Viscous thermocapillary convection at high Marangoni number

A liquid, contained in a quarter plane, undergoes steady motion due to thermocapillary forcing on its upper boundary, a free surface separating the liquid from a passive gas. The rigid vertical sidewall has a strip whose temperature is elevated compared with the liquid at infinity. A boundary-layer...

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Bibliographic Details
Published in:Journal of fluid mechanics 1983-10, Vol.135 (1), p.175-188
Main Authors: Cowley, Stephen J., Davis, Stephen H.
Format: Article
Language:English
Subjects:
boundary layers
convection
Exact sciences and technology
Fluid dynamics
Fluid Mechanics And Heat Transfer
Fundamental areas of phenomenology (including applications)
gases
liquids
Physics
Turbulent flows, convection, and heat transfer
viscosity
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Summary:A liquid, contained in a quarter plane, undergoes steady motion due to thermocapillary forcing on its upper boundary, a free surface separating the liquid from a passive gas. The rigid vertical sidewall has a strip whose temperature is elevated compared with the liquid at infinity. A boundary-layer analysis is performed that is valid for large Marangoni numbers M and Prandtl numbers P. It is found that the Nusselt number N for the horizontal heat transport satisfies $N \sim \min (M^{\frac{2}{7}}, M^{\frac{1}{5}} P^{\frac{1}{10}})$. Generalizations are discussed.
ISSN:0022-1120
1469-7645
DOI:10.1017/S002211208300302X