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The work in this paper concerns the study of different approximations forone-dimensional one-phase Stefan-like problems with a space-dependent latentheat. It is considered two different problems, which differ from each other intheir boundary condition imposed at the fixed face: Dirichlet and Robinconditions. The approximate solutions are obtained by applying the heat balanceintegral method (HBIM), a modified heat balance integral method, the refinedintegral method (RIM) . Taking advantage of the exact analytical solutions wecompare and test the accuracy of the approximate solutions. The analysis iscarried out using the dimensionless generalized Stefan number (Ste) and Biotnumber (Bi). It is also studied the case when Bi goes to infinity in theproblem with a convective condition, recovering the approximate solutions whena temperature condition is imposed at the fixed face. Some numericalsimulations are provided in order to assert which of the approximate integralmethods turns out to be optimal. Moreover, we pose an approximate techniquebased on minimizing the least-squares error, obtaining also approximatesolutions for the classical Stefan problem.

Approximate solutions to one-phase Stefan-like problems with space-dependent latent heat