Axisymmetric rotational stagnation-point flow impinging on a permeable stretching/shrinking rotating disk

This paper extends the recent work by Weidman (2015) on the steady axisymmetric rotational stagnation-point flow impinging on a rotating disk to the case of a permeable stretching/shrinking rotating disk. Similarity variables are used to convert the Navier-Stokes equations to a pair of coupled ordinary differential equations governed by a dimensionless rotation rate α, the velocity of the wall relative to the outer flow λ and the wall transfer rate S. These equations are then solved numerically using the bvp4c function from MATLAB software. The skin friction coefficients or shear stress in both the radial and azimuthal directions are determined. It is found that, for given parameter values, up to three solutions can exist. Asymptotic expressions are derived for large stretching rates λ and for strong fluid withdrawal and injection as well as for rapid rotation rates α, these being compared with the numerically determined values.