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Viscous thermocapillary convection at high Marangoni number

Published online by Cambridge University Press:  20 April 2006

Stephen J. Cowley
Affiliation:
Department of Engineering Sciences and Applied Mathematics, The Technological Institute, Northwestern University, Evanston, Illinois 60201 Present address: Department of Applied Mathematics and Theoretical Physics, Silver Street, Cambridge CB3 9EW, U.K.
Stephen H. Davis
Affiliation:
Department of Engineering Sciences and Applied Mathematics, The Technological Institute, Northwestern University, Evanston, Illinois 60201

Abstract

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.

Type
Research Article
Copyright
© 1983 Cambridge University Press

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