Magnetic and gravitational natural convection of melted silicon. Two-dimensional numerical computations for the rate of heat transfer.

Abstract

The two-dimensional natural convection of fluid under both a magnetic and a gravitational field was modeled by conservation equations. Sample computations were carried out for the fluid in a square enclosure for Rayleigh number of from 104 to 106, for Hartman number of from 1 to 103 and for Prandtl number equal to 0.054, equivalent to melted silicon. The numerical computations converged successfully and the Nusselt numbers obtained were correlated to give an empirical equation for the rate of heat transfer. The steady state solutions were graphically visualized. At Ha=103 and Ra=106, the point at which the temperature profile was almost linear, the flow was almost suppressed and elongated in a regime with high wave numbers.