The radiative heat transfer (RHT) through the melt and the crystal strongly couples with the buoyancy-driven flow during the Cz growth of oxide crystals. In the present modeling, a finite volume method was applied to compute quasi-steady and axisymmetric solutions to the fully coupled equations governing heat transfer and the melt hydrodynamics. As well, the discrete ordinate method was used to solve the RHT equation. Particular attention was paid to an undulating structure of the natural convection flow which appears in the optically thick oxide melt characterized by Pr = 4.69, Ra = Ο (10⁶). The forced convection effect and the surface tension-driven flow were ignored. It was shown that, when the internal RHT is taken into account, the wavy structure of the flow and the convective distortion of the temperature field were smeared out, and consequently the secondary vortex located nearby the crucible bottom, disappeared. The shape and position of the vortex were studied in some detail. In the optically thick oxide melt of 2×10⁶≤ Ra ≤ 3×10⁶, both the position of the vortex centroid, P, and its elliptical shape with the ratio of diameters AB/CD = 1.6 remains nearly unchanged while the area of the ellipse increases with Ra. At around the point P in the opaque melt, (dT/dr)_CD found to be considerably (~40%) larger than (dT/dz)_AB. However, in the semitransparent melt, the ration between these local gradients equals to unity. This can be inferred that, in the opaque melt the local Richardson number, Ri_P might be smaller than ¼ as necessary criterion for instability. As well, the radial flow velocity profile along the vertical line including the vortex diameter, AB were compared for the two optically different cases. The Rayleigh-Fjørtoft instability condition found to be satisfied in the opaque melt. It was demonstrated that, the instability is suppressed by the stable stratification due to the internal RHT in the melt.

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