97 97 Jnanabha  , Vol. 40, 2010 (Special Issue : Proceedings of 13 th Annual Conference of  Vijnana Parishad of India and National Symposium on Recent Developments in Applicable Mathematics held at JIET Raghogarh (Guna), M.P., India on December 04-06, 2009) EFFECTS OF MULTI-STENSOSIS AND POST-STENOSIS DILATIONS IN SMALL ARTERY By Sanjeev Kumar and Subhash Chandra Department of Mathematics, Dr. B.R. Ambedkar University, Agra Institute of Basic Science, Khandari Campus, Agra-282002, India Email: sanjeevibs@yahoo.co.in & schandra.ibs@gmail.com ABSTRACT In this paper emphasis given on the study for the effects of multi-stenosis and post stenosis dilations in small artery. The resistance to flow ratio is to examine for different values of yield stress, viscosity and flux. A consideration for fully developed one dimensional non-Newtonian fluid known as Herschel Bulkley fluid for through a single vessel is made. The vessel is assumed to be straight, rigid and axisymmetric while radius of vessel is varying. The numerical value of the resistance flow ratio is varied from the maximum radii of the two abnormal segments to minimum radii. In this work we consider the radius of the artery as 0.45 mm, the length of the artery as 45 mm and the length of the artery at abnormalities as 15 mm. The value of  is vary from 0.525 to 3.06 and the magnitude of resistance-to-flow ratio is greatest for yield stress and least for flux. Increasing the yield stress  0 and decreasing the viscosity  or flux Q the resistance ratio become close to unity. 2000 Mathematics Subject Classification: Primary 92C10; Secondary 92C35, 76Z05 Keywords: Stenosis, dilatation, yield stress, viscosity, resistance flow, flux & Herschel Bulkley fluid. 1. Introduction. Stenosis is common throughout the circulatory system but they are of particular importance in the coronary arteries. The development