Axisymmetric rotational stagnation point flow impinging on a radially stretching sheet

The normal impingement of the rotational stagnation-point flow of Agrawal (1957) [8] on a sheet radially stretching at non-dimensional stretch rate beta is studied. A similarity reduction of the Navier-Stokes equations yields an ordinary differential equation which is solved numerically over a range of beta. A unique solution exists at the turning point beta = beta(t) and dual solutions are found in the region beta > beta(t) where beta(t) = - 0.657 is the turning point in the parametric shear stress curve separating upper from lower branch solutions. An analysis of solutions near the Agrawal point beta = 0 is provided, and the large-beta asymptotic behavior of solutions is determined. Sample velocity profiles along both solution branches are presented. A linear temporal stability analysis reveals that solutions along the upper branch are stable while those on the lower branch are unstable. (C) 2016 Elsevier Ltd. All rights reserved.