Slip Effects on Pulsatile Flow of Blood through a Stenosed Arterial Segment under Periodic Body Acceleration

A theoretical investigation concerning the influence of externally imposed periodic body acceleration on the flow of blood through a time-dependent stenosed arterial segment by taking into account the slip velocity at the wall of the artery has been carried out. A mathematical model is developed by treating blood as a non-Newtonian fluid obeying the Casson fluid model. The pulsatile flow is analyzed by considering a periodic pressure gradient and the inertial effects as negligibly small. A suitable generalized geometry for time-dependent stenosis is taken into account. Perturbation method is used to solve the coupled implicit system of nonlinear differential equations that govern the flow of blood. Analytical expressions for the velocity profile, volumetric flow rate, and wall shear stress are obtained. A thorough quantitative analysis has been made through numerical computations of the variables involved in the analysis that are of special interest in this study. The computational results are presented graphically. The results for different values of the parameters involved in the problem under consideration presented here show that the flow is appreciably influenced by slip velocity in the presence of periodic body acceleration. 1. Introduction There are number of evidences available in the scientific literatures that vascular fluid dynamics plays a major role in the development and progression of arterial diseases. Local narrowing in the lumen of an arterial segment is commonly referred to as stenosis. This occurs due to deposition of various substances like cholesterol on the endothelium of arterial wall. When an obstruction is developed in an artery, one of the most serious consequences is the increased resistance and the associated reduction of the blood flow to the particular vascular bed supplied by the artery. Thus, the presence of a stenosis leads to stroke, heart attack, and serious circulatory disorders. Different studies on the flow of blood through arterial segments with obstruction have been carried out experimentally and theoretically by several investigators [1–7]. The assumption of Newtonian behavior of blood is acceptable for high shear rate flow through larger arteries [4]. But, blood, being a suspension of cells in plasma, exhibits non-Newtonian behavior at low shear rate in small diameter arteries (0.02–0.1？mm) [8]. Several studies were performed to analyze the steady flow of blood, treating it as a Newtonian fluid [9, 10]. It is well known that blood flow in the human circulatory system is caused by the pumping action of the