  In this paper, a one-phase Stefan-type problem for a semi-infinite material
which has as its main feature a variable latent heat that depends on the power
of the position and the velocity of the moving boundary is studied. Exact
solutions of similarity type are obtained for the cases when Neumann or Robin
boundary conditions are imposed at the fixed face. Required relationships
between data are presented in order that these problems become equivalent to
the problem where a Dirichlet condition at the fixed face is considered.
Moreover, in the case where a Robin condition is prescribed, the limit
behaviour is studied when the heat transfer coefficient at the fixed face goes
to infinity.
