Stefan problems for the diffusion-convection equation with temperature-dependent thermal coefficients

TL;DR

This paper investigates Stefan problems involving a moving phase change in a semi-infinite slab with temperature-dependent thermal properties, proving the existence of similarity solutions under various boundary conditions.

Contribution

It introduces a novel analysis of Stefan problems with temperature-dependent coefficients, establishing existence of solutions via fixed point methods and providing specific solutions for particular thermal coefficients.

Findings

Existence of at least one similarity solution under various boundary conditions.

Development of an equivalent ODE and integral equation system for the problem.

Solutions for specific thermal coefficient cases are provided.

Abstract

Different one-phase Stefan problems for a semi-infinite slab are considered, involving a moving phase change material as well as temperature dependent thermal coefficients. Existence of at least one similarity solution is proved imposing a Dirichlet, Neumann, Robin or radiative-convective boundary condition at the fixed face. The velocity that arises in the convective term of the diffusion-convection equation is assumed to depend on temperature and time. In each case, an equivalent ordinary differential problem is obtained giving rise to a system of an integral equation coupled with a condition for the parameter that characterizes the free boundary, which is solved though a double-fixed point analysis. Some solutions for particular thermal coefficients are provided.