This paper presents a theoretical study of the analysis of unsteady blood flow with constant and variable viscosities through a stenosed artery using a third grade fluid model. Incorporated into the models are the slip velocity and externally applied magnetic field. The methods employed in solving the equations governing the unsteady blood flow models with constant and variable viscosities are the Galerkin’s weighted residual and Forth order Runge-Kutta. Important flow parameters such as flow velocity, flow rate, shear stress and flow resistance have been computed. Graphical representation shows that, for both cases of unsteady blood flow models with constant viscosity and variable viscosity, magnetic field and shear thinning increases with flow resistance but decreases the flow velocity, flow rate and shear stress. Increases in slip velocity and shear thinning lead to increases in flow velocity, flow rate and shear stress but decrease the flow resistance. Other parameters that can positively influence the flow velocity are the pressure gradient and Reynold number. Finally, the velocity profile of unsteady blood flow model with constant viscosity is higher than that with variable viscosity.
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