On unsteady flow of an elastico-viscous fluid past an infinite plate with variable suction

Approximate solutions of the Navier-Stokes equations are derived through the Laplace transform for two dimensional, incompressible, elastico-viscous flow past a flat porous plate. The flow is assumed to be independent of the distance parallel to the plate. General formulae for the velocity distribution, skin friction and displacement thickness as functions of the given free stream velocity and suction velocity are obtained. The response of skin friction to the impulsive perturbations in the stream and suction velocities is studied. It is found that the order of singularity in the skin friction at t=0 increases due to the elastic property of the fluid in the impulsive case. When the stream is accelerated the skin friction still anticipates the velocity but the time of anticipation is reduced from 1/4 to (1/4) (1—k), where k is the elastic parameter of the fluid. It is found that in general the resistance of the elastico-viscous fluids to an impulsive increase in the stream velocity is greater than the viscous fluids, the elasticoviscous fluids also reach the steady state earlier than the viscous fluids.