Flow of a second grade fluid through constricted tube using integral method

The steady flow of a second grade fluid through constricted tube for mild stenosis is modeled and analyzed theoretically. The governing equations are simplified by implying an order-of-magnitude analysis. Based on Karman Pohlhausen procedure polynomial solution for velocity profile is presented. Expressions for pressure gradient, shear stress, separation and reattachment points are also calculated. The effects of nondimensional parameters emerging in the model on the velocity profile, shear stress, pressure gradient are discussed and depicted graphically. The effect of non-Newtonian parameter on velocity profile, wall shear stress and pressure gradient is also analyzed. It is found that the Reynolds number strongly effect the wall shear stress, separation and reattachment points.