The authors use the full capabilities of the finite element method for calculating the heat and mass transfer in the Czochralski furnace as a global problem. Each separate constituent is analyzed by means of finite elements and a full coupling is established between the various parts by means of their radiative exchanges. A calculation of the whole process relies entirely upon controllable inputs and boundary conditions.
Dupret, F., Ryckmans, Y., Wouters, P., & Crochet, M. (1986). Global finite element calculation of the Czochralski growth. Sixth International Symposium on Finite Element Methods in Flow Problems, p. 267-272. https://hdl.handle.net/2078.5/223014