A multiphase and multigrain mathematical model for the solidification of binary alloys is proposed, implemented, and validated. The model equations are derived using the volume averaging method and considering the conservation principles of mass, energy, and chemical species applied to a representative elementary volume. In the present model, grains that nucleate at different temperatures are grouped in different classes and are followed individually, enabling calculations of different growth velocities for globulitic and dendritic grains growing simultaneously. The proposed model is capable of predicting final average grain size, cooling curves during the complete primary and eutectic solidification, and the volume fraction of eutectic. These predictions are compared with experimental results for the solidification of cylindrical bars of Al-Si alloys with different Si concentrations and different amounts of inoculant additions, showing good agreement.

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