Pulsatile Flow of Hershel- Bulkley Fluid in Tapered Blood Vessels

The present paper sheds some light on investigating the effect of pulsatility on flow through a tapered artery. Blood has been represented by a nonNewtonian fluid obeying Herschel-Bulkley equation. Using the Reynolds number as the perturbation parameter, a perturbation technique is adopted to solve the resulting quasi-steady non-linear coupled implicit system of differential equations. Analytical expressions for velocity, volumetric flow rate, wall shear stress and the mean flow resistance have been obtained. It is observed that the wall shear stress and flow resistance increase for increasing value of taper angle and the axial distance. It is pertinent to point out that the phase lag between the pressure gradient and wall shear stress or flow rate is found to be 2.03 degrees and this phase lag becomes independent of the axial distance and taper angle. The present approach has; in general, validity in comparison with many mathematical models developed by others and may be applied to any mathematical model by taking into account of any type of rheological property of blood. Finally, some biorheological applications of the present model have briefly been discussed. Keywords—non-newtonian fluid; pulsatile flow, tapered artery; walls shear stress; resistance to flow