Eigenfunction expansions for transient diffusion in heterogeneous media

Detalhes bibliográficos
Autor(a) principal: Naveira-Cotta, Carolina Palma
Data de Publicação: 2009
Outros Autores: Cotta, Renato Machado, Orlande, Helcio Rangel Barreto, Fudym, Olivier
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UFRJ
Texto Completo: http://hdl.handle.net/11422/8739
Resumo: The Generalized Integral Transform Technique (GITT) is employed in the analytical solution of transient linear heat or mass diffusion problems in heterogeneous media. The GITT is utilized to handle the associated eigenvalue problem with arbitrarily space variable coefficients, defining an eigenfunction expansion in terms of a simpler Sturm-Liouville problem of known solution. In addition, the representation of the variable coefficients as eigenfunction expansions themselves has been proposed, considerably simplifying and accelerating the integral transformation process, while permitting the analytical evaluation of the coefficients matrices that form the transformed algebraic system. The proposed methodology is challenged in solving three different classes of diffusion problems in heterogeneous media, as illustrated for the cases of thermophysical properties with large scale variations found in heat transfer analysis of functionally graded materials (FGM), of abrupt variations in multiple layer transitions and of randomly variable physical properties in dispersed systems. The convergence behavior of the proposed expansions is then critically inspected and numerical results are presented to demonstrate the applicability of the general approach and to offer a set of reference results for potentials, eigenvalues, and related quantities.
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spelling Eigenfunction expansions for transient diffusion in heterogeneous mediaHeterogeneous mediaDiffusionVariable physical propertiesHeat conductionSturm-Liouville problemsIntegral transformsCNPQ::CIENCIAS EXATAS E DA TERRA::FISICA::AREAS CLASSICAS DE FENOMENOLOGIA E SUAS APLICACOES::DINAMICA DOS FLUIDOSThe Generalized Integral Transform Technique (GITT) is employed in the analytical solution of transient linear heat or mass diffusion problems in heterogeneous media. The GITT is utilized to handle the associated eigenvalue problem with arbitrarily space variable coefficients, defining an eigenfunction expansion in terms of a simpler Sturm-Liouville problem of known solution. In addition, the representation of the variable coefficients as eigenfunction expansions themselves has been proposed, considerably simplifying and accelerating the integral transformation process, while permitting the analytical evaluation of the coefficients matrices that form the transformed algebraic system. The proposed methodology is challenged in solving three different classes of diffusion problems in heterogeneous media, as illustrated for the cases of thermophysical properties with large scale variations found in heat transfer analysis of functionally graded materials (FGM), of abrupt variations in multiple layer transitions and of randomly variable physical properties in dispersed systems. The convergence behavior of the proposed expansions is then critically inspected and numerical results are presented to demonstrate the applicability of the general approach and to offer a set of reference results for potentials, eigenvalues, and related quantities.Indisponível.ElsevierBrasilNúcleo Interdisciplinar de Dinâmica dos Fluidos2019-07-09T18:49:43Z2023-12-21T03:06:10Z2009-06-24info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article0017-9310http://hdl.handle.net/11422/873910.1016/j.ijheatmasstransfer.2009.04.014engInternational Journal of Heat and Mass TransferNaveira-Cotta, Carolina PalmaCotta, Renato MachadoOrlande, Helcio Rangel BarretoFudym, Olivierinfo:eu-repo/semantics/openAccessreponame:Repositório Institucional da UFRJinstname:Universidade Federal do Rio de Janeiro (UFRJ)instacron:UFRJ2023-12-21T03:06:10Zoai:pantheon.ufrj.br:11422/8739Repositório InstitucionalPUBhttp://www.pantheon.ufrj.br/oai/requestpantheon@sibi.ufrj.bropendoar:2023-12-21T03:06:10Repositório Institucional da UFRJ - Universidade Federal do Rio de Janeiro (UFRJ)false
dc.title.none.fl_str_mv Eigenfunction expansions for transient diffusion in heterogeneous media
title Eigenfunction expansions for transient diffusion in heterogeneous media
spellingShingle Eigenfunction expansions for transient diffusion in heterogeneous media
Naveira-Cotta, Carolina Palma
Heterogeneous media
Diffusion
Variable physical properties
Heat conduction
Sturm-Liouville problems
Integral transforms
CNPQ::CIENCIAS EXATAS E DA TERRA::FISICA::AREAS CLASSICAS DE FENOMENOLOGIA E SUAS APLICACOES::DINAMICA DOS FLUIDOS
title_short Eigenfunction expansions for transient diffusion in heterogeneous media
title_full Eigenfunction expansions for transient diffusion in heterogeneous media
title_fullStr Eigenfunction expansions for transient diffusion in heterogeneous media
title_full_unstemmed Eigenfunction expansions for transient diffusion in heterogeneous media
title_sort Eigenfunction expansions for transient diffusion in heterogeneous media
author Naveira-Cotta, Carolina Palma
author_facet Naveira-Cotta, Carolina Palma
Cotta, Renato Machado
Orlande, Helcio Rangel Barreto
Fudym, Olivier
author_role author
author2 Cotta, Renato Machado
Orlande, Helcio Rangel Barreto
Fudym, Olivier
author2_role author
author
author
dc.contributor.author.fl_str_mv Naveira-Cotta, Carolina Palma
Cotta, Renato Machado
Orlande, Helcio Rangel Barreto
Fudym, Olivier
dc.subject.por.fl_str_mv Heterogeneous media
Diffusion
Variable physical properties
Heat conduction
Sturm-Liouville problems
Integral transforms
CNPQ::CIENCIAS EXATAS E DA TERRA::FISICA::AREAS CLASSICAS DE FENOMENOLOGIA E SUAS APLICACOES::DINAMICA DOS FLUIDOS
topic Heterogeneous media
Diffusion
Variable physical properties
Heat conduction
Sturm-Liouville problems
Integral transforms
CNPQ::CIENCIAS EXATAS E DA TERRA::FISICA::AREAS CLASSICAS DE FENOMENOLOGIA E SUAS APLICACOES::DINAMICA DOS FLUIDOS
description The Generalized Integral Transform Technique (GITT) is employed in the analytical solution of transient linear heat or mass diffusion problems in heterogeneous media. The GITT is utilized to handle the associated eigenvalue problem with arbitrarily space variable coefficients, defining an eigenfunction expansion in terms of a simpler Sturm-Liouville problem of known solution. In addition, the representation of the variable coefficients as eigenfunction expansions themselves has been proposed, considerably simplifying and accelerating the integral transformation process, while permitting the analytical evaluation of the coefficients matrices that form the transformed algebraic system. The proposed methodology is challenged in solving three different classes of diffusion problems in heterogeneous media, as illustrated for the cases of thermophysical properties with large scale variations found in heat transfer analysis of functionally graded materials (FGM), of abrupt variations in multiple layer transitions and of randomly variable physical properties in dispersed systems. The convergence behavior of the proposed expansions is then critically inspected and numerical results are presented to demonstrate the applicability of the general approach and to offer a set of reference results for potentials, eigenvalues, and related quantities.
publishDate 2009
dc.date.none.fl_str_mv 2009-06-24
2019-07-09T18:49:43Z
2023-12-21T03:06:10Z
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 0017-9310
http://hdl.handle.net/11422/8739
10.1016/j.ijheatmasstransfer.2009.04.014
identifier_str_mv 0017-9310
10.1016/j.ijheatmasstransfer.2009.04.014
url http://hdl.handle.net/11422/8739
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv International Journal of Heat and Mass Transfer
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Elsevier
Brasil
Núcleo Interdisciplinar de Dinâmica dos Fluidos
publisher.none.fl_str_mv Elsevier
Brasil
Núcleo Interdisciplinar de Dinâmica dos Fluidos
dc.source.none.fl_str_mv reponame:Repositório Institucional da UFRJ
instname:Universidade Federal do Rio de Janeiro (UFRJ)
instacron:UFRJ
instname_str Universidade Federal do Rio de Janeiro (UFRJ)
instacron_str UFRJ
institution UFRJ
reponame_str Repositório Institucional da UFRJ
collection Repositório Institucional da UFRJ
repository.name.fl_str_mv Repositório Institucional da UFRJ - Universidade Federal do Rio de Janeiro (UFRJ)
repository.mail.fl_str_mv pantheon@sibi.ufrj.br
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