INVERSE HEAT CONDUCTION PROBLEM OF SIMULTANEOUSLY ESTIMATING SPATIALLY VARYING THERMAL CONDUCTIVITY AND HEAT CAPACITY PER UNIT VOLUME

Abstract

An inverse heat conduction method for simultaneously estimating spatially varying thermal conductivity and heat capacity per unit volume under the conditions of a flash method type of experiment is developed. The unknown thermal properties are assumed to vary only in the space dimension normal to the slab sample and are modeled with piecewise linear representations. Lacking in the literature are specific requirements that must be satisfied by the number of measurements in the spatial domain in order to ensure uniqueness of the inverse solution. We prepared a series of numerical experiments to provide a better understanding of this issue. Multiple temperature sensors are shown to be necessary to determine spatially varying properties. The effectiveness of the method is illustrated through simulated experimental applications of the method.