Onset of buoyancy-driven convection in melting from below

When a horizontal homogeneous solid is melted from below, convection can be induced in a thermally unstable melt layer. In this study the onset of buoyancy-driven convection during time-dependent melting is investigated by using similarly transformed disturbance equations. The critical Rayleigh numbers based on the melt-layer thickness are found numerically for various conditions. For small superheats, the present predictions approach the well known results of classical Rayleigh-Bénard problems, that is, critical Rayleigh numbers are located between 1,296 and 1,708, regardless of the Prandtl number. However, for high superheats the critical Rayleigh number increases with an increase in phase change rate but with decrease in Prandtl number.