Modelling of the Czochralski flow (Q5926217)

Summary: The Czochralski method of industrial production of a silicon single crystal consists of pulling up the single cyrstal from the silicon melt. The flow of the melt during the production is called Czochralski flow. The mathematical description of the flow consists of a coupled system of six partial differential equation in cylindrical coordinates containing Navier-Stokes equations (with stream function), heat convection-conduction equations, convection-diffusion equation for oxygen impurity, and an equation describing magnetic field effect. Here, we deal with the analysis of this system in the form used for numerical simulation. A weak formulation is derived, and the existence of weak solution to stationary and evolution problems is proved.