SOLUTION OF STEFAN-PROBLEMS IMPOSED WITH CYCLIC TEMPERATURE AND FLUX BOUNDARY-CONDITIONS

Stefan problems imposed with cyclic temperature and flux boundary conditions are solved by using source and sink methods. A source front is associated with a moving freeze front while a sink front is associated with a moving melt front. The solution is expressed in a set of coupled integrodifferential equations, which are solved numerically for interface positions, temperature profiles, and cumulative and instantaneous heat storage and release. The solution methods have been shown to be unique, convergent, stable, and accurate. While they are used to test one cycle each of the temperature and flux conditions, the developed methods are general and applicable to multiple cycles. The numerical results reveal interesting phenomena not previously reported in the literature. Their relevance to energy storage and material processing and treatment is also covered.