Estimation of Spatially Dependent Coefficients in Heterogeneous Media in Diffusive Heat Transfer Problems

Lucas Lopes da Silva Costa; Eduardo Cunha Classe; Lucas da Silva Asth; Luiz Alberto da Silva Abreu; Diego Campos Knupp; Leonardo Tavares Stutz

Lucas Lopes da Silva Costa Polytechnic Institute of Rio de Janeiro https://orcid.org/0000-0003-1940-0875
Eduardo Cunha Classe Polytechnic Institute of Rio de Janeiro https://orcid.org/0000-0002-2405-3946
Lucas da Silva Asth Polytechnic Institute of Rio de Janeiro https://orcid.org/0000-0002-6189-1068
Luiz Alberto da Silva Abreu Polytechnic Institute of Rio de Janeiro https://orcid.org/0000-0002-7634-7014
Diego Campos Knupp Polytechnic Institute of Rio de Janeiro https://orcid.org/0000-0001-9534-5623
Leonardo Tavares Stutz Polytechnic Institute of Rio de Janeiro https://orcid.org/0000-0003-3005-765X

Keywords: Inverse Problem, Transition Markov Chain Monte Carlo (TMCMC), Heterogeneous Media, Estimation of Variable Coefficients, Heat Conduction

Abstract

This article addresses the solution to the inverse problem in a one-dimensional transient partial differential equation with a source term, commonly encountered in heat transfer modeling for diffusion problems. The equation is utilized in a dimensionless form to derive a more general solution that is applicable across various contexts. The Transition Markov Chain Monte Carlo (TMCMC) method is utilized to estimate spatially variable thermophysical properties within the equation. This approach involves transitioning between probability densities, gradually refining the prior distribution to approximate the posterior distribution. The results indicate the effectiveness of the TMCMC method in addressing this inverse problem, offering a robust methodology for estimating spatially variable coefficients.

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