Source and Sink Method of Solution of Two-Dimensional Phase Change for Energy Storage

Abstract

A source and sink method has been developed for the solution of heat transfer with phase change in two dimensions. In this method, the heat transfer in one direction is decoupled from that in the other direction by changing the second partial differential in the direction 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 paper is thus independent of the equations used to represent the interface as well as the conditions imposed on the boundaries. In the present paper, the method has been applied to the tracking of a single melting front formed by different phases assuming equal properties. The method has been demonstrated to be accurate, convergent, and stable by numerical computations as well as experimental measurements. Extension of the method to more general problems has also been discussed.