American Journal of Computational Mathematics, 2016, 6, 365-376 http://www.scirp.org/journal/ajcm ISSN Online: 2161-1211 ISSN Print: 2161-1203 DOI: 10.4236/ajcm.2016.64036 December 29, 2016 The Effects of Post-Stenotic Dilatations on the Flow of Couple Stress Fluid through Stenosed Arteries K. Maruthi Prasad, T. Sudha * , M. V. Phanikumari Department of Mathematics, School of Technology, GITAM University, Hyderabad, India Abstract The flow of incompressible couple stress fluid in a circular tube with stenosis and di- latations has been investigated. The stenosis was assumed to be axially symmetric and mild. The flow equations have been linearized and the expressions for the resis- tance to the flow, velocity, pressure drop, wall shear stress have been derived. The ef- fects of various parameters on these flow variables have been investigated. It is found that the resistance to the flow and pressure drop increase with height of the stenosis and decrease with post stenotic dilatation. Pressure drop decreases with couple stress fluid parameter for both stenosis and post stenotic dilatation. Further, the wall shear stress increases with height of the stenosis and couple stress parameter but decreases with post stenotic dilatation and couple stress fluid parameter. Keywords Stenosis, Dilatation, Wall Shear Stress, Resistance to the Flow, Couple Stress Fluid Parameter 1. Introduction In the present world, diseases in the blood vessels and in the heart like heart attack and stroke are major health hazards causing a large number of deaths .The main reason for these deaths is stenosis. The actual causes for stenosis are not well known but it has been suggested that deposits of fatty substances, cholesterol, cellular waste products on the arterial wall are called as stenosis. When stenosis is formed in the artery then these fatty substances can block an artery and blood flow will be restricted. This may lead to heart attacks, hypertension and brain strokes etc. Hence formation of the stenosis i.e. abnormal and unnatural growth on the arterial wall can disturb the normal functioning How to cite this paper: Maruthi Prasad, K., Sudha, T. and Phanikumari, M.V. (2016) The Effects of Post-Stenotic Dilatations on the Flow of Couple Stress Fluid through Stenosed Arteries. American Journal of Com- putational Mathematics, 6, 365-376. http://dx.doi.org/10.4236/ajcm.2016.64036 Received: November 21, 2016 Accepted: December 26, 2016 Published: December 29, 2016 Copyright © 2016 by authors and Scientific Research Publishing Inc. This work is licensed under the Creative Commons Attribution International License (CC BY 4.0). http://creativecommons.org/licenses/by/4.0/ Open Access