Axisymmetric rotational stagnation point flow impinging on a radially stretching sheet

• Rotational stagnation-point flow impinging on a radially stretching surface.
• Flow governed by stretch rate to strain rate ratio β.
• Large beta asymptotics are presented.
• Wall shear stress is calculated.
• Dual solutions are found.
• Linear temporal stability analysis of dual solutions is performed.

The normal impingement of the rotational stagnation-point flow of Agrawal (1957) [8] on a sheet radially stretching at non-dimensional stretch rate β is studied. A similarity reduction of the Navier–Stokes equations yields an ordinary differential equation which is solved numerically over a range of β  . A unique solution exists at the turning point β=βtβ=βt and dual solutions are found in the region β>βtβ>βt where βt=−0.657βt=−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 β=0β=0 is provided, and the large-β 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.