Estimation of temperature dependent heat transfer coefficient in a vertical rectangular fin using liquid crystal thermography

Abstract

This paper presents a methodology for the estimation of temperature dependent heat transfer coefficient for a vertical rectangular fin by using the inverse heat transfer method with Liquid crystal thermography (LCT) data. Steady state, laminar natural convection experiments have been done on a vertical rectangular fin of size 150×250×4, (L×w×t, all dimensions are in mm). The variation of heat transfer coefficient is considered as a power law function of temperature excess (h=aoθb) and is derived from the basic Nusselt number equation used for laminar natural convection, Nu=aRab. With this functional form, the one dimensional fin equation in finite difference form is repeatedly solved using the Gauss–Seidel iterative method. Treating this as a one parameter estimation in ‘a’ the sum of the squares of the difference between the simulated and Thermochromic Liquid Crystal (TLC) measured temperatures is minimized with the Golden section search algorithm to retrieve ‘a’. Estimate of ‘a’ and the accompanying uncertainties are first reported for synthetically generated temperature distribution for assumed values of ‘a’. The effect of noise on the estimate of ‘a’ is discussed. This is followed by retrievals with experimentally obtained TLC temperature distribution for a range of heat inputs to the fin base. The required temperature distributions for accomplishing the retrievals over the surface are obtained using calibrated R40C5W Thermochromic Liquid Crystal (TLC) sheets. As an additional proof of the accuracy of the method, the retrieved value of ‘a’ is used to simulate the temperature distribution in the fin which is then compared with the actual TLC measured temperature distribution.