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

Abstract

This study investigates the melting process of a three-phase Stefan problem in a semi-infinite material, imposing a convective boundary condition at the fixed face. By employing a similarity-type transformation, the problem is reduced to a solvable form, yielding a unique explicit solution. The analysis uncovers significant equivalences among the solutions of three different three-phase Stefan problems: one with a Robin boundary condition, another with a Dirichlet boundary condition, and a third one with a Neumann boundary condition at the fixed face. These equivalences are established under the condition that the problem data satisfy a specific relationship, providing new insights into the behaviour of phase change problems under varying boundary conditions.