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

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Applied Nonlinear Analysis

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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.

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References

  1. Franců, J. (1992). On modelling of Czochralski flow. (Czech), Thesis, Masaryk University, Brno.

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  2. Franců, J. (1994). Weakly continuous operators. Applications to differential equations Appl. Math., 39:45–56.

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  3. Franců, J. (1998). Modelling of Czochralski flow. Abstr. Appl. Anal., 3,1–2:1–39.

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  4. Feistauer, M. (1993). Mathematical Methods in fluid dynamics. Longman Scientific & Technical.

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  5. Kufner, A. (1980). Weighted Sobolev spaces. Teubner-Texte zurMathematik — Band 31, Teubner Leipzig.

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  6. Knobloch, P. (1996). Solvability and finite element discretization of a mathematical model related to Czochralski crystal growth, Otto-von-Guericke-Universitat Magdeburg, Preprint MBI-96-5.

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Authors
  1. Jan Franců
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Editors and Affiliations

  1. I.S.T. Technical University, Lisbon, Portugal

    Adélia Sequeira  & Juha Hans Videman  & 

  2. University of Pisa, Pisa, Italy

    Hugo Beirão da Veiga

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© 2002 Kluwer Academic Publishers

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Franců, J. (2002). On Modelling of Czochralski Flow, the Case of Non Plane Free Surface. In: Sequeira, A., da Veiga, H.B., Videman, J.H. (eds) Applied Nonlinear Analysis. Springer, Boston, MA. https://doi.org/10.1007/0-306-47096-9_10

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  • DOI: https://doi.org/10.1007/0-306-47096-9_10

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-0-306-46303-7

  • Online ISBN: 978-0-306-47096-7

  • eBook Packages: Springer Book Archive

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