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Interaction of the Basic Mechanisms of Buoyancy–Driven Convection:
Fundamentals, Technical and Material Sciences Applications
Vadim I. Polezhaev and Sergey A. Nikitin

A classification on the basis of driven forces and definition of the convective interactions are done. Coupling of the two basic types of thermal buoyancy-driven convection is studied in this paper. For the first type the equilibrium is absent, convection is governed by the Grashof (Gr) number and exists for every value of this number. For the second one, governed by the Rayleigh (Ra) number, the equilibrium exists, but unstable for Ra > Rac (Rac – critical value). The paper deals with 2D and 3D modeling on the basis of Navier-Stokes equations (Boussinesq approach) interaction of these two types of convection. A focus of the paper is concentrated on the material sciences problem of the convective instability for a model of a crucible filled by the melt with side heating and cooling from the top. Global convective structure for small Prandtl (Pr) number and the thermals – type structure for high Pr number are studied. It is shown, that the most dangerous mode changes from 3D for low Pr number to 2D (axisymmetric) for high Pr number.

Keywords: Thermal buoyancy-driven convection, side –and bottom heating, convective instability, convective interaction, mathematical modeling, Navier-Stokes equations, Boussinesq approach, cryogenic fuel storage, Czochralski growth, education and tutorial.

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