Theoretical–experimental analysis of heat transfer in nonhomogeneous solids via improved lumped formulation, integral transforms and infrared thermography

Abstract

Theoretical and experimental methodologies for the identification of spatially variable thermophysical properties and for simulating multidimensional heat transfer in heterogeneous materials are illustrated by using plate samples with aluminum oxide nanoparticles dispersed in a polymeric matrix. First, the heterogeneous nanocomposite plate is thermally characterized by means of a fairly simple experimental setup which can be modeled by a one-dimensional heat conduction formulation with space variable properties. Non-intrusive temperature measurements are obtained via infrared thermography, while the direct problem is handled by an error-controlled integral transform solution with an improved lumped-differential formulation, and the inverse analysis is undertaken via Bayesian inference, making use of the Markov Chain Monte Carlo method. Then, in order to illustrate the application of the methodologies here presented, an experimental multidimensional demonstration is provided consisting of a small electrical resistance attached to the plate, simulating a heat generating electronic device installed on the nanocomposite substrate, which in such situation works as a heat spreader modeled by an improved lumped-differential two-dimensional heat conduction formulation. The integral transform solution of the lumped-differential two-dimensional problem is then critically compared against the infrared thermography experimental results.