Effect of uniform crystal rotation on convective and radiation-convective heat transfer in the Czochralski method

Abstract

The conjugate heat transfer in different regimes of heat transfer in the system “crystal – environment – walls of the growth vessd”, geometrically similar to the simplified scheme of the upper part of the thermal node in the Czochralski method, is studied numerically by the finite element method. The system of equations of thermo-gravitational and mixed convection in variables of vortex, stream function and temperature is solved. In addition, the uniform rotation of crystals is taken into account. Calculations are carried out at convective and radiation-convective heat transfer with fixed crystal length. Calculations of radiation fluxes are carried out on the basis of the zonal method under the following assumptions: the calculated area is limited by a closed system of surfaces; all surfaces of the system are grey, diffuse- emitting and diffuse-reflecting; the surfaces are divided into zones within which the radiation properties and temperature can be considered constant; the medium filling the growth chamber is diathermic. The calculations were performed with the Prandtl number equal to 0.68 (argon) and the Grashof number of 16000, typical of the real process. The effect of uniform crystal rotation from 1 to 25 rpm on radiation-convective heat transfer is studied. It is shown that under the action of rotation the spatial form of convective flows loses stability. Secondary vortices appear. As a result, the cooling efficiency of the crystal increases significantly.