Explicit solution for a two-phase fractional Stefan problem with a heat flux condition at the fixed face

ROSCANI, SABRINA D.; TARZIA, DOMINGO A.

MATEMATICA APLICADA E COMPUTACIONAL

SOC BRASILEIRA MATEMATICA APLICADA & COMPUTACIONAL

Año: 2018

0101-8205

A generalized Neumann solution for the two-phase fractional Lamé-Clapeyron-Stefan problem for a semi-infinite material with constant initial temperature and a particular heat flux condition at the fixed face is obtained, when a restriction on data is satisfied. The fractional derivative in the Caputo sense of order α ∈ (0, 1) respect on the temporal variable is considered in two governing heat equations and in one of the conditions for the free boundary. Furthermore, we find a relationship between this fractional free boundary problem and another one with a constant temperature condition at the fixed face and based on that fact, we obtain an inequality for the coefficient which characterizes the fractional phase-change interface obtained in Roscani and Tarzia (Adv Math Sci Appl 24(2):237-249, 2014). We also recover the restriction on data and the classical Neumann solution, through the error function, for the classical two-phase Lamé-Clapeyron-Stefan problem for the case α = 1.