Relationship among solutions for three-phase change problems with Robin, Dirichlet and Neumann boundary conditions

Abstract

This study presents a novel approach to the melting process in a three-phase Stefan problem, applied to a semi-infinite material with a convective boundary condition at the fixed face. By using a similarity-type transformation, the problem is simplified and solved explicitly, yielding a unique solution. Additionally, a computational example is provided to illustrate the temperature distribution and the evolution of the free boundaries in a melting semi-infinite material with an intermediate zone. The principal key contribution lies in revealing new equivalences among solutions to three distinct three-phase Stefan problems, each with different boundary conditions (Robin, Dirichlet and Neumann). These equivalences are established under specific data relationships, providing fresh insights into phase change behavior across varying boundary conditions. This research significantly advances the understanding of multi-phase heat transfer problems.