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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

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