On Modelling of Czochralski Flow, the Case of Non Plane Free Surface

Jan Franců

A chapter in Applied Nonlinear Analysis, 2002, pp 133-148 from Springer

Abstract: Abstract The flow of the melt during the industrial production of single crystal from melt by Czochralski method is called 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 vorticity and swirl), heat convection-conduction equation, convection-diffusion equation for oxygen impurity and an equation describing magnetic field effect. The paper deals with analysis of the system in the form used for numerical simulation. Weak formulation and existence of the weak solution to stationary and evolution problem is studied. The results from paper [J. Franců: Modelling of Czochralski flow, Abstract and Applied Analysis, 3 (1998) No.1–2, pp. 1–39] are extended to the case of non-plane free surface of the melt.

Keywords: Navier-Stokes equations; Czochralski method; single crystal growth; operator equation; existence theorem; weighted Sobolev spaces; Rothe method (search for similar items in EconPapers)
Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-0-306-47096-7_10

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DOI: 10.1007/0-306-47096-9_10

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