Integral Transforms, Bayesian Inference, and Infrared Thermography in the Simultaneous Identification of Variable Thermal Conductivity and Diffusivity in Heterogeneous Media

Abstract

This work deals with the simultaneous estimation of spatially variable thermal conductivity and diffusivity for one-dimensional heat conduction in heterogeneous media. The direct problem solution is analytically obtained via integral transforms and the related eigenvalue problem is solved by the Generalized Integral Transform Technique (GITT). The inverse problem is handled by Bayesian inference through a Markov Chain Monte Carlo (MCMC) method. Instead of seeking the function estimation in the form of a sequence of local values for the thermal properties, an alternative approach is utilized here, which is based on the eigenfunction expansion of the thermal conductivity and diffusivity themselves. Then, the unknown parameters become the corresponding expansion coefficients. In addition, the inverse analysis is performed on the transformed temperature field, instead of employing the actual local temperature measurements, thus promoting a significant data reduction through the integral transformation of the experimental measurements. A demonstration experiment is built involving a partially heated thin bakelite plate. Temperature measurements obtained via infrared thermography are used in the inverse analysis.