Summary

The subject of the present thesis is the numerical modelling of the binary alloy solidification problem, with emphasis on metallic alloys. The problem is approached on the metallurgical and on the engineering and thermal sciences point of view. First general aspects associated with the heat and mass transfer mechanisms are treated, and different formulations are revised and presented in detail. The classical models with their analytical solutions are revised and discussed, culminating with the integral method. Under the scope of numerical methods, the Stefan and Neumann problems are presented in temperature and enthalpy formulations. The natural convection in the liquid phase is also considered. Once pure substances and eutectic alloys are explored, those mixtures that change phase in a temperature range are focused, including the metallurgical aspects of their solidification. Next, a complete model representing the state of art for the binary alloy solidification is presented. Some limitations of this model are pointed out, including the hypothesis of thermodynamical equilibrium between phases, im p a irin g the treatment in detail of the solid-liquid interface. A diffusive model is then proposed where the solid and liquid phases are treated separatelly, not adopting the hypothesis of thermodynamical equilibrium between phases. The model is able to simulate the heat and mass transfer in directional solidification, including high rates of solidification where the interface between phases is not planar.

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