed to be developed along one direction, across two homogeneous and isotropic materials. Analytical and numerical solutions are obtained under continuity conditions at the interface, that is a perfect assembly. The lateral side is assumed to be isolated and a constant thermal source is located at the left-boundary while the right-end stays free allowing the heat to transfer to the surrounding fluid by a convective process. The differences between the analytic solution and temperature measurements at any point on the right would indicate the presence of discontinuities. The greater these differences, the greater the discontinuity in the interface due to thermal resistances, providing a measure of its propagation from the interface and they could be modeled as temperature perturbations. The problem of interest may be described by a parabolic equation with initial, interface and boundary conditions, where the thermal properties, the conductivity and diffusivity coefficients, are piecewise constant functions. The analytic solution is derived by using Fourier methods. Special attention is given to the Sturm-Liouville problem that arises when deriving the solution, since a complicated eigenvalue equation must to be solved. Numerical simulations are conducted by using finite difference schemes where its convergence and stability properties are discussed along with physical interpretations of the results.
Fil: Rubio, Aurora Diana. Universidad Nacional de San Martin. Escuela de Ciencia y Tecnología. Centro de Matemática Aplicada; Argentina
Fil: Tarzia, Domingo Alberto. Universidad Austral. Facultad de Ciencias Empresariales. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Umbricht, Guillermo Federico. Universidad Nacional de General Sarmiento. Instituto del Desarrollo Humano; Argentina. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Materia
EIGENVALUES PROBLEMS
HEAT EQUATION
MATHEMATICAL MODELING
SOLID-SOLID INTERFACE
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/167413
Acceder
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network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Heat transfer process with solid-solid interface: Analytical and numerical solutionsRubio, Aurora DianaTarzia, Domingo AlbertoUmbricht, Guillermo FedericoEIGENVALUES PROBLEMSHEAT EQUATIONMATHEMATICAL MODELINGSOLID-SOLID INTERFACEhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1This work is aimed at the study and analysis of the heat transport on a metal bar of length L with a solid-solid interface. The process is assumed to be developed along one direction, across two homogeneous and isotropic materials. Analytical and numerical solutions are obtained under continuity conditions at the interface, that is a perfect assembly. The lateral side is assumed to be isolated and a constant thermal source is located at the left-boundary while the right-end stays free allowing the heat to transfer to the surrounding fluid by a convective process. The differences between the analytic solution and temperature measurements at any point on the right would indicate the presence of discontinuities. The greater these differences, the greater the discontinuity in the interface due to thermal resistances, providing a measure of its propagation from the interface and they could be modeled as temperature perturbations. The problem of interest may be described by a parabolic equation with initial, interface and boundary conditions, where the thermal properties, the conductivity and diffusivity coefficients, are piecewise constant functions. The analytic solution is derived by using Fourier methods. Special attention is given to the Sturm-Liouville problem that arises when deriving the solution, since a complicated eigenvalue equation must to be solved. Numerical simulations are conducted by using finite difference schemes where its convergence and stability properties are discussed along with physical interpretations of the results.Fil: Rubio, Aurora Diana. Universidad Nacional de San Martin. Escuela de Ciencia y Tecnología. Centro de Matemática Aplicada; ArgentinaFil: Tarzia, Domingo Alberto. Universidad Austral. Facultad de Ciencias Empresariales. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Umbricht, Guillermo Federico. Universidad Nacional de General Sarmiento. Instituto del Desarrollo Humano; Argentina. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaWorld Scientific and Engineering Academy and Society2021-09-02info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/167413Rubio, Aurora Diana; Tarzia, Domingo Alberto; Umbricht, Guillermo Federico; Heat transfer process with solid-solid interface: Analytical and numerical solutions; World Scientific and Engineering Academy and Society; Wseas Transactions on Mathematics; 20; 2-9-2021; 404-4141109-27692224-2880CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://wseas.com/journals/articles.php?id=533info:eu-repo/semantics/altIdentifier/doi/10.37394/23206.2021.20.42info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/2110.14542info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T12:07:55Zoai:ri.conicet.gov.ar:11336/167413instacron: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:34982025-10-22 12:07:55.35CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Heat transfer process with solid-solid interface: Analytical and numerical solutions
title Heat transfer process with solid-solid interface: Analytical and numerical solutions
spellingShingle Heat transfer process with solid-solid interface: Analytical and numerical solutions
Rubio, Aurora Diana
EIGENVALUES PROBLEMS
HEAT EQUATION
MATHEMATICAL MODELING
SOLID-SOLID INTERFACE
title_short Heat transfer process with solid-solid interface: Analytical and numerical solutions
title_full Heat transfer process with solid-solid interface: Analytical and numerical solutions
title_fullStr Heat transfer process with solid-solid interface: Analytical and numerical solutions
title_full_unstemmed Heat transfer process with solid-solid interface: Analytical and numerical solutions
title_sort Heat transfer process with solid-solid interface: Analytical and numerical solutions
dc.creator.none.fl_str_mv Rubio, Aurora Diana
Tarzia, Domingo Alberto
Umbricht, Guillermo Federico
author Rubio, Aurora Diana
author_facet Rubio, Aurora Diana
Tarzia, Domingo Alberto
Umbricht, Guillermo Federico
author_role author
author2 Tarzia, Domingo Alberto
Umbricht, Guillermo Federico
author2_role author
author
dc.subject.none.fl_str_mv EIGENVALUES PROBLEMS
HEAT EQUATION
MATHEMATICAL MODELING
SOLID-SOLID INTERFACE
topic EIGENVALUES PROBLEMS
HEAT EQUATION
MATHEMATICAL MODELING
SOLID-SOLID INTERFACE
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv This work is aimed at the study and analysis of the heat transport on a metal bar of length L with a solid-solid interface. The process is assumed to be developed along one direction, across two homogeneous and isotropic materials. Analytical and numerical solutions are obtained under continuity conditions at the interface, that is a perfect assembly. The lateral side is assumed to be isolated and a constant thermal source is located at the left-boundary while the right-end stays free allowing the heat to transfer to the surrounding fluid by a convective process. The differences between the analytic solution and temperature measurements at any point on the right would indicate the presence of discontinuities. The greater these differences, the greater the discontinuity in the interface due to thermal resistances, providing a measure of its propagation from the interface and they could be modeled as temperature perturbations. The problem of interest may be described by a parabolic equation with initial, interface and boundary conditions, where the thermal properties, the conductivity and diffusivity coefficients, are piecewise constant functions. The analytic solution is derived by using Fourier methods. Special attention is given to the Sturm-Liouville problem that arises when deriving the solution, since a complicated eigenvalue equation must to be solved. Numerical simulations are conducted by using finite difference schemes where its convergence and stability properties are discussed along with physical interpretations of the results.
Fil: Rubio, Aurora Diana. Universidad Nacional de San Martin. Escuela de Ciencia y Tecnología. Centro de Matemática Aplicada; Argentina
Fil: Tarzia, Domingo Alberto. Universidad Austral. Facultad de Ciencias Empresariales. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Umbricht, Guillermo Federico. Universidad Nacional de General Sarmiento. Instituto del Desarrollo Humano; Argentina. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
description This work is aimed at the study and analysis of the heat transport on a metal bar of length L with a solid-solid interface. The process is assumed to be developed along one direction, across two homogeneous and isotropic materials. Analytical and numerical solutions are obtained under continuity conditions at the interface, that is a perfect assembly. The lateral side is assumed to be isolated and a constant thermal source is located at the left-boundary while the right-end stays free allowing the heat to transfer to the surrounding fluid by a convective process. The differences between the analytic solution and temperature measurements at any point on the right would indicate the presence of discontinuities. The greater these differences, the greater the discontinuity in the interface due to thermal resistances, providing a measure of its propagation from the interface and they could be modeled as temperature perturbations. The problem of interest may be described by a parabolic equation with initial, interface and boundary conditions, where the thermal properties, the conductivity and diffusivity coefficients, are piecewise constant functions. The analytic solution is derived by using Fourier methods. Special attention is given to the Sturm-Liouville problem that arises when deriving the solution, since a complicated eigenvalue equation must to be solved. Numerical simulations are conducted by using finite difference schemes where its convergence and stability properties are discussed along with physical interpretations of the results.
publishDate 2021
dc.date.none.fl_str_mv 2021-09-02
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/11336/167413
Rubio, Aurora Diana; Tarzia, Domingo Alberto; Umbricht, Guillermo Federico; Heat transfer process with solid-solid interface: Analytical and numerical solutions; World Scientific and Engineering Academy and Society; Wseas Transactions on Mathematics; 20; 2-9-2021; 404-414
1109-2769
2224-2880
CONICET Digital
CONICET
url http://hdl.handle.net/11336/167413
identifier_str_mv Rubio, Aurora Diana; Tarzia, Domingo Alberto; Umbricht, Guillermo Federico; Heat transfer process with solid-solid interface: Analytical and numerical solutions; World Scientific and Engineering Academy and Society; Wseas Transactions on Mathematics; 20; 2-9-2021; 404-414
1109-2769
2224-2880
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://wseas.com/journals/articles.php?id=533
info:eu-repo/semantics/altIdentifier/doi/10.37394/23206.2021.20.42
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/2110.14542
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv World Scientific and Engineering Academy and Society
publisher.none.fl_str_mv World Scientific and Engineering Academy and Society
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 12.982451

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