e-ΠİȡȚοįȚțό ΕπȚıIJȒȝηȢ & ΤİχȞοȜογȓαȢ e-Journal of Science & Technology (e-JST) http://e-jst.teiath.gr 1 BLOOD FLOW THROUGH A BELL-SHAPED STENOSIS IN CATHETERIZED ARTERIES Rupesh K. Srivastav and Atul Kumar Agnihotri 1 Department of Mathematics, Ambalika Institute of Management & Technology, Lucknow, India 1 Department of Mathematics, Kanpur Institute of Technology, Kanpur, India Corresponding Author e-mail: rupeshk.srivastav@gmail.com Abstract We consider the problem of blood flow through a catheterized artery in the presence of a bell shaped stenosis using Newtonian fluid model. The analytical expression for the blood flow characteristics, namely, the velocity profile, the flow rate, the impedance, the wall shear stress in the stenotic region and the shear stress at stenosis throat have been derived. The combined effect of stenosis and catheterization on flow characteristics is studied for different values of parameters. Key words: Stenosis, Newtonian fluid, Impedance, Catheter, Shear Stress INTRODUCTION The frequently occurring cardiovascular disease, stenosis, is a medical term which means narrowing of anybody passage, tubes, or orifice (Young, 1979). It occurs due to the deposit of cholesterol, fatty substances, cellular waste products, calcium and fibrin in the inner lining of an artery. It is believed that stenosis caused by the impingement of extravascular masses or due to intravascular atherosclerotic plaque which develop at the wall of the artery and protrude into lumen. Regardless of the cause, it is well established that once an obstruction has developed, it results into significant changes in blood flow characteristics, pressure distribution, wall shear stress and the impedance (flow resistance). The flow through stenosed artery would provide the possibility of diagnosing the disease in early stages, by making treatment possible even before the stenosis becomes clinically significant. With the knowledge that the cardiovascular disease, stenosis is closely associated with the flow conditions and other hemodynamic factors, a large number of researchers including Young (1968), Young and Tsai (1973), Caro et al. (1978), Shukla et al. (1980), Ahmed and Giddens (1983), Sarkar and Jayaraman (1998), Pralhad and Schultz (2004), Jung et al. (2004), Liu et al. (2004), Srivastava and coworkers (2009, 2010, 2012), Mishra et al. (2006), Ponalagusamy (2007), Layek et al. (2009), Joshi et al. (2009), Mekheimer and El-Kot (2008), Tzirtzilakis (2008), Mandal and coworkers (2007), Misra and Verma (2007); Politis et al. (2008), Singh et al. (2010), Medhavi et al. (2012); Sankar, A. R. et al. (2013), Srivastav et al. (2013a, b, 2014a, b, c) and many others have addressed the stenotic development problems under various flow situations since the first investigation of Mann et al.(1938). Being a suspension of corpuscles, at low shear rates blood in general behaves like a non-Newtonian fluid in small diameter tubes. The experimental observations of Cokelet (1972) and theoretical investigation of Haynes (1960) indicate that blood cannot be treated as a single-phase homogeneous viscous fluid while flowing through