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Time-dependent thermocapillary convection in a rectangular cavity: numerical results for a moderate Prandtl number fluid

Published online by Cambridge University Press:  26 April 2006

L. J. Peltier  and
S. Biringen
L. J. Peltier
Affiliation:
Department of Aerospace Engineering Sciences, University of Colorado, Boulder, CO, USA Present address: Department of Meteorology, Pennsylvania State University, State College, Pennsylvania, PA 16802, USA.
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Abstract

The present numerical simulation explores a thermal–convective mechanism for oscillatory thermocapillary convection in a shallow rectangular cavity for a Prandtl number 6.78 fluid. The computer program developed for this simulation integrates the two-dimensional, time-dependent Navier–Stokes equations and the energy equation by a time-accurate method on a stretched, staggered mesh. Flat free surfaces are assumed. The instability is shown to depend upon temporal coupling between large-scale thermal structures within the flow field and the temperature sensitive free surface. A primary result of this study is the development of a stability diagram presenting the critical Marangoni number separating the steady from the time-dependent flow states as a function of aspect ratio for the range of values between 2.3 and 3.8. Within this range, a minimum critical aspect ratio near 2.3 and a minimum critical Marangoni number near 20 000 are predicted, below which steady convection is found.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 257 , December 1993 , pp. 339 - 357
Copyright
© 1993 Cambridge University Press

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