Experimental Identification of Thermophysical Properties in Heterogeneous Materials with Integral Transformation of Temperature Measurements from Infrared Thermography

Abstract

This work deals with the experimental estimation of spatially variable thermal conductivity and diffusivity in heterogeneous media, with temperature measurements obtained via infrared thermography being used in the inverse analysis. The direct problem solution for a one-dimensional heat conduction experiment is analytically obtained via integral transforms, and the related eigenvalue problem is solved by the generalized integral transform technique. The inverse problem is handled by Bayesian inference through a Markov chain Monte Carlo algorithm. The functional representation and estimation is based on the eigenfunction expansion of the thermal conductivity and diffusivity themselves, and the unknown parameters become the corresponding expansion coefficients. The inverse analysis is performed on the transformed experimental 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 partially heated thin plates made of bakelite and polystyrene, including a variable thickness plate to simulate spatially variable thermophysical properties.

keywords:

• heterogeneous media
• inverse problem
• Bayesian inference
• Markov chain Monte Carlo method
• integral transforms
• infrared thermography

Notes

^a N = Gaussian distribution; U = non informative uniform distribution.

^a Bakelite plates experiment.

^b Polystyrene plates with increasing thickness experiment.

^c Polystyrene plates with decreasing thickness experiment.

^a Bakelite plates experiment.

^b Polystyrene plates with increasing thickness experiment.

^c Polystyrene plates with decreasing thickness experiment.