An analytical solution to unsteady axisymmetrical stagnation flow

Abstract

The problem of unsteady axisymmetrical stagnation flow is treated with the help of Gyarmati’s variational principle which genuinely describes non-equilibrium linear transport processes in space and time. An optimal third degree polynomial trial function is selected to represent the flow field inside the boundary layer region and the variational principle is elegantly formulated. The hydrodynamical boundary layer thickness which depends on time alone is derived in a closed form as the Euler-Lagrange equation of the variational principle. The accuracy of the current analytical solution is tested by comparing it with an exact solution available for the case of steady flow. The agreement is excellent: the error involved in the present solution hardly exceeds 0.2%.