Analysis of axisymmetric flow of a second order fluid near a stagnation point

The steady, laminar axisymmetric flow of a second order viscoelastic fluid near a stagnation point is considered. The viscoelasticity of the fluid gives rise to a boundary value problem in which the order of the differential equation exceeds the number of available boundary conditions. Nevertheless an exact numerical solution is obtained without imposing any restriction on the size of the non-Newtonian fluid parameters. It is shown that the solutions are possible only within certain range of values of these parameters. A perturbation solution valid for small values of the non-Newtonian parameters is also developed. It can not satisfactorily explain certain important features of the flow which can possibly be revealed by the exact solution only.