The notion of mathematical study for the flow of blood through blood vessel which is tapered and under diseased conditions is the topic of this dissertation. Heat, Arteries, and Blood vessels are the three major components of the cardiovascular system. We developed a mathematical model of pressure on artery walls caused by blood flow in this study. We employed Poiseuille's equation, the Navier-Stoke equation, and the continuity equation in this process. We developed a mathematical model for two-fluid blood flow using the Navier-Stoke equation, with non-Newtonian fluid in the core and Newtonian fluid in the periphery. For the scientific definition, a barrel-shaped coordinate framework was used. The framework's controlling conditions of movement are first sought in the Laplace change space, and its solution is reached by the use of a limited distinction conspire. The current model is designed to be applicable to both converging and diverging arteries. We investigated the variation of blood viscosity with regard to stenosis shape for various flow rates, as well as the variation of flow rate with respect to stenosis form for various pressures.