- We present a catalogue of explicit similarity solutions to the Stefan problem and the binary alloy problem; the most general case includes convective heat transfer due to a fluid motion driven by a density change at the solid-liquid interface. The free boundary is either an ellipsoid or a hyperboloid; in the latter case we note that for certain parameter regimes there may be two solutions (with different initial data), a situation which does not occur in the one-dimensional case. © 1988 Oxford University Press.
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SIMILARITY SOLUTIONS TO THE STEFAN PROBLEM AND THE BINARY ALLOY PROBLEM
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