Is there a well established mass transfer correlation for fluid-solid interfaces in a rectangular channel?
When you don't have specific experimental results or empirical correlations, use Reynolds Analogy (St=f/2) for heat transfer. For mass transfer, use the Chilton-Colburn Analogy (f/2=Sh/Re/Sc^(1/3)). This works for entrances, exits, bundles, tube sheets, and all sorts of other complex geometries. If you need the friction factor (f) you can find Crane Technical Paper 410 (Flow of Fluids through Valves, Fittings, and Pipe) free online.
By analogy, you can use any suitable heat transfer correlation, just replace Nu with Sh and Pr with Sc. For laminar flows, be cautious of the boundary condition. Also, for significant mass transfer rates, the mass transfer coefficient should be corrected by using the Ackerman correction.
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