Blood flow analysis plays an essential role in understanding cardiovascular health and disease. An accurate mathematical modeling is necessary in context of representation of arterial domains and blood flow to learn about the intricate blood dynamics. In this paper we concentrate on the mathematical representation of the geometry of the blood artery and find numerical solutions with mild to severe degree of stenosis. Blood dynamics has steady state, in-compressible and laminar nature. The shear thinning non-viscous effects of blood are assumed to obey Carreau model. Fluid flow is based on coupled Navier-Stokes equation in three dimensions and is simulated with finite volume approach over hexahedral elements. Application of a constant mass flow rate at the inlet of the artery results in a number of observations to analyze. It is found that with increasing the severity of stenosis, blood velocity becomes higher in stenotic region, pressure drop along the arterial domain is increased and shear stresses exerted by blood on walls of artery are increased.