Author(s)

R. Grzymkowski, D. Slota

Abstract

Numerical calculations of the heat-transfer coefficient during solidification of alloys R. Grzymkowski, D. Slota Institute of Mathematics, Silesian University of Technology, Poland Abstract In the paper, three-phase inverse Stefan problems are formulated and de- scribed by means of the optimization method. These problems consist in the reconstruction of the function which describes the coefficient of heat- transfer, when the positions of the moving solidus and Hquidus interfaces are well-known. In numerical calculations the Nelder-Mead optimization method and the generalized alternating phase truncation method were used. 1 Introduction Solidification of pure metals can be modelled by two-phase Stefan prob- lems. However, it is often the case that solidification of alloys (solidification with mushy zone) may also be modelled by three-phase Stefan problems. The solidification of alloys is characterized by two types of temperature of change: liquidus temperature (beginning of t

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