A Stefan problem in which a semi-infinite molten material at the fusion temperature solidifies as a result of imperfect thermal contact with a cooler semi-infinite solid is considered. The contact resistance, due to surface roughness, is modeled by a convective boundary condition. Biot’s variational principle is used to reduce the coupled partial differential equations to a pair of coupled ordinary differential equations that are solved numerically. The position of the moving boundary as a function of time is given for both bismuth and aluminum solidifying on stainless steel.

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