Abstract

This paper deals with an analytical solution of oscillatory flow of an incompressible second grade fluid in a channel. The flow in the channel is driven by suction at the permeable walls, whereas small amplitude time harmonic pressure waves are responsible for oscillations in the velocity field. The time independent axial velocity and the time dependent oscillatory axial velocity are calculated analytically. The important physical quantities like the velocity profile, amplitude of the oscillation and penetration depth of the wave are given special emphasis. The effects of second grade parameter and suction parameter on these quantities are particularly examined. A comparative study of the oscillatory flow for second grade with viscous fluid is also made.

Key words: Oscillatory channel flow, second grade fluid, shear stress, perturbation solution, Wentzel-Kramers-Brillouin (WKB) approximation.