The present study considers the mathematical modeling of unsteady non-Newtonian hydro-magnetic nano-hemodynamics through a rigid cylindrical artery featuring two different stenoses (composite and irregular). The Ostwald-De Waele power-law fluid model is adopted to simulate the non-Newtonian characteristics of blood. Inspired by drug delivery applications for cardiovascular treatments, blood is considered doped with a homogenous suspension of biocompatible nanoparticles. The arterial vessel exhibits the permeability effect (lateral influx/efflux), and an external magnetic field is also applied in the radial direction to the flow. A combination of the Buongiorno and Tiwari-Das nanoscale models is adopted. The strongly nonlinear nature of the governing equations requires a robust numerical method, and therefore the finite difference technique is deployed to solve the resulting equations. Validation of solutions for the pure blood case (absence of nanoparticles) is included. Comprehensive solutions are presented for shear-thickening (n = 1.5) and shear-thinning (n = 0.5) blood flow for the effects of crucial nanoscale thermophysical, solutal parameters, and hydrodynamic parameters. Comparison of profiles (velocity, temperature, wall shear stress, and flow rate) is also made for composite and irregular stenosis. Colour visualization of streamline plots is included for pure blood and nano mediated blood both with and without applied magnetic field. The inclusion of nanoparticles (Cu/blood) within blood increases the axial velocity of blood. By applying external magnetic field in the radial direction, axial velocity is significantly damped whereas much less dramatic alterations are computed in blood temperature and concentration profiles. The simulations are relevant to the diffusion of nano-drugs in magnetic targeted treatment of stenosed arterial diseases.
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