Effect of couple stresses on the pulsatile flow through a constricted annulus

In this Note, the pulsatile flow of an incompressible couple stress fluid through an annulus with mild constriction at the outer wall is considered. This configuration is intended as a simple model for studying blood flow in a stenosed artery when a catheter is inserted into it. An analytical expression in terms of Bessel functions of the first and second kind is obtained for the velocity component. The impedance (resistance to the flow) and wall shear stress are calculated and their variation with respect to the couple stress fluid parameter, height of the constriction and size of the catheter on the impedance and wall shear stress is studied graphically. It is observed that increase in the catheter size increases the resistance to the flow as well as the wall shear stress while the trend is reversed in case of couple stress fluid parameter.