  Recently it was obtained in [Tarzia, Thermal Sci. 21A (2017) 1-11] for the
classical two-phase Lam\'e-Clapeyron-Stefan problem an equivalence between the
temperature and convective boundary conditions at the fixed face under a
certain restriction. Motivated by this article we study the two-phase Stefan
problem for a semi-infinite material with a latent heat defined as a power
function of the position and a convective boundary condition at the fixed face.
An exact solution is constructed using Kummer functions in case that an
inequality for the convective transfer coefficient is satisfied generalizing
recent works for the corresponding one-phase free boundary problem. We also
consider the limit to our problem when that coefficient goes to infinity
obtaining a new free boundary problem, which has been recently studied in
[Zhou-Shi-Zhou, J. Engng. Math. (2017) DOI 10.1007/s10665-017-9921-y].
