Bayesian estimation of heat flux and thermal diffusivity using liquid crystal thermography

This paper presents a methodology for the estimation of heat flux ( q s ) strength and thermal diffusivity ( α ) of a Teflon block by using liquid crystal thermography (LCT) experiments and Bayesian inference. Steady and transient state, laminar natural convection experiments have been conducted at various heat fluxes on a Teflon block of size 60 × 60 × 60, ( L × W × H , all in mm). At the center of the Teflon block, a 10 mm diameter heater combined with a hollow hemispherical (ID = 10 mm and OD = 20 mm) aluminum ball is placed where heat generation takes place. The temperature distribution at the front face of the Teflon block has been captured for transient heating, steady and transient cooling experiments, using calibrated R40C5W thermochromic liquid crystals (TLCs). Similarly, the simulated temperature distribution during transient heating, steady and transient cooling cases, has been determined by solving the three dimensional conduction model of the Teflon block using FLUENT to arrive at the average heat transfer coefficient, h avg on all faces by match up with limited experiments with various heat fluxes at the center face of Teflon are boundary conditions. With the matched up h avg , further simulations are carried out and the input ( q s and α ) and target (temperature) data sets from the numerical solution are trained using an artificial neural network (ANN) and this is used as a forward model for estimating parameters q s and α . For guess sample of parameter(s), the simulated and experimental temperatures are compared using a Bayesian frame work. The Metropolis-Hasting algorithm has been used to sample the parameter space. Two point estimates namely mean and the maximum a posterior (MAP) along with the associated standard deviation (SD) are determined. At steady state, q s and during transient cooling, α has been estimated sequentially. During transient heating, q s and α have been estimated simultaneously and the mean of the estimates obtained previously from sequential estimation are incorporated into the estimation process as priors for the simultaneous estimation. The effect of the priors has been quantified.