  The work in this paper concerns the study of different approximations for
one-dimensional one-phase Stefan-like problems with a space-dependent latent
heat. It is considered two different problems, which differ from each other in
their boundary condition imposed at the fixed face: Dirichlet and Robin
conditions. The approximate solutions are obtained by applying the heat balance
integral method (HBIM), a modified heat balance integral method, the refined
integral method (RIM) . Taking advantage of the exact analytical solutions we
compare and test the accuracy of the approximate solutions. The analysis is
carried out using the dimensionless generalized Stefan number (Ste) and Biot
number (Bi). It is also studied the case when Bi goes to infinity in the
problem with a convective condition, recovering the approximate solutions when
a temperature condition is imposed at the fixed face. Some numerical
simulations are provided in order to assert which of the approximate integral
methods turns out to be optimal. Moreover, we pose an approximate technique
based on minimizing the least-squares error, obtaining also approximate
solutions for the classical Stefan problem.
