Extended Neumann's Solution Accounting for Rayleigh–Bénard Convection in the Melt Layer of a Phase Change Material

Abstract

Neumann's solution has been perceived to be inapplicable for the Stefan problem when Rayleigh–Bénard (R–B) convection exists. Yet, this article challenges this perception by demonstrating the applicability of Neumann's solution in the context of R–B convection. The temporal, countergravitational progression of a liquid–solid interface is distinctively attributed by R–B convection, sequentially transforming from diffusive to convective state as the melt phase thickens. We thus incorporate a lumped parameter, “convective conductivity” that accounts for the distinctive temporal thickening of the melt phase and replaces “stagnant thermal conductivity” in Neumann's solution. Thus, the extended Neumann's solution that includes R–B convection, enables the temporal progression of the liquid–solid interface to be precisely determined for quasi-steady phase transition.