We consider fractional Stefan melting problems which involve a memory of the latent-heat accumulation. We show that the manner in which the memory of the latent-heat accumulation is recorded depends on the assumed nature of the transition between the liquid and the solid phases. When a sharp interface between the liquid and the solid phases is assumed, the memory of the accumulation of the latent heat is "lumped" in the history of the speed of the interface. In contrast, when a diffuse interface is assumed, the memory of the accumulation is "distributed" throughout the liquid phase. By use of an example problem, we demonstrate that the equivalence of the sharp- and diffuse-interface models can only occur when there is no memory in the system.
|Original language||English (US)|
|Journal||Physical Review E - Statistical, Nonlinear, and Soft Matter Physics|
|State||Published - Apr 2 2013|