Analytic continuation of series solution representing flow between plates

The flow of an incompressible fluid between two rectangular and circular plates is reinvestigated. The problem admits similarity solutions there by reducing unsteady Navier-Stokes equations to non-linear ordinary differential equation of order four involving a small parameter α=h(t)h(t)/v. The proposed new semi-analytic semi-numerical scheme is convenient in obtaining analytic continuation of series solution. The series so generated yields expression for pressure gradient and it is analyzed using Pade' approximants and other useful techniques (Van Dyke¹⁰) of series analysis.