Estimation of thermo-physical and transport properties with Bayesian inference using transient liquid crystal thermography experiments

Abstract

An inverse methodology is proposed to estimate thermo-physical and transport properties individually and simultaneously from in-house experimental data obtained using the transient Liquid Crystal Thermography (LCT) technique. A vertical rectangular fin made of mild steel and size of 75 × 250 × 3 (L × W × t) (all in mm) has been used. Thermochromic Liquid Crystals (TLCs) are used to obtain transient temperature distribution along the fin surface to determine the temperature dependent heat transfer coefficient, hθ and the thermal diffusivity, α of the fin. The variation of heat transfer coefficient is considered as a power law function of temperature excess (hθ = a''θb(x,t)) and is derived from the basic Nusselt number equation, Nuθ = aRabθ used for laminar natural convection for a vertical plate in ambient air. Using this functional form, the 1–D transient fin equation solved using the finite difference technique for assumed values of 'a' and 'α'. Treating the inverse problem as a one parameter estimation in 'a' or 'α' or a two parameter estimation problem in 'a' and 'α', the sum of the squares of the difference between the TLC measured and simulated temperatures are minimized with the Bayesian frame work in the inverse model to determine the point estimates for 'a' and 'α'. Two point estimates namely the (i) mean and (ii) maximum a posterior (MAP) are used to report the retrieved quantities together with the associated standard deviation.