  Similarity solutions for a one-dimensional mathematical model for thawing in
a saturated semi-infinite porous media is considered when change of phase
induces a density jump and a convective boundary condition is imposed at the
fixed face $x=0$. Different cases depending on physical parameters are analysed
and an explicit solution of a similarity type is obtained if and only if an
inequality for data is verified. Moreover, a monotony property respect to the
coefficient which characterizes the heat transfer at the fixed face $x=0$ is
obtained for the coefficient involved in the definition of the free boundary.
  Relationship between the Stefan problem with convective condition at $x=0$
considered in this paper and the Stefan problem with temperature condition at
the same face studied in (Fasano-Primicerio-Tarzia, Math. Models Meth. Appl.
Sci., 9 (1999), 1-10) is analized and conditions for physical parameters under
which both problems became equivalents are obtained. Furthermore, an inequality
to be satisfied for the coefficient which characterizes the free boundary of
the problem with a temperature or a convective boundary condition at the fixed
face $x=0$ is also obtained.
