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arXiv · 2502.05545

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

Julieta Bollati·María Fernanda Natale·José Abel Semitiel·Domingo Alberto Tarzia
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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.

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Julieta Bollati, María Fernanda Natale, José Abel Semitiel, Domingo Alberto Tarzia. 2025-02-08. Relationship among solutions for three-phase change problems with Robin, Dirichlet, and Neumann boundary conditions. https://arxiv.org/abs/2502.05545

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