Prediction of Orthotropic Thermal Conductivities Using Bayesian-Inference from Experiments under Vacuum Conditions

Abstract

This work reports a novel “divide and conquer” approach to estimate the principal thermal conductivities of an orthotropic material, specifically engineered with a view to demonstrate the potency of the inverse heat transfer method with unsteady temperature data. The sample is placed in a vacuum chamber maintained at a pressure of 8.6 mbar. The heat capacity of the engineered orthotropic material was determined via estimating the heat capacity of a solid SS304 in a sequential fashion. First steady-state experiments followed by a Bayesian estimation with the Metropolis Hastings-Markov Chain Monte Carlo method were done to obtain the thermal conductivity of a solid SS304 block. Using this as a prior, the heat capacity of solid SS304 was obtained through unsteady experiments followed by Bayesian estimation. The heat capacity of SS304 thus obtained is multiplied by the solidity of the engineered orthotropic material, and using this information, the three components of the orthotropic conductivity are estimated again using the Bayesian route. To expedite the estimation, a surrogate for the forward model was developed using artificial neural network. Finally, the retrieved parameters are used to determine the simulated temperatures through the forward model for the orthotropic material. These, when compared with the measured temperatures, gave excellent agreement.