AN ALTERNATIVE FORMULATION OF THE APPARENT HEAT CAPACITY METHOD FOR PHASE-CHANGE PROBLEMS

Abstract

In the apparent heat capacity method (AHCM) for heat transfer problems with phase change, the conventional time discretization is subject to severe restrictions on time steps in spite of the various approximation techniques that have been developed so far. To improve the conventional AHCM we propose an alternative formulation. By introducing a nominal heat capacity, the new time discretization can better approximate the time derivative of enthalpy while maintaining the same form as the conventional AHCM. The new formulation also establishes an equivalent relation between the full enthalpy formulation and the AHCM. A one-dimensional (I-D) Stefan problem is used as a test problem, and comparison is made between the solutions of the conventional and the new AHCM formulations. It is found that for implicit schemes with large time steps, the new formulation performs much better than the conventional AHCM