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A similarity solution of a multiphase Stefan problem incorporating general nonlinear heat conduction. (English) Zbl 0926.76119

Summary: A nonlinear diffusion model of Fujita is adapted to obtain an analytic solution describing the temperature distribution and position of any number of phase boundaries as a material cools on an effectively semi-infinite base material. Each material is initially homogeneous and at a uniform temperature. The solution method may incorporate any materials with temperature-dependent thermal properties undergoing any number of phase changes. As an example, we incorporate transitions through five phases of iron with nonlinear heat conduction, as the iron cools on a copper base.

MSC:

76T99 Multiphase and multicomponent flows
80A22 Stefan problems, phase changes, etc.
80A20 Heat and mass transfer, heat flow (MSC2010)
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