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Influence of Variable Viscosity on the Onset of Hydrothermal Waves in Thermocapillary Liquid Bridges
Author(s) -
Kozhoukharova Zh.,
Kuhlmann H.C.,
Wanschura M.,
Rath H.J.
Publication year - 1999
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/(sici)1521-4001(199908)79:8<535::aid-zamm535>3.0.co;2-7
Subject(s) - viscosity , mechanics , reynolds number , wavenumber , flow (mathematics) , inviscid flow , thermodynamics , physics , rotational symmetry , marangoni number , convection , materials science , optics , turbulence , marangoni effect
Abstract The float‐zone crystal‐growth process is investigated in the framework of the half‐zone model. The influence of a temperature‐dependent viscosity on the axisymmetric steady thermocapillary flow and its stability with respect to nonaxisymmetric perturbations is examined by means of a linear‐stability analysis. The onset of oscillatory convection is studied numerically by a mixed Chebyshev‐collocation finite‐difference method. Detailed calculations have been carried out for PR = 4 and unit aspect ratio. It is found that the temperature‐dependent viscosity decreases the critical Reynolds number for the onset of three‐dimensional flow. Since the threshold shift is a function of the azimuthal wavenumber of the neutral mode, the critical mode may depend on the magnitude of the viscosity variation.

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