

MATHEMATICAL MODEL AND METHOD OF CALCULATION OF CRYSTALLIZATION OF TWOCOMPONENT MELTS
Ginkin V.P.^{1}, Ganina S.M.^{1}, Kartavykh A.V.^{2}, Chernov K.G.^{1}
^{1} State Scientific Center of the Russian Federation  Institute For Physics And Power Engineering Named After A.I.Leypunsky, Obninsk, Russia ^{2}Institute of Chemical Problems of Microelectronics, Moscow, Russia
Citation:
Ginkin, V.P., Ganina, S.M., Kartavykh, A.V. and Chernov, K.G., (2010) Mathematical model and method of calculation of crystallization of twocomponent melts, Modern Science: Researches, Ideas, Results, Technologies, Iss. #2(4), PP. 48  55.

Keywords: twocomponent melts crystallization; mathematical model; flow in porous media; Stefan problem; numerical calculation method; experiment calculation 
Abstracts:
A mathematical model of the crystallization process is proposed in which a Stefan problem with two boundaries is solved numerically, the boundaries being between the solid phase and the twophase transition zone and between the twophase transition zone and the liquid phase. The twophase zone is represented as a porous medium with variable porosity. The authors pioneer the use of squarelaw dependance of porosity on temperature in a twophase zone. An additional force introduced by analogy with Darcy’s law is taken into account in the twophase zone, namely, a force resisting to the melt flow due to conditions of porosity. The resulting equation system is solved by an implicit relaxation method making use of an exponential approximation method, the PatankarSpalding method, and the incomplete factorization method. The testing of the model in the calculation of the Sn+20%Pb (mass percentage) alloy crystallization experiment shows good agreement between the calculation and experimental data. 
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