Determination of the heat-transfer coefficient during solidification of alloys

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 well-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 over-determined data at the moving liquid (solid) interface taking into account the transmission condition. At the end we present numerical calculations in one dimension using piecewise linear continuous finite elements in order to demonstrate the efficiency of the designed numerical algorithm. (C) 2004 Elsevier B.V. All rights reserved.