Abstract
In a number of physical systems a surface tension driven flow is established in a shallow layer of liquid as a result of heat or mass transfer to the free surface. Such transfer processes often produce a thin temperature or concentration boundary layer near the free surface. We have considered the relatively simple situation when this occurs in shallow two-dimensional channel flow under steady conditions. It is shown that the properties of the boundary layer can be obtained by solving a sequence of parabolic partial differential equations and that the shape of the free surface results from the solution of an integral equation. The simple case of uniform surface transfer has been considered, but the analysis developed can be extended to more complex situations.
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