Unsteady contact melting of a rectangular cross-section material on a flat plate

The work in this paper concerns a mathematical model of the contact melting process of a rectangular material in contact with a hot plate. The problem is described by a coupled system of heat equations in the solid and melt layer, fluid flow in the melt, a Stefan condition at the melt interface, and a force balance between the weight of the solid and the fluid pressure. Since the melt layer remains thin throughout the process, we use the lubrication approximation to the fluid equations and assume that the heat flow in the fluid is dominated by conduction across the thin film. In the solid we employ a heat balance integral method. Results show that the film height has initial and final rapid increases, whereas for intermediate times the height slowly increases. The quasisteady state of previous models is never attained: This is shown to be an effect of neglecting the change in mass and conduction in the solid. The previously observed initial infinite velocity of the melt is shown to be a result of the perf...