Power law fluid model for blood flow through a tapered artery with a stenosis S. Nadeem a,⇑ , Noreen Sher Akbar a , Awatif A. Hendi b , T. Hayat a,b a Department of Mathematics, Quaid-i-Azam University 45320, Islamabad 44000 Pakistan b Department of Physics, Faculty of Science, King Saud University, P.O.Box 1846, Riyadh 11321, Saudi Arabia article info Keywords: Power law fluid Blood flow Tapered artery Stenosis Exact solution abstract In the present paper, blood flow through a tapered artery with a stenosis is analyzed, assuming the flow is steady and blood is treated as non-Newtonian power law fluid model. Exact solution has been evaluated for velocity, resistance impedance, wall shear stress and shearing stress at the stenosis throat. The graphical results of different types of tapered arteries (i.e. converging tapering, diverging tapering, non-tapered artery) have been exam- ined for different parameters of interest. Some special cases of the problem are also presented. Ó 2011 Elsevier Inc. All rights reserved. 1. Introduction Blood flow analysis through tapered arteries has been identified as one of the important area of research in the recent few decades, because blood flow analysis through tapered tubes or tapered arteries is an important factor in the pressure devel- opment. Blood flow problem through tapered arteries becomes difficult at some region because it has been observed through clinical and sub-clinical examinations that such a condition can lead to heomorrhage and local thrombosis. To see the effects of stenosis in the lumen of an artery, many researchers have studied blood flow in stenosed arteries. Some recent investi- gations in these areas are cited in the Refs. [1–5]. Few investigations have been made to study the blood flow in arteries by assuming blood as Newtonian fluid [6–8], but this assumption is not valid when there is a low shear rate. Taking into account the non-Newtonian behavior of blood, described by the micropolar fluid, Mekheimer and El Kot [9] studied the micropolar fluid model for blood flow through a tapered artery with a stenosis. Analysis of non-linear blood flow in a ste- nosed flexible artery was studied by [10]. They observed that arteries are narrowed by the development of atherosclerotic plaques that protrude into the lumer resulting in stenosed arteries. The pulsatile flow of blood through mild stenosed artery is studied by Sankar and Lee [11]. Casson fluid and Herschel–Bulkley fluid are used in the studies of blood flow by Kapur and Iida [12,13] in order to analyze the arterial constriction on the flow characteristics of blood. A non-Newtonian blood flow through a tapered overlapping stenosed artery is considered by Zuhaila et al. [14]. They mentioned in their study that blood flow through a stenosed artery is very important because of the fact that the development of many cardiovascular diseases are related to the nature of blood vessels walls. Keeping in viewing the importance of above analysis, the aim of the present article is to discuss the power law fluid model for blood flow through a tapered artery with mild stenosis. Exact solution of the governing equations along with the bound- ary conditions of stenosed symmetric artery has been calculated. The expressions for velocity, resistance impedance, wall shear stress and shearing stress at the stenosis throat have been examined. The graphical behavior of different types of tapered arteries have been examined for different parameters of interest. 0096-3003/$ - see front matter Ó 2011 Elsevier Inc. All rights reserved. doi:10.1016/j.amc.2011.01.026 ⇑ Corresponding author. E-mail addresses: snqau@hotmail.com (S. Nadeem), noreensher@yahoo.com (Noreen Sher Akbar). Applied Mathematics and Computation 217 (2011) 7108–7116 Contents lists available at ScienceDirect Applied Mathematics and Computation journal homepage: www.elsevier.com/locate/amc