Mass transfer from a cylindrical body in a linear ambient velocity distribution

We consider the two-dimensional problem of mass transport from a cylindrical body of circular cross section which is immersed in a fluid whose ambient velocity varies linearly with position. Such a flow is quantified by a single parameter ω representing the ratio of its associated vorticity to its characteristic rate-of-strain magnitude, ω=±1 corresponding to simple shear. Using matched asymptotic expansions to analyze the limit of small Péclet numbers, Peâ‰1, we find that the leading-order Nusselt number is 2/log(1/Pe)+λ(ω),wherein the function λ(ω) is provided in terms of simple quadratures. No steady solutions exist for |ω|>1, where the streamlines of the ambient flow are closed. The case of simple shear, analyzed by Frankel and Acrivos [Phys. Fluids 11, 1913 (1968)PFLDAS0031-917110.1063/1.1692218], is accordingly a borderline one. Using conformal mappings, the more general problem of arbitrary cross-sectional shape is recast as the above transport problem about a circle, with the Péclet number appropriately modified. While the more general problem is unsteady in the case of a freely suspended cylinder, the associated Nusselt number is independent of time.