Implementation of Phase Change in Numerical Models of Heat Transfer

Abstract

This paper investigates some of the numerical problems involved in simulating heat transfer in porous media in the presence of phase change. Applications of this type of simulation include modeling of certain metal forming processes, of biological tissues and organs during cryosurgery or cyropreservation, and of heat transfer in frozen soils subjected to transient environmental conditions. A two-dimensional finite element model was used in which the latent heat is treated directly as an energy source in the problem formulation. Several parameters addressed in this work are crucial to the successful implementation of numerical methods for nonlinear heat transport with phase change, including: the effect of nodal point spacing on the occurrence and magnitude of numerical oscillations in the temperature solution and the use of grid point spacing to control these oscillations; the limiting element size which should be used in order to insure stable temperature fields; and the effect which the range of temperatures over which latent heat is liberated has on the solution. The results indicate that numerical stability is achieved for combinations of the foregoing parameters which yield small values of the Stefan number.