A mathematical model of unidirectional solidification in cooled mold

For the unidirectional solidification in a mold cooled by air or water, several mathematical models have been proposed. However, some are complex series solutions, and some are good approximations only when solidification time is sufficiently small. Therefore, our research team proposes the present mathematical model, which is a good approximation when solidification time is sufficiently large. In order to estimate the convergency characteristics of the present model, numerical solutions were calculated with mold/solid heat transfer coefficients, which are experimentally determined by a previous and the present model.