Radial stagnation flow on a rotating circular cylinder with uniform transpiration
Radial stagnation flow of strain rate \(k\) impinging on a cylinder with uniform transpiration \(U_0\) and rotating at constant angular velocity \(\omega\) is investigated. An exact reduction of the Navier-Stokes equations to a primary nonlinear equation for the meridional flow and a secondary linear equation for the azimuthal flow is obtained. The governing parameters are the stagnation-flow Reynolds number \(R= ka^2/2 \nu\), the dimensionless transpiration \(S=U_0/k a\), and the dimensionless rotation rate \(\Omega= \omega/k\), where \(a\) is the cylinder radius and \(\nu\) 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 summarized in plots of the axial and azimuthal shear-stress parameters as functions of \(R\) and \(S\).
primary nonlinear equation for meridional flow
secondary linear equation for azimuthal flow
double-layer structure in azimuthal velocity profile
scientific article; zbMATH DE number 1182026