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Mass transfer from a cylindrical body in a linear ambient velocity distribution
Phys. Rev. Fluids 4, 124503 – Published 11 December, 2019
DOI: https://doi.org/10.1103/PhysRevFluids.4.124503
Abstract
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 representing the ratio of its associated vorticity to its characteristic rate-of-strain magnitude, corresponding to simple shear. Using matched asymptotic expansions to analyze the limit of small Péclet numbers, , we find that the leading-order Nusselt number is wherein the function is provided in terms of simple quadratures. No steady solutions exist for , where the streamlines of the ambient flow are closed. The case of simple shear, analyzed by Frankel and Acrivos [Phys. Fluids 11, 1913 (1968)], 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.
Physics Subject Headings (PhySH)
Corrections
17 December, 2019
Correction: A misprint introduced during the production process has been fixed in the equation appearing in the abstract.
Article Text
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