TY - JOUR
T1 - Fractional Stefan problems exhibiting lumped and distributed latent-heat memory effects
AU - Voller, Vaughan R.
AU - Falcini, Federico
AU - Garra, Roberto
PY - 2013/4/2
Y1 - 2013/4/2
N2 - 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.
AB - 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.
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U2 - 10.1103/PhysRevE.87.042401
DO - 10.1103/PhysRevE.87.042401
M3 - Article
AN - SCOPUS:84876722376
SN - 1539-3755
VL - 87
JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
IS - 4
M1 - 042401
ER -