Travelling wave solutions for the unsteady flow of a third grade fluid induced due to impulsive motion of flat porous plate embedded in a porous medium

Abstract

This work describes the time-dependent flow of an incompressible third grade fluid filling the porous half space over an infinite porous plate. The flow is induced due to the motion of the porous plate in its own plane with an arbitrary velocity V(t). Translational type symmetries are employed to perform the travelling wave reduction into an ordinary differential equation of the governing nonlinear partial differential equation which arises from the laws of mass and momentum. The reduced ordinary differential equation is solved exactly, for a particular case, as well as by using the homotopy analysis method (HAM). The better solution from the physical point of view is argued to be the HAM solution. The essentials features of the various emerging parameters of the flow problem are presented and discussed.