Single correlation for theoretical contact melting results in various geometries

The melting rates due to close-contact heating of a block of phase-change material have been analyzed in the past based on thin-film lubrication theory in several internal and external configurations. The scale analysis of close-contact melting in a region of general shape shows that the melting rate in all configurations is anticipated by the expression in which V is the speed with which the solid advances into the melting front (the melting rate), ϱ/ϱ s is the liquid/solid density ratio, Ste is the Stefan number for liquid superheating (Ste >>1), and α and υ are the viscosity and the t hermal diffusivity of the liquid phase. The film exess pressure scale Δ is defined as the net weight of the object surrounded by liquid divided by the horizontal projected area of that object. The flow length scale of liquid film, ℓ, stands for the diameter of the cylinder or the sphere, or the smaller of the two sides of the rectangular shape of the contact area during melting against a flat heater.