The Evolution of Solidification Models

"Solidification systems from conduction controlled freezing of a pure material through to alloy phase change that include flow and segregation processes are described. The components in a general solidification model-variables, governing transport equations, and local scale relationship-are outlined. A central focus is the presentation of an explicit procedure for coupling between macroscopic and local scale variables.IntroductionSince the seminal work of Byres et al.[!] in the 1940's there has been a steady progress in modeling solidification systems with increasing levels of complexity. The object of this paper is to track the evolution of these solidification models and present a general modeling approach that applicable to a wide range of the solidification systems of current interest.Solidification SystemsIn a broad sense the underlying physics in a solidification process occur at two distinct length scales:1. The macroscopic scale of the process over which the governing transport equations of heat, mass and momentum hold.2. The local scale at the solid-liquid interface where the solidification phenomena are operative."