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

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.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