The motion of a plate in a melting solid medium

Abstract

The motion of a semi-infinite heated flat plate through a solid medium, with the deformation of a melt layer at the plate surface, is considered. The flow of the melt is determined in the thin-layer approximation taking into account inertial terms in the equation of motion and a dissipative term in the heat equation. A procedure for determining an exact selfsimilar solution is described and an asymptotic method is developed for the approximate representation of the solution in terms of simple formulae. Simple estimating formulae are obtained for the length of the fluid cavity behind a plate of finite length.