Pulsatile flow of biviscous fluid through a tube of varying cross-section

In this paper, a pulsatile flow of a biviscous fluid in a circular tube of varying cross-section has been considered for investigation. The study helps to draw the characteristics of blood, the pressure drop and the wall shear stress on the inner wall of small blood vessels and capillaries where suction/injection velocity arises and Reynolds number is very low. The effects of Reynolds number, apparent viscosity coefficient and leakage parameter on the streamlines, pressure drop and wall shear stress have been discussed and shown graphically for suction and injection, respectively. The wall of the tube is supposed to be permeable and a normal velocity of the fluid at the wall is prescribed to consider the fluid exchange across the wall. Both analytic and numerical solutions are given. Using the perturbation technique, we analyze the problem for low Reynolds numbers and small oscillation amplitude. Lastly, the simulations are given to demonstrate the effectiveness and excellent tracking performance of the proposed control scheme.