Diffusion to a Circular Cylinder in Shear Flows

Fixed cylinder. Let us consider diffusion to the surface of a fixed circular cylinder in a steady-state linear shear Stokes (Re - 0) flow in the plane normal to the cylinder axis. The velocity distribution of such a flow remote from the 

Coefficients A and m in formula (4.11.2) for rods of various shapes perpendicular to the flow direction 

The solution of the corresponding mass exchange problem for a circular cylinder and an arbitrary shear flow was obtained in [353] in the diffusion boundary layer approximation. It was shown that an increase in the absolute value of the angular velocity Cl of the shear flow results in a small decrease in the intensity of mass and heat transfer between the cylinder and the ambient 

It follows from (4.11.3) that in the region -1 fl +1, the mean Sherwood number varies only slightly (the relative increment in the mean Sherwood number as Iflfil varies from 0 to 1 is at most 1.3%). In the special cases of purely straining (CIe = 0) and purely shear (Ifi l = 1) linear Stokes flow past a circular cylinder, formula (4.11.3) turns into those given in [342, 343]. 

In the mass exchange problem for a circular cylinder freely suspended in linear shear flow, no diffusion boundary layer is formed as Pe - oo near the surface of the cylinder. The concentration distribution is sought in the form of a regular asymptotic expansion (4.8.12) in negative powers of the Peclet number. The mean Sherwood number remains finite as Pe - oo. This is due to the fact that mass and heat transfer to the cylinder is blocked by the region of closed circulation. As a result, mass and heat transfer to the surface is mainly determined by molecular diffusion in the direction orthogonal to the streamlines. In this case, the concentration is constant on each streamline (but is different on different streamlines). 

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