NATURAL-CONVECTION IN AN ALUMINUM INGOT - A MATHEMATICAL-MODEL

Strong buoyancy-driven flows are known to occur in the liquid metal po ol of an aluminum ingot caster. These flows have a significant influen ce on the metallurgical structure of the ingot, largely through the re distribution of heat, fragmented dendrites, and segregated material wi thin the pool. In this paper, we have developed a simple, analytical m odel of this process which predicts the distribution of temperature an d velocity throughout the liquid metal pool. We demonstrate that the f low field can be separated into a relatively quiescent, stratified cor e bounded by thermally driven wall jets. The flows in the two regions then are matched through a global continuity equation, and the wall je ts are handled using a momentum-integral technique. The result is a pa ir of coupled, nonlinear, ordinary differential equations. These equat ions are solved for two particular cases: one where the feed of liquid metal into the top of die pool is ignored and one where it is taken t o be uniform over the top surface. Finally, our model predictions are compared with numerical experiments performed using a finite-differenc e code. The comparison is found to be satisfactory.