Effect of a time dependent stenosis on flow of a second grade fluid through porous medium in constricted tube using integral method

In this article, effect of a time-dependent stenosis on the flow of a non-Newtonian fluid through porous medium in axially symmetric constricted tube is analyzed using integral method. The study is based on a second grade fluid model. An order of magnitude analysis is performed to simplify the model for mild constriction. Integral approach coupled with the fourth-order polynomial solution for the velocity profile is used. The effect of different non-dimensional parameters such as Reynolds number, non-Newtonian parameter, porous parameter and time emerging in the model on velocity profile, pressure gradient, wall shear stress, separation and reattachment data are presented and discussed graphically. Velocity of the fluid increases with an increase in time, while with the increase in porous parameter velocity of the fluid decreases. It is noted that Reynolds number provides a mechanism to control the attachment and de-attachment points for different values of porous parameter. The present study is valid only for mild stenosis.