Flow of a second grade fluid through curved channel of non-uniform width bounded below by a permeable bed

Creeping flow of an incompressible second grade fluid in a channel of varying width bounded below by a porous bed is solved using three approximate methods based on three different geometrical configurations. Expressions for velocity and pressure gradient are calculated for each method. Weight functions are calculated for all three methods and are evaluated for different values porous layer parameter. It is observed that the weight functions are influenced by porous layer parameter. The obtained results are applied to idealized stenosis geometry and resistance to the flow and shear stress are calculated. It is noticed that as we increase the value of porous layer parameter resistance to the flow in the stenosed region decreases as expected. However with increasing the values of porous layer parameter and non-Newtonian parameter, the shear stress increases in stenosed region. Previous published results are obtained as special case to current study.