Abstract and Applied Analysis
Volume 3 (1998), Issue 1-2, Pages 1-40

Modelling of the Czochralski flow

Jan Franc

Department of Mathematics, Technical University Brno, Technická 2, Brno 616 69, Czech Republic

Received 3 August 1996

Copyright © 1998 Jan Franc. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The Czochralski method of the industrial production of a silicon single crystal consists of pulling up the single crystal from the silicon melt. The flow of the melt during the production is called the Czochralski flow. The mathematical description of the flow consists of a coupled system of six P.D.E. in cylindrical coordinates containing Navier-Stokes equations (with the stream function), heat convection-conduction equations, convection-diffusion equation for oxygen impurity and an equation describing magnetic field effect.

This paper deals with the analysis of the system in the form used for numerical simulation. The weak formulation is derived and the existence of the weak solution to the stationary and the evolution problem is proved.