The three-dimensional starting solution for a melting slab

Abstract

Abstract A short-time closed-form solution is developed for the melting or solidification of a half­space under a general surface heat input, such that change of phase starts at a point of the surface, and then spreads simultaneously both towards the interior of the body and along its surface. The solution is obtained by the embedding technique, and show that the shape of the phase intersurface is, when suitably normalized, a universal function, i. e. it is independent of the distribution and rate of the applied heat input and of the material properties. Initial melt propagation in directions normal to and along the surface are respectively proportional to (t - tm)3/2 and (t - tm)½, where tm is the time of start of melting.