  Different one-phase Stefan problems for a semi-infinite slab are considered,
involving a moving phase change material as well as temperature dependent
thermal coefficients. Existence of at least one similarity solution is proved
imposing a Dirichlet, Neumann, Robin or radiative-convective boundary condition
at the fixed face. The velocity that arises in the convective term of the
diffusion-convection equation is assumed to depend on temperature and time. In
each case, an equivalent ordinary differential problem is obtained giving rise
to a system of an integral equation coupled with a condition for the parameter
that characterizes the free boundary, which is solved though a double-fixed
point analysis. Some solutions for particular thermal coefficients are
provided.
