TREATMENT OF DISCONTINUOUS THERMAL CONDUCTIVITY IN CONTROL-VOLUME SOLUTIONS OF PHASE-CHANGE PROBLEMS

Abstract

Phase-change problems often involve discontinuities in the thermal properties at the phase-change boundary. This feature needs to be handled carefully when seeking a numerical solution based on a fixed space grid. Of particular concern are discontinuities in the thermal conductivity. In the context of a control-volume finite-difference solution, the requirement is an appropriate approximation of the conductivity values at the control-volume interfaces. In this article, using the Kirchhoff transformation, an approximation for the interface conductivity is developed. The approach is tested on a range of one- and two-dimensional, steady and transient phase-change problems. In addition, a discussion on the extension of the approach to finite-element schemes is included.