www.mdpi.com/journal/mathematics Article One-Dimensional Nonlinear Stefan Problems in Storm’s Materials

Abstract: We consider two one-phase nonlinear one-dimensional Stefan problems for a semi-infinite material x> 0, with phase change temperature Tf. We assume that the heat capacity and the thermal conductivity satisfy a Storm’s condition. In the first case, we assume a heat flux boundary condition of the type q(t) = q0√ t, and in the second case, we assume a temperature boundary condition T = Ts < Tf at the fixed face. Solutions of similarity type are obtained in both cases, and the equivalence of the two problems is demonstrated. We also give procedures in order to compute the explicit solution