A coordinate transformation method for solving a convection phase change problem

A computational method is presented for solving certain types of problems involving pure conduction or natural convection heat transfer in two dimensions in which a portion of the domain boundary is irregular and/or moving with respect to a fixed Cartesian coordinate system. The method is developed specifically for a problem involving axisymmetric melting of a solid around a vertical heating tube in a container of a finite height. The solid is initially at the melting temperature; thus heat transfer occurs only in the melted liquid. Equal liquid and solid densities are assumed, and the outer wall is assumed to be beyond the extent of the liquid region.