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Energy stability of thermocapillary convection in a model of the float-zone crystal-growth process

Published online by Cambridge University Press:  26 April 2006

Y. Shen ,
G. P. Neitzel ,
D. F. Jankowski  and
H. D. Mittelmann
Y. Shen
Affiliation:
Department of Mechanical and Aerospace Engineering, Arizona State University, Tempe, AZ 85287, USA
G. P. Neitzel
Affiliation:
Department of Mechanical and Aerospace Engineering, Arizona State University, Tempe, AZ 85287, USA
D. F. Jankowski
Affiliation:
Department of Mechanical and Aerospace Engineering, Arizona State University, Tempe, AZ 85287, USA
H. D. Mittelmann
Affiliation:
Department of Mathematics, Arizona State University, Tempe, AZ 85287, USA
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Abstract

Energy stability theory has been applied to a basic state of thermocapillary convection occurring in a cylindrical half-zone of finite length to determine conditions under which the flow will be stable. Because of the finite length of the zone, the basic state must be determined numerically. Instead of obtaining stability criteria by solving the related Euler–Lagrange equations, the variational problem is attacked directly by discretization of the integrals in the energy identity using finite differences. Results of the analysis are values of the Marangoni number, MaE, below which axisymmetric disturbances to the basic state will decay, for various values of the other parameters governing the problem.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 217 , August 1990 , pp. 639 - 660
Copyright
© 1990 Cambridge University Press

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