ESTIMATION OF TEMPERATURE-DEPENDENT THERMAL CONDUCTIVITY AND HEAT CAPACITY PER UNIT VOLUME WITH A SIMPLE INTEGRAL APPROACH

Abstract

We present an integral approach to estimate temperature-dependent thermal conductivity and heat capacity per unit volume simultaneously in a transient non-linear heat conduction medium. It is assumed that the thermal property is a monotonic function of the temperature and it can be expressed as a piecewise linear function. Hence, the present inverse heat conduction problem is converted to a parameter identification problem determining the unknown coefficients of the model functions of the thermal conductivity and heat capacity per unit volume. The spatial temperature distribution required for the integral approach is modeled as a third-order function of position in a one-dimensional heat conduction domain with heated and insulated walls. Four coefficients of the approximated temperature distribution are determined from the heat fluxes imposed and the temperatures measured at both ends at each measurement. Hence, the proposed algorithm does not require any internal measurements