A numerical method for the treatment of discontinuous thermal conductivity in phase change problems

Presents a physical model for determining the effective thermal conductivity of a two-phase composite medium with fixed or moving interfaces. A rigorous numerical method for removing oscillations in the thermal field is proposed. The methodology is based on the volume averaging technique with the assumption that the phases may coexist at a temperature different from that of fusion. The analysis reveals that the effective conductivity of a two-phase medium is dependent on the phase volume fractions, on their thermal conductivities and on a constitutive constant which determines the geometric structure of the medium and the nature of the interface (fixed or moving). The results for the one and two dimensional conduction-dominated phase change problem show that the oscillations produced by previous fixed-grid methods are eliminated.