A methodology to determine boundary conditions from forced convection experiments using liquid crystal thermography

Abstract

This paper reports the results of an experimental study to estimate the heat flux and convective heat transfer coefficient using liquid crystal thermography and Bayesian inference in a heat generating sphere, enclosed in a cubical Teflon block. The geometry considered for the experiments comprises a heater inserted in a hollow hemispherical aluminium ball, resulting in a volumetric heat generation source that is placed at the center of the Teflon block. Calibrated thermochromic liquid crystal sheets are used to capture the temperature distribution at the front face of the Teflon block. The forward model is the three dimensional conduction equation which is solved within the Teflon block to obtain steady state temperatures, using COMSOL. Match up experiments are carried out for various velocities by minimizing the residual between TLC and simulated temperatures for every assumed loss coefficient, to obtain a correlation of average Nusselt number against Reynolds number. This is used for prescribing the boundary condition for the solution to the forward model. A surrogate model obtained by artificial neural network built upon the data from COMSOL simulations is used to drive a Markov Chain Monte Carlo based Metropolis Hastings algorithm to generate the samples. Bayesian inference is adopted to solve the inverse problem for determination of heat flux and heat transfer coefficient from the measured temperature field. Point estimates of the posterior like the mean, maximum a posteriori and standard deviation of the retrieved heat flux and convective heat transfer coefficient are reported. Additionally the effect of number of samples on the performance of the estimation process has been investigated.