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

TL;DR

This paper derives explicit solutions for a one-phase Stefan problem with temperature-dependent thermal properties and two heat sources, proving existence and uniqueness of solutions using similarity transformations.

Contribution

It introduces a novel explicit solution approach for a Stefan problem with variable thermal coefficients and multiple heat sources, including rigorous mathematical proof of solution properties.

Findings

Explicit solutions derived for specific thermal property functions

Existence and uniqueness of solutions proved

Applicable to problems with different heat source terms

Abstract

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.