Beyond Stefan Problems: The Structure of Sheared Solidification Fronts,
CORNELL UNIV ITHACA NY DEPT OF THEORETICAL AND APPLIED MECHANICS
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Determination of the motion of a solidification front into a molten metal, a so-called Stefan problem, does not depend on detail of the solidification process inside the front. Such details are needed, however, when the liquid is being stirred by a magnetic field, since they determine the structure of the coincident Hartman viscous layer, and hence the secondary motion in the liquid. Within this layer the viscosity is variable, due to the spacial variation in the concentration of solid particles. In the absence of a theory in the nucleation literature, a growth law for the concentration of solid particles is proposed for the small undercooling that must occur in such a layer. The asymptotic analysis is carried out for the slow solidification of a cylinder of molten metal that is being stirred by a rotating, uniform magnetic field, but the results are of general validity.