Source-and-sink method of solution of two and three-dimensional Stefan problems

A source-and-sink method has been developed for the solution of conduction heat transfer with phase change in multiple dimensions. In this method, the heat transfer in one direction is decoupled from the other directions by changing the second partial differential in these directions where the phase change is less dominant to a finite difference form and solving the problem in the other direction with an analytical solution that accounts for the motion of the interface in a phase change problem. The solution developed in this work is thus independent of the equations used to represent the interface as well as the conditions imposed on the boundaries.; The method has been applied to the tracking of single, double, and coalescing interface fronts formed by different phases assuming equal properties. The method has been demonstrated to be accurate, convergent, and stable by numerical computation as well as experimental measurements. The method has also been applied to the solution of conjugate heat transfer including convection in a fluid medium and conduction in the phase change material, a problem applicable to the analysis of latent heat thermal energy storage systems.