Numerical investigation of thermocapillary and buoyancy convection in horizontal ribbon growth with lid-driven boundary

Abstract

The melt flow stability has a direct effect on crystal quality during the horizontal ribbon growth (HRG) process. The mixed convection in the HRG system includes thermocapillary convection, buoyancy convection, and the convection induced by the lid-driven boundary. In this study, the influences of relevant parameters such as Marangoni number, Rayleigh number, Biot number, and horizontal motion of the ribbon on flow and temperature fields have been analyzed using computational fluid dynamics. A thermal-fluid numerical model was developed by solving the Navier–Stokes and energy equations to obtain the flow, pressure, and temperature fields. The horizontal motion of the ribbon was assumed the lid-driven boundary. The results showed that the magnitude of the Marangoni number played a decisive role in the flow and temperature distribution inside the melt. In the case of a small Marangoni number, the increase in horizontal motion velocity of the ribbon was the main factor to induce convection in the melt, and the internal temperature distribution was carried out in a heat conduction mode. With the increasing Marangoni number, the thermocapillary convection was enhanced, and the convection induced by the ribbon motion was overwhelmed by the thermocapillary effect. Moreover, the increase in Biot number could reduce the temperature nonlinearity of the free surface. Particularly, the free surface temperature begins to oscillate as the Marangoni number is increased above a threshold. A larger Marangoni number could easily result in a temperature oscillation with a larger amplitude. The results indicated that the thermocapillary effect was more sensitive to temperature and flow oscillations, and should receive more attention.