Estimation of local heat transfer coefficient from natural convection experiments using liquid crystal thermography and Bayesian method

Abstract

In this work, an inverse methodology is developed for estimating the local heat transfer coefficients on a vertical plate embedded with the three discrete heat sources, under steady state natural convection, with the temperatures measured at the adiabatic surface without disturbing the fluid flow, using simple conduction/surrogate model and Bayesian inference. Liquid crystal thermography (LCT), an optical measurement method based on the colour-temperature relationship of thermochromic liquid crystal sheet (TLC) is used to determine the temperature field of the adiabatic surface. Bayesian framework with Metropolis Hastings-Markov chain Monte Carlo (MH-MCMC) sampling method is considered for exploring the posterior distribution to estimate the parameters in terms of point estimates like mean, Maximum a posteriori (MAP) and standard deviation. A parity plot between simulated (using retrieved parameters) and measured TLC temperatures shows good agreement.