Homann stagnation-point flow impinging on a biaxially stretching surface

The normal impingement of axisymmetric Homann stagnation-point flow on a surface executing perpendicular, planar, biaxial stretching is studied. The flow field generated is an exact solution of the steady, three-dimensional Navier-Stokes equations in the form of a similarity solution. It is shown that two sets of dual solutions exist, forming four different branches of steady solutions. For sufficiently small stretches (including compressions of the surface) the four branches exhibit a multi-branch spiralling behaviour in the surface shear stress parameter plane. The linear stability of the solutions are also examined, identifying only one stable solution for each set of parameters. (C) 2020 Elsevier Masson SAS. All rights reserved.