Radial stagnation flow on a rotating circular cylinder with uniform transpiration

Abstract

Radial stagnation flow of strain rate k impinging on a cylinder with uniform transpiration U₀ and rotating at constant angular velocity ω is investigated. An exact reduction of the Navier-Stokes equations to a primary nonlinear equation for the meridional flow similar to that found by Wang [1] and a secondary linear equation for the azimuthal flow is obtained. The governing parameters are the stagnation-flow Reynolds number R = ka²/2v, the dimensionless transpiration S = U⁰/ka, and the dimensionless rotation rate ω = ω/k, where a is the cylinder radius and v is the kinematic viscosity of the fluid. The boundary-value problem is solved by numerical integration and by asymptotic analysis in certain limits. The results are succinctly summarized in plots of the axial and azimuthal shear-stress parameters as functions of R and S. Sample velocity profiles, meridional streamfunction plots, and projections of particle paths for both suction and blowing are given. An interesting double-layer structure in the azimuthal velocity profile, consisting of a removed free shear layer connected to a wall boundary layer, is observed at large values of blowing. This feature is consistent with results obtained from the asymptotic analysis.