Forced convection: IV. Asymptotic forms for laminar and turbulent transfer rates

Mass transfer rates in laminar and turbulent nonseparated boundary layers are asymptotically expanded for small values of the diffusivity AB , with a uniform state on the mass transfer surface. Results for heat transfer follow by analogy. The thermal or binary Nusselt number at small net mass transfer rates is given asymptotically by a generalized penetration expression\documentclass{article}\pagestyle{empty}\begin{document}$$ \langle Nu\rangle \, = \,a_{00} Pe^{1/2} \, + \,a_{01} Pe^0 \, + \,.\,.\,.\,{\rm (A)} $$\end{document} for short times, or for boundary layers that duplicate the surface tangential motion. For flows past rigid interfaces, the long‐time average of 〈 Nu 〉 is given asymptotically by a generalized Chilton‐Colburn relation\documentclass{article}\pagestyle{empty}\begin{document}$$ \langle \overline {Nu} \rangle \, = \,b_{00} Pe^{1/3} \, + \,b_{01} Pe^0 \, + \,.\,.\,.\,{\rm (B)} $$\end{document} in regions of nonrecirculating motion. The measurable functions a ij and b ij depend only on the system shape and laminar or turbulent velocity field. Formal expressions for a 00 are given, and an expression for b 00 in steady flows. These results agree well with data on mass transfer operations in tubes, packed beds, and fluid‐fluid contactors.