María F. Natale | Searcharxiv

arXiv2022

Explicit solution for non-classical one-phase Stefan problem with variable thermal coefficients and two different heat source terms

A one-phase Stefan problem for a semi-infinite material is investigated for special functional forms of the thermal conductivity and specific heat depending on the temperature of the phase-change material. Using the similarity transformation technique, an explicit solution for these situations are showed. The mathematical analysis is made for two different kinds of heat source terms, and the existence and uniqueness of the solutions are proved.

math.AP↗

arXiv2019

Approximate solutions to the one-phase Stefan problem with non-linear temperature-dependent thermal conductivity

In this chapter we consider different approximations for the one-dimensional one-phase Stefan problem corresponding to the fusion process of a semi-infinite material with a temperature boundary condition at the fixed face and non-linear temperature-dependent thermal conductivity. The knowledge of the exact solution of this problem, allows to compare it directly with the approximate solutions obtained by applying the heat balance integral method, an alternative form to it and the refined balance integral method, assuming a quadratic temperature profile in space. In all cases, the analysis is carried out in a dimensionless way by the Stefan number (Ste) parameter.

cond-mat.stat-mech↗