On Solution to Phase Transition Problem in Multicomponent Alloy in the Cylindrical Ampule

The paper presents a self-consistent model of multicomponent alloy crystallization in a cylindrical ampule. The mathematical model accounts for the heat and matter transfer in both solid and liquid phases. We described the system by the interface position and radially average temperature and concentrations. Special efforts are required to solve a corresponding one dimensional phase transition problem in multicomponent alloy. To handle evolution of solid/liquid interface, the moving boundary problem is mapped to a new coordinate system. We obtained a conservative and implicit finite difference scheme in a new coordinate system with control volume technique and constructed a fully implicit coupled approach. Furthermore, we solved a corresponding set of nonlinear equations by Newton method for the unknown vector, whose components are concentrations of all species, interface rate and temperature. The proposed method was used for numerical simulation of the crystallization process of А-В-С solution

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