Holow 1-D cylinders with heat generation: a sufficiently general approach to solving problems with a time variable Dirichlet condition
Autor(a) principal: | |
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Data de Publicação: | 2021 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | por eng |
Título da fonte: | Remat (Bento Gonçalves) |
Texto Completo: | https://periodicos.ifrs.edu.br/index.php/REMAT/article/view/4638 |
Resumo: | In this work, a sufficiently approximated general solution to transient heat conduction problems in 1-D cylindrical geometry, with heat generation and time variable Dirichlet conditions, was presented using the Green’s function method. An important integral involving Bessel functions, that is part of the solution, has been solved in detail here. The results obtained from the use of this solution, when applied in some particular cases of practical interest, were aligned with the solutions reported by the literature. We have adopted, in this sense, a methodology that consists of addressing a non-homogeneous problem solution with non-homogeneous boundary conditions in a non-homogeneous problem solution with homogeneous border conditions and two more stationary solutions related to the given Dirichlet conditions. As a result, the solution obtained has no problems of convergence at the boundaries of the cylindrical region with the temperature prescribed conditions. |
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Holow 1-D cylinders with heat generation: a sufficiently general approach to solving problems with a time variable Dirichlet conditionCilindros ocos 1-D com geração de calor: uma aproximação suficientemente geral de solução para problemas com condição de Dirichlet variável no tempoHollow CylinderBessel FunctionsGreen’s Function MethodApproximated General SolutionCilindro OcoFunções de BesselMétodo de Funções de GreenSolução Geral AproximadaIn this work, a sufficiently approximated general solution to transient heat conduction problems in 1-D cylindrical geometry, with heat generation and time variable Dirichlet conditions, was presented using the Green’s function method. An important integral involving Bessel functions, that is part of the solution, has been solved in detail here. The results obtained from the use of this solution, when applied in some particular cases of practical interest, were aligned with the solutions reported by the literature. We have adopted, in this sense, a methodology that consists of addressing a non-homogeneous problem solution with non-homogeneous boundary conditions in a non-homogeneous problem solution with homogeneous border conditions and two more stationary solutions related to the given Dirichlet conditions. As a result, the solution obtained has no problems of convergence at the boundaries of the cylindrical region with the temperature prescribed conditions.Neste trabalho, uma solução aproximada suficientemente geral para problemas de condução de calor transiente em geometria cilíndrica 1-D, com geração de calor e condições de Dirichlet variável no tempo foi apresentada usando o método de funções de Green. Uma importante integral envolvendo funções de Bessel, que faz parte da solução, foi aqui resolvida com detalhes. Os resultados obtidos com o uso dessa solução, quando aplicada em alguns casos particulares de interesse prático, ficaram em boa concordância com as soluções reportadas na literatura. Foi adotada uma metodologia que consiste em fatiar a solução do problema não homogêneo com condições de fronteira não homogêneas em uma solução do problema não homogêneo com condições de fronteira homogêneas mais duas soluções estacionárias relacionadas com as condições de Dirichlet dadas. Com isso, a solução obtida não tem problemas de convergência nas fronteiras da região cilíndrica com as condições prescritas de temperaturas.Instituto Federal de Educação, Ciência e Tecnologia do Rio Grande do Sul2021-06-30info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArtigo avaliado pelos paresapplication/pdfapplication/pdfhttps://periodicos.ifrs.edu.br/index.php/REMAT/article/view/463810.35819/remat2021v7i1id4638REMAT: Revista Eletrônica da Matemática; Vol. 7 No. 1 (2021); e3015REMAT: Revista Eletrônica da Matemática; Vol. 7 Núm. 1 (2021); e3015REMAT: Revista Eletrônica da Matemática; v. 7 n. 1 (2021); e30152447-2689reponame:Remat (Bento Gonçalves)instname:Instituto Federal de Educação, Ciência e Tecnologia do Rio Grande do Sul (IFRS)instacron:IFRSporenghttps://periodicos.ifrs.edu.br/index.php/REMAT/article/view/4638/2931https://periodicos.ifrs.edu.br/index.php/REMAT/article/view/4638/2985Copyright (c) 2021 REMAT: Revista Eletrônica da Matemáticahttps://creativecommons.org/licenses/by/4.0info:eu-repo/semantics/openAccessAraújo, Jorge Corrêa deMárquez, Rosa María García2022-12-28T16:06:35Zoai:ojs2.periodicos.ifrs.edu.br:article/4638Revistahttp://periodicos.ifrs.edu.br/index.php/REMATPUBhttps://periodicos.ifrs.edu.br/index.php/REMAT/oai||greice.andreis@caxias.ifrs.edu.br2447-26892447-2689opendoar:2022-12-28T16:06:35Remat (Bento Gonçalves) - Instituto Federal de Educação, Ciência e Tecnologia do Rio Grande do Sul (IFRS)false |
dc.title.none.fl_str_mv |
Holow 1-D cylinders with heat generation: a sufficiently general approach to solving problems with a time variable Dirichlet condition Cilindros ocos 1-D com geração de calor: uma aproximação suficientemente geral de solução para problemas com condição de Dirichlet variável no tempo |
title |
Holow 1-D cylinders with heat generation: a sufficiently general approach to solving problems with a time variable Dirichlet condition |
spellingShingle |
Holow 1-D cylinders with heat generation: a sufficiently general approach to solving problems with a time variable Dirichlet condition Araújo, Jorge Corrêa de Hollow Cylinder Bessel Functions Green’s Function Method Approximated General Solution Cilindro Oco Funções de Bessel Método de Funções de Green Solução Geral Aproximada |
title_short |
Holow 1-D cylinders with heat generation: a sufficiently general approach to solving problems with a time variable Dirichlet condition |
title_full |
Holow 1-D cylinders with heat generation: a sufficiently general approach to solving problems with a time variable Dirichlet condition |
title_fullStr |
Holow 1-D cylinders with heat generation: a sufficiently general approach to solving problems with a time variable Dirichlet condition |
title_full_unstemmed |
Holow 1-D cylinders with heat generation: a sufficiently general approach to solving problems with a time variable Dirichlet condition |
title_sort |
Holow 1-D cylinders with heat generation: a sufficiently general approach to solving problems with a time variable Dirichlet condition |
author |
Araújo, Jorge Corrêa de |
author_facet |
Araújo, Jorge Corrêa de Márquez, Rosa María García |
author_role |
author |
author2 |
Márquez, Rosa María García |
author2_role |
author |
dc.contributor.author.fl_str_mv |
Araújo, Jorge Corrêa de Márquez, Rosa María García |
dc.subject.por.fl_str_mv |
Hollow Cylinder Bessel Functions Green’s Function Method Approximated General Solution Cilindro Oco Funções de Bessel Método de Funções de Green Solução Geral Aproximada |
topic |
Hollow Cylinder Bessel Functions Green’s Function Method Approximated General Solution Cilindro Oco Funções de Bessel Método de Funções de Green Solução Geral Aproximada |
description |
In this work, a sufficiently approximated general solution to transient heat conduction problems in 1-D cylindrical geometry, with heat generation and time variable Dirichlet conditions, was presented using the Green’s function method. An important integral involving Bessel functions, that is part of the solution, has been solved in detail here. The results obtained from the use of this solution, when applied in some particular cases of practical interest, were aligned with the solutions reported by the literature. We have adopted, in this sense, a methodology that consists of addressing a non-homogeneous problem solution with non-homogeneous boundary conditions in a non-homogeneous problem solution with homogeneous border conditions and two more stationary solutions related to the given Dirichlet conditions. As a result, the solution obtained has no problems of convergence at the boundaries of the cylindrical region with the temperature prescribed conditions. |
publishDate |
2021 |
dc.date.none.fl_str_mv |
2021-06-30 |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Artigo avaliado pelos pares |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
https://periodicos.ifrs.edu.br/index.php/REMAT/article/view/4638 10.35819/remat2021v7i1id4638 |
url |
https://periodicos.ifrs.edu.br/index.php/REMAT/article/view/4638 |
identifier_str_mv |
10.35819/remat2021v7i1id4638 |
dc.language.iso.fl_str_mv |
por eng |
language |
por eng |
dc.relation.none.fl_str_mv |
https://periodicos.ifrs.edu.br/index.php/REMAT/article/view/4638/2931 https://periodicos.ifrs.edu.br/index.php/REMAT/article/view/4638/2985 |
dc.rights.driver.fl_str_mv |
Copyright (c) 2021 REMAT: Revista Eletrônica da Matemática https://creativecommons.org/licenses/by/4.0 info:eu-repo/semantics/openAccess |
rights_invalid_str_mv |
Copyright (c) 2021 REMAT: Revista Eletrônica da Matemática https://creativecommons.org/licenses/by/4.0 |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf application/pdf |
dc.publisher.none.fl_str_mv |
Instituto Federal de Educação, Ciência e Tecnologia do Rio Grande do Sul |
publisher.none.fl_str_mv |
Instituto Federal de Educação, Ciência e Tecnologia do Rio Grande do Sul |
dc.source.none.fl_str_mv |
REMAT: Revista Eletrônica da Matemática; Vol. 7 No. 1 (2021); e3015 REMAT: Revista Eletrônica da Matemática; Vol. 7 Núm. 1 (2021); e3015 REMAT: Revista Eletrônica da Matemática; v. 7 n. 1 (2021); e3015 2447-2689 reponame:Remat (Bento Gonçalves) instname:Instituto Federal de Educação, Ciência e Tecnologia do Rio Grande do Sul (IFRS) instacron:IFRS |
instname_str |
Instituto Federal de Educação, Ciência e Tecnologia do Rio Grande do Sul (IFRS) |
instacron_str |
IFRS |
institution |
IFRS |
reponame_str |
Remat (Bento Gonçalves) |
collection |
Remat (Bento Gonçalves) |
repository.name.fl_str_mv |
Remat (Bento Gonçalves) - Instituto Federal de Educação, Ciência e Tecnologia do Rio Grande do Sul (IFRS) |
repository.mail.fl_str_mv |
||greice.andreis@caxias.ifrs.edu.br |
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1798329706047602688 |