Abstract and Applied Analysis

Modelling of the Czochralski flow

Jan Franců

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Abstract

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.

Article information

Source
Abstr. Appl. Anal., Volume 3, Number 1-2 (1998), 1-40.

Dates
First available in Project Euclid: 8 April 2003

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1049832679

Digital Object Identifier
doi:10.1155/S1085337598000426

Mathematical Reviews number (MathSciNet)
MR1700275

Zentralblatt MATH identifier
0993.76084

Subjects
Primary: 76D05: Navier-Stokes equations [See also 35Q30] 76Rxx
Secondary: 35Q10 46E35

Keywords
mathematical modelling viscous flow Czochralski method single crystal growth weak solution operator equation existence theorem weighted Sobolev spaces Rothe method

Citation

Franců, Jan. Modelling of the Czochralski flow. Abstr. Appl. Anal. 3 (1998), no. 1-2, 1--40. doi:10.1155/S1085337598000426. https://projecteuclid.org/euclid.aaa/1049832679


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