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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/167413
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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 Técnicas2025-09-29T10:35:35Zoai: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:34982025-09-29 10:35:35.556CONICET 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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1844614374546735104 |
score |
13.070432 |