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Determination of the heat transfer coefficient during solidification of alloys. (English) Zbl 1086.76073
Summary: We consider a three-phase inverse Stefan problem. Such a problem consists in a reconstruction of the function describing the coefficient of heat transfer, when the positions of the moving solid and liquid interfaces are known. We introduce three partial problems for each phase (liquid, solid and mushy) separately. The solutions of these problems are used for the determination of the unknown heat transfer coefficient. The missing data for a mushy (solid) phase are computed from overdetermined data at the moving liquid (solid) interface taking into account the transmission condition. At the end, we present numerical calculations in one dimension using continuous piecewise linear finite elements in order to demonstrate the efficiency of the designed numerical algorithm.

MSC:
76T99 Multiphase and multicomponent flows
76M10 Finite element methods applied to problems in fluid mechanics
80A22 Stefan problems, phase changes, etc.
80A23 Inverse problems in thermodynamics and heat transfer
80A20 Heat and mass transfer, heat flow (MSC2010)
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