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The Quarterly Journal of Mechanics and Applied Mathematics 1990 43(1):135-159; doi:10.1093/qjmam/43.1.135
© 1990 by Oxford University Press
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HEAT AND MASS TRANSFER FROM A FILM INTO STEADY SHEAR FLOW

CHRISTOPHER G. PHILLIPS

( Physiological Flow Studies Unit and Department of Mathematics, Imperial College Prince Consort Road, London SW7 2AZ )

The problem of mass or heat transfer into steady shear flow from a conducting film, mounted flush in an insulating wall, is considered. Under suitable conditions, the transfer rate depends only on the Péclet number (a dimensionless measure of shear rate) and on the geometry of the film. We present a calculation of the transfer rate for a disc-shaped film at low Péclet number by the method of matched asymptotic expansions. A corrected version of the series of Springer (1) for a strip-shaped film at high Péclet number is given, and the corresponding case of a disc is discussed. The results are compared with existing analytical and numerical expressions.


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