High-Reynolds-number flow in a narrow gap driven by solidification. I. Theory

Flow driven by solidification is studied in a limit when fluid dynamics and heat transfer decouple. The governing equations are derived by integrating the mass and momentum equations over a narrow gap of any shape within whic h rapid solidification occurs. These equations are then simplified by explo iting the high-Reynolds-number characteristics of the flow. The modeling le ads to fluid dynamics with a suction-type boundary layer established at the solid/liquid interface due to solid pulling and phase change. In part II [ Phys. Fluids 13, 834 (2001)], the method is applied to planar-flow melt-spi nning where liquid metal, held by surface tension in the gap between the in jection nozzle and spinning chill-wheel, forms a long thin puddle. (C) 2001 American Institute of Physics.