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-Benard (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, counter-gravitational 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.