Simultaneous estimation of temperature-dependent thermal conductivity and heat capacity based on modified genetic algorithm

Abstract

An inverse heat conduction analysis is presented to simultaneously estimate the temperature-dependent thermal conductivity and heat capacity based on a modified elitist genetic algorithm (MEGA). In this study, MEGA is used to minimize a least squares objective function containing estimated and simulated (filtered) temperatures. The estimated temperatures are obtained from the direct numerical solution (finite differences method, or FDM) of the finite one-dimensional conductive model by using an estimate for the unknown temperature-dependent thermophysical properties (TDTPs). The accuracy of the MEGA is assessed by comparing the estimated and the preselected TDTPs. The results of the MEGA are used as the starting point for a locally convergent optimization algorithm, i.e., the Levenberg-Marquardt (L-M) method. It is shown in this work that hybridization of the MEGA with the L-M method can lead to accurate estimates. From the results, it is found that the RMS error between estimated and simulated temperatures is very small irrespective of whether measurement errors are included or excluded. In addition to estimation of the TDTPs, sensitivity analysis is performed to investigate the effects of heating duration. Also, it is found that the results of the MEGA are highly satisfactory with only single-sensor measurements on the heated surface.