An analytical solution of the Navier-Stokes equations for unsteady backward stagnation-point flow with injection or suction

A particular solution of the unsteady axisymmetric incompressible Navier-Stokes equations is obtained in the classical Birkhoff similarity framework. The solution describes a decelerating backward stagnation-point flow with uniform injection or suction from a porous boundary (plate). Although the solution is completely analytical, it is limited in scope to one particular case each of injection and suction. In the case of suction, a single dividing streamline is found in the lee of the plate, while in the case of injection, two dividing streamlines are found. In this latter case, the dividing streamlines bound a nearly stagnant layer containing a weak vortex. Analytical results are also presented for the temperature field in the forced convection regime.