Eigenfunction expansions for transient diffusion in heterogeneous media
Autor(a) principal: | |
---|---|
Data de Publicação: | 2009 |
Outros Autores: | , , |
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. |
id |
UFRJ_ac4de051d5b107528ec1ce10985bc983 |
---|---|
oai_identifier_str |
oai:pantheon.ufrj.br:11422/8739 |
network_acronym_str |
UFRJ |
network_name_str |
Repositório Institucional da UFRJ |
repository_id_str |
|
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 |
_version_ |
1815455992213667840 |