Hindawi Publishing Corporation ISRN Biomedical Engineering Volume 2013, Article ID 925876, 10 pages http://dx.doi.org/10.1155/2013/925876 Research Article Slip Effects on Pulsatile Flow of Blood through a Stenosed Arterial Segment under Periodic Body Acceleration A. Sinha, G. C. Shit, and P. K. Kundu Department of Mathematics, Jadavpur University, Kolkata 700032, India Correspondence should be addressed to G. C. Shit; gopal iitkgp@yahoo.co.in Received 17 June 2013; Accepted 7 July 2013 Academic Editors: A. Cappozzo and D. S. Naidu Copyright © 2013 A. Sinha et al. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. A theoretical investigation concerning the infuence of externally imposed periodic body acceleration on the fow 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 fuid obeying the Casson fuid model. Te pulsatile fow is analyzed by considering a periodic pressure gradient and the inertial efects 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 diferential equations that govern the fow of blood. Analytical expressions for the velocity profle, volumetric fow 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. Te computational results are presented graphically. Te results for diferent values of the parameters involved in the problem under consideration presented here show that the fow is appreciably infuenced by slip velocity in the presence of periodic body acceleration. 1. Introduction Tere are number of evidences available in the scientifc literatures that vascular fuid 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. Tis occurs due to deposition of vari- ous 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 fow to the particular vascular bed supplied by the artery. Tus, the presence of a stenosis leads to stroke, heart attack, and serious circulatory disorders. Diferent studies on the fow of blood through arterial segments with obstruction have been carried out experimentally and theoretically by several investigators [1–7]. Te assumption of Newtonian behavior of blood is acceptable for high shear rate fow through larger arteries [4]. But, blood, being a suspension of cells in plasma, exhibits non-Newtonian behavior at low shear rate (̇  < 10/) in small diameter arteries (0.02– 0.1 mm) [8]. Several studies were performed to analyze the steady fow of blood, treating it as a Newtonian fuid [9, 10]. It is well known that blood fow in the human circulatory system is caused by the pumping action of the heart, which in turn produces a pulsatile pressure gradient throughout the system [11]. Human heart is a muscular pump and due to contraction and expansion of heart muscles, there produces a pressure diference in its systolic and diastolic conditions, popularly known as pressure pulse which physicians check at the wrist. Te cyclic nature of heart pump creates pulsatile conditions in all arteries. Te ejects and flls with blood in alternating cycles are called systolic and diastolic. Blood is pumped out of the heart during systolic, whereas the heart rests during diastole and no blood is ejected. Pressure and fow rate are characteristic in pulsatile shapes that vary in diferent parts of the arterial system. Tus, several researchers have studied pulsatile fow of blood, treating it as a Newtonian fuid [12–14]. Long et al. [8] numerically investigated the pulsatile fow behaviour of blood in the poststenotic region by considering inlet diameter as 8 mm, prestenotic length 48 mm, poststenosis domain 180 mm, and stenosis length 16.07 mm. Clark [1] performed the experimental studies of the pulsatile fow in a model of aortic stenosis taking the