Analysis of solidification interface shape during continuous casting of a slab

An analysis was made of the two-dimensional interface shape of a slab ingot being cast continuously by withdrawing it from a mold. The sides of the ingot are being cooled and the upper boundary of the ingot is in contact with a pool of molten metal. The solidification interface shape was determined from the analysis of the heat flow, utilizing the condition that the solidification interface is at constant temperature and must be normal to the lines of heat flow carrying away latent heat of fusion from the interface. The analysis includes the effect of interface curvature which, for a constant rate of withdrawing the cast ingot from the mold, causes the solidification to be nonuniform along the interface. The analysis was carried out by a conformal mapping procedure.