A theoretical investigation concerning hematocrit and slip velocity influence on the flow of blood and heat transfer by taking into account the externally applied magnetic field has been carried out. The mathematical models considered in this work treated blood as a non-Newtonian fluid obeying the third grade fluid model. A suitable geometry of the stenosis is taken into account. Galerkin weighted residual and Newton Raphson methods are used to solve the equations that govern the flow of blood and heat transfer. Analytical expression for the velocity profile, temperature profile, volume flow rate, wall shear stress and resistance to flow were obtained. Graphical representation of results shows that the flow velocity, volumetric flow rate and shear stress increase while resistance to flow and heat transfer rate decrease when the slip velocity increases. Also, flow velocity and volume flow rate decrease while shear stress, heat transfer rate, and resistance to flow increase when the hematocrit parameter increases. Finally, increases in magnetic field parameter lead to decrease in flow velocity, flow rate and shear stress but increase the flow resistance.

In this research, we modeled MHD third grade blood flow in a stenosed artery. The blood viscosity and the density have been modeled into the shear thinning/thickening parameters, the most important rheological properties of blood. We used regular perturbation method and obtained the flow characteristics such as the flow velocity, the volume flow rate, the shear stress and the resistance to the flow considering a single layered stenosed artery. The results however showed that there is significant increase in volume flow rate and the velocity with increase in the magnetic field intensity H and the shear thinning Λ and reduces with increase in the shear thickening Ω.