Estimation of Time-Varying Thermal Contact Conductance in Thermally Thin Plates via MCMC Method
Autor(a) principal: | |
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Data de Publicação: | 2022 |
Outros Autores: | , , |
Tipo de documento: | Artigo |
Idioma: | por |
Título da fonte: | Vetor (Online) |
Texto Completo: | https://periodicos.furg.br/vetor/article/view/14304 |
Resumo: | This work deals with the solution of an inverse heat conduction problem to estimate a time-varying thermal contact conductance, in a one-dimensional problem in a composite medium with two thermally thin layers which is heated by a heat flux applied to the upper surface and exposed thermal convection on the bottom surface. The Classic Lumped method was applied to the direct problem mathematical formulation, considering thermally thin plates. This formulation reduces the original problem into two coupled ordinary differential equations, reducing the computational cost needed to solve the associated direct problem, which is solved with the NDSolve function, intrinsic to the Mathematica software. The inverse problem was solved with the Markov Chain Monte Carlo method within a Bayesian approach, applying the classic Metropolis-Hastings algorithm. The method was analyzed from simulated temperature measurements and proved to be capable of estimating a temporal function of the contact thermal conductance. This methodology allows taking into account the uncertainties associated with the parameters present in the models, as well as those associated with the estimation of thermal conductance varying with time, which is not observed in the methods aimed at temporal estimation of the contact thermal conductance currently found in the literature. |
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Estimation of Time-Varying Thermal Contact Conductance in Thermally Thin Plates via MCMC MethodEstimativa da Variação Temporal de Condutância Térmica de Contato em Placas Termicamente Finas via Método MCMCCondutância térmica de contatoMétodo de Monte Carlo via Cadeias de MarkovClassic LumpedCondutância térmica de contatoMétodo de Monte Carlo via Cadeias de MarkovClassic LumpedThermal contact conductanceMarkov Chain Monte Carlo MethodClassic LumpedClassic LumpedThermal contact conductanceMarkov Chain Monte Carlo MethodThis work deals with the solution of an inverse heat conduction problem to estimate a time-varying thermal contact conductance, in a one-dimensional problem in a composite medium with two thermally thin layers which is heated by a heat flux applied to the upper surface and exposed thermal convection on the bottom surface. The Classic Lumped method was applied to the direct problem mathematical formulation, considering thermally thin plates. This formulation reduces the original problem into two coupled ordinary differential equations, reducing the computational cost needed to solve the associated direct problem, which is solved with the NDSolve function, intrinsic to the Mathematica software. The inverse problem was solved with the Markov Chain Monte Carlo method within a Bayesian approach, applying the classic Metropolis-Hastings algorithm. The method was analyzed from simulated temperature measurements and proved to be capable of estimating a temporal function of the contact thermal conductance. This methodology allows taking into account the uncertainties associated with the parameters present in the models, as well as those associated with the estimation of thermal conductance varying with time, which is not observed in the methods aimed at temporal estimation of the contact thermal conductance currently found in the literature.Este trabalho trata da solução de um problema inverso de condução de calor visando estimar a variação temporal de condutância térmica de contato, num problema unidimensional em um material de duas camadas termicamente finas, aquecidas por meio de um fluxo de calor aplicado na superfície superior e exposto a convecção térmica na superfície inferior. Para a formulação do problema direto, considerando placas termicamente finas, foi utilizado o método Classic Lumped. Esta formulação reduz o problema original em duas equações diferenciais ordinárias acopladas, desta forma, possibilita diminuir o custo computacional necessário para solucionar o problema direto associado, que foi resolvido utilizando a função NDSolve, intrínseca do software Mathematica. Para a solução do problema inverso foi utilizado o método Monte Carlo via Cadeias de Markov, dentro de uma abordagem Bayesiana, aplicando o algoritmo de Metropolis-Hastings. O método foi analisado a partir de medidas simuladas de temperatura e se mostrou capaz para estimar uma função temporal da condutância térmica de contato. Esta metodologia permite levar em conta as incertezas associadas aos parâmetros presentes nos modelos, bem como, àquelas associadas com a estimativa da condutância térmica variando com o tempo, o que não é observado nos métodos voltados para estimativa temporal da condutância térmica de contato encontrados atualmente na literatura.Universidade Federal do Rio Grande2022-12-28info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://periodicos.furg.br/vetor/article/view/1430410.14295/vetor.v32i2.14304VETOR - Journal of Exact Sciences and Engineering; Vol. 32 No. 2 (2022); 21-36VETOR - Revista de Ciências Exatas e Engenharias; v. 32 n. 2 (2022); 21-362358-34520102-7352reponame:Vetor (Online)instname:Universidade Federal do Rio Grande (FURG)instacron:FURGporhttps://periodicos.furg.br/vetor/article/view/14304/10002Copyright (c) 2022 VETOR - Revista de Ciências Exatas e Engenhariasinfo:eu-repo/semantics/openAccessWatanabe, KenjiAbreu, Luiz A. S.Knupp, Diego C.Watanabe, Eiji2022-12-28T14:09:24Zoai:periodicos.furg.br:article/14304Revistahttps://periodicos.furg.br/vetorPUBhttps://periodicos.furg.br/vetor/oaigmplatt@furg.br2358-34520102-7352opendoar:2022-12-28T14:09:24Vetor (Online) - Universidade Federal do Rio Grande (FURG)false |
dc.title.none.fl_str_mv |
Estimation of Time-Varying Thermal Contact Conductance in Thermally Thin Plates via MCMC Method Estimativa da Variação Temporal de Condutância Térmica de Contato em Placas Termicamente Finas via Método MCMC |
title |
Estimation of Time-Varying Thermal Contact Conductance in Thermally Thin Plates via MCMC Method |
spellingShingle |
Estimation of Time-Varying Thermal Contact Conductance in Thermally Thin Plates via MCMC Method Watanabe, Kenji Condutância térmica de contato Método de Monte Carlo via Cadeias de Markov Classic Lumped Condutância térmica de contato Método de Monte Carlo via Cadeias de Markov Classic Lumped Thermal contact conductance Markov Chain Monte Carlo Method Classic Lumped Classic Lumped Thermal contact conductance Markov Chain Monte Carlo Method |
title_short |
Estimation of Time-Varying Thermal Contact Conductance in Thermally Thin Plates via MCMC Method |
title_full |
Estimation of Time-Varying Thermal Contact Conductance in Thermally Thin Plates via MCMC Method |
title_fullStr |
Estimation of Time-Varying Thermal Contact Conductance in Thermally Thin Plates via MCMC Method |
title_full_unstemmed |
Estimation of Time-Varying Thermal Contact Conductance in Thermally Thin Plates via MCMC Method |
title_sort |
Estimation of Time-Varying Thermal Contact Conductance in Thermally Thin Plates via MCMC Method |
author |
Watanabe, Kenji |
author_facet |
Watanabe, Kenji Abreu, Luiz A. S. Knupp, Diego C. Watanabe, Eiji |
author_role |
author |
author2 |
Abreu, Luiz A. S. Knupp, Diego C. Watanabe, Eiji |
author2_role |
author author author |
dc.contributor.author.fl_str_mv |
Watanabe, Kenji Abreu, Luiz A. S. Knupp, Diego C. Watanabe, Eiji |
dc.subject.por.fl_str_mv |
Condutância térmica de contato Método de Monte Carlo via Cadeias de Markov Classic Lumped Condutância térmica de contato Método de Monte Carlo via Cadeias de Markov Classic Lumped Thermal contact conductance Markov Chain Monte Carlo Method Classic Lumped Classic Lumped Thermal contact conductance Markov Chain Monte Carlo Method |
topic |
Condutância térmica de contato Método de Monte Carlo via Cadeias de Markov Classic Lumped Condutância térmica de contato Método de Monte Carlo via Cadeias de Markov Classic Lumped Thermal contact conductance Markov Chain Monte Carlo Method Classic Lumped Classic Lumped Thermal contact conductance Markov Chain Monte Carlo Method |
description |
This work deals with the solution of an inverse heat conduction problem to estimate a time-varying thermal contact conductance, in a one-dimensional problem in a composite medium with two thermally thin layers which is heated by a heat flux applied to the upper surface and exposed thermal convection on the bottom surface. The Classic Lumped method was applied to the direct problem mathematical formulation, considering thermally thin plates. This formulation reduces the original problem into two coupled ordinary differential equations, reducing the computational cost needed to solve the associated direct problem, which is solved with the NDSolve function, intrinsic to the Mathematica software. The inverse problem was solved with the Markov Chain Monte Carlo method within a Bayesian approach, applying the classic Metropolis-Hastings algorithm. The method was analyzed from simulated temperature measurements and proved to be capable of estimating a temporal function of the contact thermal conductance. This methodology allows taking into account the uncertainties associated with the parameters present in the models, as well as those associated with the estimation of thermal conductance varying with time, which is not observed in the methods aimed at temporal estimation of the contact thermal conductance currently found in the literature. |
publishDate |
2022 |
dc.date.none.fl_str_mv |
2022-12-28 |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
https://periodicos.furg.br/vetor/article/view/14304 10.14295/vetor.v32i2.14304 |
url |
https://periodicos.furg.br/vetor/article/view/14304 |
identifier_str_mv |
10.14295/vetor.v32i2.14304 |
dc.language.iso.fl_str_mv |
por |
language |
por |
dc.relation.none.fl_str_mv |
https://periodicos.furg.br/vetor/article/view/14304/10002 |
dc.rights.driver.fl_str_mv |
Copyright (c) 2022 VETOR - Revista de Ciências Exatas e Engenharias info:eu-repo/semantics/openAccess |
rights_invalid_str_mv |
Copyright (c) 2022 VETOR - Revista de Ciências Exatas e Engenharias |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
Universidade Federal do Rio Grande |
publisher.none.fl_str_mv |
Universidade Federal do Rio Grande |
dc.source.none.fl_str_mv |
VETOR - Journal of Exact Sciences and Engineering; Vol. 32 No. 2 (2022); 21-36 VETOR - Revista de Ciências Exatas e Engenharias; v. 32 n. 2 (2022); 21-36 2358-3452 0102-7352 reponame:Vetor (Online) instname:Universidade Federal do Rio Grande (FURG) instacron:FURG |
instname_str |
Universidade Federal do Rio Grande (FURG) |
instacron_str |
FURG |
institution |
FURG |
reponame_str |
Vetor (Online) |
collection |
Vetor (Online) |
repository.name.fl_str_mv |
Vetor (Online) - Universidade Federal do Rio Grande (FURG) |
repository.mail.fl_str_mv |
gmplatt@furg.br |
_version_ |
1797041760351813632 |