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An explicit solution of a similarity type is obtained for a one-phase Stefanproblem in a semi-infinite material using Kummer functions. Motivated by [D.A.Tarzia, Relationship between Neumann solutions for two phaseLam\'e-Clapeyron-Stefan problems with convective and temperature boundaryconditions, Thermal Sci.(2016) DOI 10.2298/TSCI 140607003T, In press], and [Y.Zhou, L.J. Xia, Exact solution for Stefan problem with general power-typelatent 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 apower function of the position with a non-negative real exponent and aconvective boundary condition at the fixed face $x=0$. Existence and uniquenessof the solution is proved. Relationship between this problem and the problemsalready solved by Zhou and Xia with temperature and flux boundary condition isanalysed. Furthermore it is studied the limit behaviour of the solution whenthe coefficient which characterizes the heat transfer at the fixed boundarytends to infinity. Numerical computation of the solution is done over certainexamples, with a view to comparing this results with those obtained by generalalgorithms that solve Stefan problems.

Explicit solution for Stefan problem with latent heat depending on the  position and a convective boundary condition at the fixed face using Kummer  functions