Temperature and moving boundary in two-phase freezing due to an axisymmetric cold spot

Abstract

Short time analytic solution of the problem of two-phase freezing due to an axisymmetric cold spot is presented. The melt could be superheated and it occupies an infinite region bounded internally by a cylinder of finite radius. Although the method of solution is valid for various other types of boundary conditions, the results in the paper are given for prescribed flux which could be time and space dependent. The method of solution is simple and straightforward and consists of assuming fictitious initial temperatures in some fictitious extensions of the region originally occupied by the melt. The spread of the solidification is much faster along the surface of the cylinder than along the interior of the cylinder and the spread along the surface always depends on material parameters. Several interesting results can be deduced as particular cases of the general results.