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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 ~ min (M2/7, M1/5 P1/10) . Generalizations are discussed.
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Cowley et al. (1983) studied this question.
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