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Relationship between Neumann solutions for two-phase Lamé-Clapeyron-Stefan problems with convective and temperature boundary conditions

Tarzia Domingo Alberto (Universidad Austral, Departamento de Matemática, Paraguay, SFZF Rosario, Argentina + CONICE, Argentina)

We obtain for the two-phase Lamé-Clapeyron-Stefan problem for a semi-infinite material an equivalence between the temperature and convective boundary conditions at the fixed face in the case that an inequality for the convective transfer coefficient is satisfied. Moreover, an inequality for the coefficient which characterizes the solid-liquid interface of the classical Neumann solution is also obtained. This inequality must be satisfied for data of any phase-change material, and as a consequence the result given in Tarzia, Quart. Appl. Math., 39 (1981), 491-497 is also recovered when a heat flux condition was imposed at the fixed face.

Keywords: Lamé-Clapeyron-Stefan Problem, PCM, free boundary problem, explicit solutions, similarity solutions, Neumann solution, convective boundary condition