Transient Flow of Jeffrey Fluid over a Permeable Wall

Transient incompressible flows of Jeffrey fluids over a permeable, flat, and infinite plate have been investigated. The plate motion is an oscillatory translation along the x-axis. Using the Laplace transform and perturbation method, the analytical solution for the velocity field in the transform domain has been obtained. The velocity field in the real domain has been determined by using the numerical Stehfest’s algorithm for the Laplace transform inversion. To have a validation of the obtained solution, we have determined the analytical solution for the flow without transpiration. It was found that when the transpiration parameter approaches zero, the solution for the flow with transpiration tends to the solution corresponding to the case without perspiration. The influence of the system parameters on fluid motion has been investigated by numerical simulations and graphical illustrations prepared with the software package Mathcad.