A novel method to detect hot spots and estimate strengths of discrete heat sources using liquid crystal thermography

This paper reports the results of an investigation to solve the inverse problem of estimating the strengths of different strip heat sources embedded in a flat plate under laminar steady-state forced convection and by way of this propose a novel method to detect hot spots from remote measurements. A Bayesian framework is adopted to infer the strength of the heat sources from thermochromic liquid crystal (TLC) temperature measurements. This framework consists of the forward model, the measured data, and the inverse model. The forward model simulates the conjugate three-dimensional heat transfer problem with the specified thermophysical properties, and the boundary conditions. The input data for the forward model is a combination of different heat source strengths, and the output is temperature data obtained at the bottom surface of the cork. The input-output data of the numerical simulations are used to build a proxy or surrogate (artificial neural network, ANN) that acts as a replacement for the actual forward model to increase the computational speed and decrease the computational time while solving the inverse problem. Calibrated thermochromic liquid crystal sheets are attached at the bottom surface of the cork for mapping the temperature data, so that the top surface where the convection takes place is undisturbed. In the inverse model, Bayesian statistics, along with the Gibbs sampling algorithm is adopted for analyzing the posterior distribution to estimate the mean, the maximum a posteriori and the standard deviation of the heat source strengths. Validation and robustness of the inverse methodology have been examined. The estimated heat source values are input to the forward model to determine the hot spot temperatures on the flat plate. This is a key spin-off from the present study, wherein based on temperature measurements at a convenient place, the hot spot in a geometry can be remotely 'estimated.' A comparison of the simulated and the measured values of the hot spot temperatures is reported for different flow Reynolds numbers.