One-phase stefan problem with a latent heat depending on the position of the free boundary and its rate of change

Abstract

From the one-dimensional consolidation of ne-grained soils withthreshold gradient, it can be derived a special type of Stefan problems wherethe seepage front, because of the presence of this threshold gradient, exhibitsthe features of a moving boundary. In this type of problems, in contrast withthe classical Stefan problem, the latent heat is considered to depend inverselyto the rate of change of the seepage front. In this paper, we study a one-phase Stefan problem with a latent heat that depends on the rate of changeof the free boundary and on its position. The aim of this analysis is to extendprior results, nding an analytical solution that recovers, by specifying someparameters, the solutions that have already been examined in the literatureregarding Stefan problems with variable latent heat. Computational examplesare presented to examine the eect of this parameters on the free boundary.