Formulation and solution of hyperbolic Stefan problem

Abstract

The interface condition for hyperbolic phase change problems, which includes sensible heat at the interface, is derived as an extension of the interface condition for standard parabolic phase change problems. The enthalpy formulation of the hyperbolic Stefan problem is presented and is used to numerically solve for the temperature distributions and the interface position. MacCormack’s predictor–corrector method is applied to solve the hyperbolic phase change problem and is validated by comparing the limiting case where the thermal relaxation parameter approaches zero to the parabolic phase change problem, in which the relaxation parameter is zero. Solutions with an applied surface temperature greater than the melt temperature are presented for two different Stefan numbers. It is noted that a discontinuity occurs at the phase change interface as well as at the thermal front.