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From the one-dimensional consolidation of fine-grained soils with thresholdgradient, it can be derived a special type of Stefan problems where the seepagefront, due to the presence of this threshold gradient, exhibits the features ofa moving boundary. In this kind of problems, in contrast with the classicalStefan problem, the latent heat is considered to depend inversely with the rateof change of the seepage front. In this paper a one-phase Stefan problem with alatent heat that not only depends on the rate of change of the free boundarybut also on its position is studied. The aim of this analysis is to extendprior results, finding 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 exampleswill be presented in order to examine the effect of this parameters on the freeboundary.

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