  From the one-dimensional consolidation of fine-grained soils with threshold
gradient, it can be derived a special type of Stefan problems where the seepage
front, due to the presence of this threshold gradient, exhibits the features of
a moving boundary. In this kind of problems, in contrast with the classical
Stefan problem, the latent heat is considered to depend inversely with the rate
of change of the seepage front. In this paper a one-phase Stefan problem with a
latent heat that not only depends on the rate of change of the free boundary
but also on its position is studied. The aim of this analysis is to extend
prior results, finding an analytical solution that recovers, by specifying some
parameters, the solutions that have already been examined in the literature
regarding Stefan problems with variable latent heat. Computational examples
will be presented in order to examine the effect of this parameters on the free
boundary.
