Simultaneous estimation of thermal properties via measurements using one active heating surface and Bayesian inference

Abstract This paper proposes an experimental method to simultaneously measure, the thermal conductivity and thermal diffusivity of solid conductive and non-conductive materials, such as carbon steel alloy (AISI 1045), tungsten carbide, and polyvinyl chloride. The samples were partially heated on one active surface, and the temperature was measured at different points on the surface to estimate the thermal properties. The method was further applied to two different thermal models using the same experimental dataset. The first model used the gain ratio between two acquired surface temperatures to determine the thermal diffusivity. The inverse problem was then solved using Bayesian inference. The second model applied the Bayesian inference on the theoretical and experimental values of the properties to obtain the maximum likelihood of the square error function of temperature for estimating the thermal conductivity. Thus, the thermal conductivity of both conductive and non-conductive materials was determined. The experimental apparatus setup exposed the samples to a vacuum medium to obtain optimal results.