Abstract
An analysis of blood flow through a tapered artery with stenosis and dilatation has been carried out where the blood is treated as incompressible Herschel-Bulkley fluid. A comparison between numerical values and analytical values of pressure gradient at the midpoint of stenotic region shows that the analytical expression for pressure gradient works well for the values of yield stress till 2.4. The wall shear stress and flow resistance increase significantly with axial distance and the increase is more in the case of converging tapered artery. A comparison study of velocity profiles, wall shear stress, and flow resistance for Newtonian, power law, Bingham-plastic, and Herschel-Bulkley fluids shows that the variation is greater for Herschel-Bulkley fluid than the other fluids. The obtained velocity profiles have been compared with the experimental data and it is observed that blood behaves like a Herschel-Bulkley fluid rather than power law, Bingham, and Newtonian fluids. It is observed that, in the case of a tapered stenosed tube, the streamline pattern follows a convex pattern when we move from r/R = 0 to r/R = 1 and it follows a concave pattern when we move from r/R = 0 to r/R = −1. Further, it is of opposite behaviour in the case of a tapered dilatation tube which forms new information that is, for the first time, added to the literature.
Highlights
Blood flow through a stenosed artery is one of the important areas of research because a stenosed artery affects the entire cardiovascular system
A comparison between numerical values and analytical values of pressure gradient at the midpoint of stenotic region shows that, up to τy = 2.4, the maximum error is less than 1.4% and for dilatation region the maximum error is less than 6%
This implies that the analytical expression for pressure gradient works well for the values of yield stress till 2.4
Summary
Blood flow through a stenosed artery is one of the important areas of research because a stenosed artery affects the entire cardiovascular system. Young [1] and Young and Tsai [2] studied the effects of stenosis on blood flow through arteries. Pulsatile flow of blood through a stenosed porous medium under the influence of periodic body acceleration considering blood as a Newtonian fluid has been studied by El-Shahed [11]. El-Shehawey et al [12] have examined the pulsatile flow of blood through a tube considering blood as a Newtonian fluid taking into account the body acceleration and porosity of the tube. Sharma et al [13] investigated the effects of radial variation of hematocrit and magnetic field on the flow of blood as a Newtonian fluid through a porous medium in a stenosed artery
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