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In this chapter we consider different approximations for the one-dimensionalone-phase Stefan problem corresponding to the fusion process of a semi-infinitematerial with a temperature boundary condition at the fixed face and non-lineartemperature-dependent thermal conductivity. The knowledge of the exact solutionof this problem, allows to compare it directly with the approximate solutionsobtained by applying the heat balance integral method, an alternative form toit and the refined balance integral method, assuming a quadratic temperatureprofile in space. In all cases, the analysis is carried out in a dimensionlessway by the Stefan number (Ste) parameter.

Approximate solutions to the one-phase Stefan problem with non-linear temperature-dependent thermal conductivity