Narrowing of the arteries caused by atherosclerosis reduces blood flow to the heart, which results shows ischemia, angina pectoris, cerebral strokes, and other coronary artery disease signs and symptoms. Curvature is seen in blood vessels at various locations. The stenotic surface provides an additional curvature and the point of maximum shear which varies with the cross-section. A cylindrical form of the Navier-Stokes equations in polar coordinate system have been extended to include dynamic curvature along the axial direction. The blood flow behavior of taking different values of blood parameters like viscosity, the radius of the artery, and the thickness of the stenosis has been studied with and without curvature by using an extended blood flow model with dynamic curvature. Moreover, the aspects of blood flow, such as dynamic curvature velocity profile, volumetric flow rate, pressure drop, and shear stress, have been studied in relation to blood flow around curved arteries with stenosis, variations in the radii of the artery, thickness of the stenosis, and viscosity. The information may reveal that by increasing the values of curvature, viscosity, and thickness of stenosis, velocity, and volumetric flow rate can be quickly reduced. Increasing the curvature, viscosity, and thickness of stenosis also results in an increase in shear stress and a pressure drop. The presence of curved stenotic arteries has a significant impact on the flow parameters, and it is crucial to know about these dynamics in order to study the cardiovascular system.