  An explicit solution of a similarity type is obtained for a one-phase Stefan
problem in a semi-infinite material using Kummer functions. Motivated by [D.A.
Tarzia, Relationship between Neumann solutions for two phase
Lam\'e-Clapeyron-Stefan problems with convective and temperature boundary
conditions, Thermal Sci.(2016) DOI 10.2298/TSCI 140607003T, In press], and [Y.
Zhou, L.J. Xia, Exact solution for Stefan problem with general power-type
latent heat using Kummer function, Int. J. Heat Mass Transfer, 84 (2015)
114-118], we consider a phase-change problem with a latent heat defined as a
power function of the position with a non-negative real exponent and a
convective boundary condition at the fixed face $x=0$. Existence and uniqueness
of the solution is proved. Relationship between this problem and the problems
already solved by Zhou and Xia with temperature and flux boundary condition is
analysed. Furthermore it is studied the limit behaviour of the solution when
the coefficient which characterizes the heat transfer at the fixed boundary
tends to infinity. Numerical computation of the solution is done over certain
examples, with a view to comparing this results with those obtained by general
algorithms that solve Stefan problems.
