INVERSE ESTIMATION OF TEMPERATURE-DEPENDENT THERMAL CONDUCTIVITY AND HEAT CAPACITY PER UNIT VOLUME WITH THE DIRECT INTEGRATION APPROACH

Abstract

In this work an integration approach is proposed to simultaneously estimate temperature-dependent thermal conductivity and heat capacity per unit volume without internal measurements. The unknown thermal properties are assumed to vary linearly with respect to temperature. The integration approach to the inverse heat conduction problem requires the time-dependent temperature distribution, which is not given a priori. For a one-dimensional heat conduction medium with a heated and an insulated wall, this study approximates the spatial temperature distribution as a function of a third-order polynomial with unknown coefficients, which can be expressed in terms of boundary heat fluxes and measured wall temperatures. The integral heat conduction equations are solved to determine the unknown coefficients with the Levenberg-Marquardt method. Some numerical examples are introduced to show the performance of the proposed approach.