A sensitivity analysis for the determination of unknown thermal coefficients through a phase-change process with temperature-dependent thermal conductivity

In Tarzia, Int. Comm. in Heat and Mass Transfer, 25 (1998), 139–147, explicit formulas for the simultaneous determination of unknown thermal coefficients of a semi-infinite material through a phase-change process with temperature-dependent thermal conductivity were obtained. Moreover, ten different cases were studied: four cases of free boundary problems (i.e. Stefan-like problems) and six cases of moving boundary problems (i.e. inverse Stefan-like problems). The goal of this paper is to obtain a numerical sensitivity analysis of the mentioned ten cases for the simultaneous determination of unknown thermal coefficients and to determine the coefficients which are more sensitive with respect to the given parameters. We show numerical result for the aluminum.