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Thermal vibrational convection in near-critical fluids. Part 2. Weakly non-uniform heating

Published online by Cambridge University Press:  15 September 2006

D. LYUBIMOV ,
T. LYUBIMOVA ,
A. VOROBEV ,
A. MOJTABI  and
B. ZAPPOLI
D. LYUBIMOV
Affiliation:
Theoretical Physics Department, Perm State University, Perm, 614990, Russia
T. LYUBIMOVA
Affiliation:
Institute of Continuous Media Mechanics, Perm, 614013, Russia
A. VOROBEV
Affiliation:
Theoretical Physics Department, Perm State University, Perm, 614990, Russia Present address: The University of Michigan – Dearborn, Dearborn MI 48128, USA.
A. MOJTABI
Affiliation:
Institut de Mecanique des Fluides, Toulouse, 31062, France
B. ZAPPOLI
Affiliation:
Centre National d'Etudes Spatiales, Toulouse, 31055, France
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Abstract

The governing equations and effective boundary conditions to describe thermal vibrational convection in a near-critical fluid are derived with the help of the multiple-scale method and averaging procedure. In contrast to Part 1, this paper focuses on the effects of density non-homogeneities caused not by external heating but by vibrational and gravity stratifications due to the divergent mechanical compressibility of near-critical media. It is shown that vibrations generate non-homogeneities in the average temperature, which result in the onset of thermal convection even under isothermal boundary conditions. An agreement with the results of previous numerical and asymptotical analyses and with experiments is found.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 564 , 10 October 2006 , pp. 185 - 196
Copyright
© 2006 Cambridge University Press

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