Hermite-Pade approximation approach to nonlinear wall driven steady flow in a tube

Abstract

This paper investigates the nonlinear flow of an incompressible viscous fluid in a tube produced by the axial motion of the boundary wall. The problem admits similarity solutions, thereby reducing the steady Navier-Stokes equations to a parameter dependent fourth order ordinary differential equation. Analytical solutions are constructed for the problem using perturbation technique together with a special type of Hermite-Pade approximant. We obtained accurately the two turning points $R_1$, $R_2$ between which no similarity solutions exist. In addition, our results revealed exactly the asymptotic behaviour of skin friction, axial pressure gradient and the centre-line axial velocity as $R\rightarrow 0$ on the secondary solution branch.