This research article was published by Communications in Mathematical Biology and Neuroscience, 2020A mathematical model of non-Newtonian blood flow, heat and mass transfer through a stenosed artery is studied. The non-Newtonian model is chosen to suit the Herschel-Bulkley fluid characteristics, taking into account the presence of body acceleration, magnetic fields and chemical reaction. The study assumed that, the flow is unsteady, laminar, two-dimensional and axisymmetric. The governing flow equations of motion were solved numerically using explicit finite difference schemes. The study found that velocity profile diminishes with increase in Hartman number and increases with body acceleration. The temperature profile is raised by the increase of body acceleration and the Eckert number, while it diminishes with the increase of the Peclet number. It was found also that the concentration profile increases with the increase of the Soret number and decreases with the increase of the chemical reaction. It was further observed that the shear stress deviates more when n > 1 than when n < 1. Shear stress for power law fluid when n > 1 exhibited higher magnitude value than Newtonian, Bingham and Herschel-Bulkley fluids.