EFFECTS OF STENOSIS ON POWER LAW FLUID FLOW OF BLOOD IN BLOOD VESSELS

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Journal for Research| Volume 01| Issue 09 | November 2015 ISSN: 2395-7549

Effects of Stenosis on Power Law Fluid Flow of Blood in Blood Vessels Subhash Chandra Department of Mathematical Science Indian Institute of Technology (Baranas Hindu University), Varanasi 221002, India

Pragya Singh Department of Mathematical Science Indian Institute of Technology (Baranas Hindu University), Varanasi 221002, India

Rana Waleed Bhnam Hndoosh Department of Software Engineering College of Computers Sciences & Mathematics, Mosul University, Iraq

Abstract In this paper we assume that the blood is to be a Non-Newtonian and incompressible and Homogeneous fluid. An investigation has been done for the resistance to flow across mild stenosis situated symmetrically on steady blood flow through arteries with uniform or non-uniform cross section. An analytical solution for Power law fluid has been obtained. For the physiological insight of the problem various parameters systemic and pulmonary artery are taken and the study reveals that as the height of the stenosis increases in uniform or non-uniform portion of the artery, the resistance parameter and shear stress also steadily increases, whereas, flow rate decreases steadily and we analyze some cases between flux, pressure gradient and radius and give some significant results. Keywords: Resistance Parameter, Arterial Stenosis, Power Law Fluid, Wall Shear Stress, Flux, Pressure Gradient, Pulmonary Artery, Flow Rate _______________________________________________________________________________________________________

I. INTRODUCTION Diseases in the blood vessels and in the heart, such as heart attack and stroke, are the major causes of mortality worldwide. The underlying cause for these events is the formation of lesions, knows as atherosclerosis, in the large and medium sized arteries in the human circulation. The term stenosis or we can say that the deposit of cholesterol is the development of arteriosclerotic or other types of abnormal tissue development. When stenosis is constructed in artery then blood flow is obstructed. Stenosis could affect one or more segments of the human cardiovascular system studies on initiation and growth of stenosis (arteriosclerotic plaques) in the human cardiovascular system have been carried out from several view-points. Arteriosclerosis is a common disease, which severely influences human health. Our body is made up of miles and miles of hollow tubes. Many small and large hollow space and even well establish and reinforce canals. It has been found that the initiation and localization of arteriosclerosis is closely related to local heamodynamic factors. Due to these serious consequences, attention has been given in studies of blood flow in stenosis region under different conditions. Different mathematical models have been studied by some researchers to explore the various aspects of blood flow in stenosed artery (Smith et al. 2002 and Shukla et al. (1980a, b). Srivastava (2002) investigated the effects of stenosis shape and red cell concentration (hematocrit) on blood flow characteristics due to the presence of stenosis. Ponalagusamy (2007) considered a mathematical model for blood flow through stenosed arteries with axially variable peripheral layer thickness and variable slip at the wall. Mishra et al. (2010) studied that as the height of the stenosis increases in blood vessels, the shear stress and resistance parameter steadily increases whereas, flow rate decreases steadily.

Fig. 1: Blood Artery

Fig. 2: Stenosis in Artery

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