A model for transient directional solidification of a binary off-eutectic alloy is presented in this paper. This model exhibits all features necessary for dendritic solidification. In contrary to a big majority of existing models it additionally contains most of the essentials characterizing gravity-driven casting process. After implementation of a certain simplification a first simulation based upon this model is possible. This refers to the boundary layer that forms after beginning of solidification. For AlSi5 results of simulation are presented and discussed. This especially refers to phase boundary kinetics as well as to formation of constitutionally supercooled regions in the liquid remainder.
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