Abstract
With no assumptions regarding the shape and mode of growth of the interface, Ivantsov's method is extended to solve two phase problems involving non-isothermal solid and liquid phases separated by an isothermal interface. The interfacial energy balance is generalized to yield a nonlinear partial differential equation, involving an arbitrary function, for the temperature throughout each phase. The complete integral for each of these equations is obtained and is used to find the singular integral which gives both the shape and mode of growth of the interface. The temperature distribution itself is determined from the conduction equation for each phase. For the illustrative problem considered, the singular integral yields a spherical crystal growing unsteadily in a shape preserving manner. Planar and cylindrical crystals occur as special one and two-dimensional cases.
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