Determination of one thermal coefficient through an overspecified Stefan problem with temperature-dependent thermal conductivity, considering flux and convective boundary conditions

Formulae are obtained for the determination of one unknown thermal coefficient of a semi-infinite material with temperature-dependent thermal conductivity through a phase-change process with an overspecified condition on the fixed face (flux and convective boundary conditions) through a free boundary problem (Ste-fan problem with 5 cases). A new error function is introduced as part of the similarity-type solution, which depends on a parameter related to thermal conductivity. For the special case in which the parameter assumes values close to zero (positive or negative), we show that the new error function presents some characteristic features of the classical error function, such as monotony, concavity, and boundedness. We also study the sensitivity of the solution depending on different thermal parameters applied to aluminum and uranium.