Hydrodynamics and heat exchange of crystal pulling from melts. Part II: Numerical study of free convection mode

Abstract

This work is a brief overview of numerical study results for hydrodynamics and convective heat exchange for the classic Czochralski technique obtained at the Institute of Thermophysics, Siberian Branch of the Russian Academy of Sciences. Flow structure evolution has been compared for melts with Prandtl numbers Pr = 0.05, 16, 50 and 2700. The regularities of local and integral convective heat exchange in the crucible/melt/crystal system for thermal gravity, thermocapillary and heat-induced gravity capillary convection have been studied. The calculations have been carried out using the finite and compact difference methods. This work is a continuation of an article: Berdnikov VS (2019) Hydrodynamics and heat exchange of crystal pulling from melts. Part I: Experimental studies of free convection mode. Modern Electronic Materials 5(3): 91–100. https://doi.org/10.3897/j.moem.5.3.46647