An analysis was made of the two-dimensional solidification of an ingot being cooled and withdrawn vertically downward from a mold consisting of parallel walls of finite length. In some metallurgical solidification processes the liquid metal is maintained superheated so that it transfers heat into the solidification interface as a means of controlling the metal structure during solidification. This energy plus the latent heat of fusion is removed by the coolant along the sides of the ingot. Increasing the ingot withdrawal rate or the heat addition at the solidification interface causes the interface to move downward within the mold and have a nonplanar shape as a result of the curved paths for heat flow into the coolant. This distortion of the interface in the case of directional solidification leads to an undesirable metallic structure. The present heat transfer analysis shows how the flatness of the interface is related to the ingot thickness, the withdrawal rate, the heat addition from the superheated liquid metal, and the temperature difference available for cooling. This provides an understanding of the conditions that will yield a maximum rate of casting while achieving the desired flatness of the interface. The results are interpreted with respect to the conditions for obtaining an aligned eutectic structure by directional solidification. In this process an additional constraint must be included that relates the ingot withdrawal rate and the heat transfer rate from the liquid metal to the solidification interface.

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