In this current work, we assume the mathematical modelling of non-Newtonian time-dependent hybrid nanoparticles via a cylindrical stenosis artery. In this work, blood is used as a base fluid, and the nanoparticles (copper and aluminum oxide) of cylindrical shape are inserted inside the artery to combine with blood to form hybrid nanofluid (HNF). The homotopy analysis method (HAM) is deployed for the solution of nonlinear resulting equations. For the validation of this current work, the results of the existing work have been compared with our proposed model results. A comparison of key profiles like velocity, temperature, wall shear stress, and flow rate is also performed at a specific critical height of the stenosis. It is also observed that the thermal conductance of hybrid nanofluids is greater than that of nanofluids. Including the hybrid nanoparticles (copper and aluminum oxide) inside the blood enhances the blood axial velocity. These simulations are applicable to the magnetic targeting treatment of stenosed artery disorders and the diffusion of nanodrugs.