The finite volume method with an implementation of Newton's scheme is used to study steady heat transfer, fluid flow, and interfaces in a floating molten zone that is set up between a heating rod and a sample rod, i.e., the so-called half-zone system. Stream function/vorticity and temperature formulation of the Navier-Stokes equation, the energy equation, and their associated boundary conditions are written in generalized curvilinear coordinates and conservative-law form with Boussinesq approximation. Sample calculations are reported for sodium nitrate, a high-Prandtl-number material (Pr=9.12). Both natural convection and thermocapillary flow in the molten zone, as well as unknown interfaces and an overall mass balance constraint, are considered. The effects of heating temperature, gravity, and surface tension gradient on the flow patterns and interfaces are illustrated through computer simulation.
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JOURNAL OF THE CHINESE INSTITUTE OF CHEMICAL ENGINEERS
