Advances in Applied Mathematical Biosciences. ISSN 2248-9983 Volume 5, Number 1 (2014), pp. 9-18 © International Research Publication House http://www.irphouse.com A Mathematical Model for Different Shapes of Stenosis and Slip Velocity at the Wall through Mild Stenosis Artery Harjeet Kumar 1 , R.S. Chandel 2 , Sanjeev Kumar 3 and Sanjeet Kumar 4 1,4: Department of Mathematics, Lakshmi Narain College of Technology, Bhopal (M.P)-462021, India, harjeetkumar01@gmail.com, sanjeet_418@yahoo.com 2: Department of Mathematics, Government Geetanjali Girls College, Bhopal (M.P)-462001 India, rs_chandel2009@yahoo.co.in 3:Department of Mathematics, Institute of Basic Science, (Dr. B. R. Ambedkar University), Khandari Campus, Agra (U.P) - 282002, India, sanjeevibs@yahoo.co.in Abstract: The Present investigation deals with the two-layered mathematical model of blood flow for a mild stenosis artery in the presence of axially variable, peripheral layer thickness and variable slip at the wall. The model consists of a core surrounded by a peripheral layer. It is assumed that the fluids of both the regions (core and peripheral) are Newtonian having different viscosity. The geometry of the interface between the peripheral layer and the core region has been determined and the result obtained in the analysis have been evaluated numerically and discussed briefly. In the present analysis, new analytic expression for the thickness of the peripheral layer has been obtained in terms of measurable quantities flow rate   Q , centerline velocity   U , pressure gradient   dz dp  , plasma velocity   c  . It is important to mention that in the present analysis, core viscosity has been obtained by two methods. Firstly by calculating from the formula obtained in the present analysis and second by calculating the red cell concentration in the core and then using concentration versus relative viscosity curve. It is found that the agreement between the two is very good (error<1.4%). The significance of the present model over the existing models could be useful in the development of new diagnosis tools for many diseases. Key words: Blood flow, axially variable slip velocity, stenosed artery, different shapes of stenosis AMS Subject Classification (1991): 760z05, 92c35