TRANSIENT BEHAVIOR OF A NaNO₃ FLOAT ZONE OPERATING AT HIGH MARANGONI NUMBER UNDER μg CONDITIONS

Abstract

This work is concerned with the problem of transient behavior of the ansymmetric thermocapillary laminar flow that occurs inside a NaNO₃ cylindrical float zone subject to variable surface tension. The molten liquid is assumed to be incompressible, with constant properties, except for the fluid density, which appears in buoyancy forces. It has been shown that the problem under study can be characterized by a set of five dimensionless parameters. The system of governing equations subject to appropriate hydrodynamic and thermal boundary and initial conditions has been solved by employing the modified SIMPLE method. Numerical results have allowed investigation of the rather complex flow structure and the thermal field as well as the temporal behavior for the case of a half-tone operating under μ-g conditions. It has been clearly confirmed in this study that the Marangoni number could not be the unique relevant parameter that dictates the onset of oscillatory flow. Numerical results have also allowed establishment of the structure of the hydrodynamic and thermal fields within the zone while operating at very high Marangoni numbers. The dependence of the fluid circulation velocity on the fret surface has also been determined.