This model is designed to investigate the hemodynamics of the overlapped stenotic artery. The configuration of the overlapped stenotic artery is considered and for the purpose to create resemblance with living organism tapering effects (non-tapered, divergent and convergent) are taken into account. The problem is governed for silver and hybrid mediated blood flow model. The convective and constant slip phenomenon is also considered. For theoretical investigation of formulated equations experimental values of base fluid and considered solid nanoparticles are used. These patterns give us a graphical way to understand the theoretical contribution of this problem to biomedical field. At the end, It is obtained from the comparison of Ag and hybrid blood, that the use of hybrid blood is more appropriate to minimizes the hemodynamics (i.e. shear stress on wall and resistance to blood flow) of the overlapped stenotic artery.