Estimativa da Variação Temporal de Condutância Térmica de Contato em Placas Termicamente Finas via Método MCMC

Kenji Watanabe; Luiz A. S. Abreu; Diego C. Knupp; Eiji Watanabe

doi:10.14295/vetor.v32i2.14304

Authors

Kenji Watanabe Universidade do Estado do Rio de Janeiro
Luiz A. S. Abreu Universidade do Estado do Rio de Janeiro https://orcid.org/0000-0002-7634-7014
Diego C. Knupp Universidade do Estado do Rio de Janeiro https://orcid.org/0000-0001-9534-5623
Eiji Watanabe Universidade do Estado do Rio de Janeiro

DOI:

https://doi.org/10.14295/vetor.v32i2.14304

Keywords:

Thermal contact conductance, Markov Chain Monte Carlo Method, Classic Lumped

Abstract

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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