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A Stefan problem is a moving-boundary problem in which a phase boundary moves as latent heat is released or absorbed. Temperature satisfies a heat equation in each phase and the Stefan condition supplies the interfacial energy balance.

For equal thermal properties and bounded travelling profiles on two deep half-spaces, the solid temperature is $T_m$ and the liquid profile is exponential. The Stefan condition requires $L=c_p\Delta T$. This balances the latent heat of solidification with warming of the initially supercooled liquid.