The unsteady flow of a third-grade fluid caused by the periodic motion of an infinite wall with transpiration

In this work, the unidirectional flow of an incompressible electrically conducting third-grade fluid past a vertical transpiration wall through a porous medium with time-dependent periodic motion is presented. The nonlinear partial differential equations are transformed to ordinary differential equation by means of symmetry reductions. The reduced equation is then solved analytically for steady-state and time-dependent transient parts. The time series of the transient flow velocity for different pertinent parameters are examined through plots. During the course of computation, it was observed that the time-dependent transient and steady-state solutions agree very ell at large value of time when the ratio is related to fluid parameters gamma(*)/gamma > 1. (C) 2015 Faculty of Engineering, Alexandria University. Production and hosting by Elsevier B.V.