The present investigation deals with the numerical simulation of Newtonian fluid flow employing the control volume method, which simulates blood flow in a stenotic blood artery in the presence of magnetic effects. The induced magnetic effects are neglected. The process is described by use of an interpenetrating model of two phase media. An artery side becomes lessened and an aneurysm is caused by the tangent stress pressure produced by a stenotic blood vessel. Under appropriate simplifying assumptions, we obtain from this model the Navier-Stokes equations in the free zone (which typically is, outside the stenosis region) and a system of equations generalizing the filtration equation in the stenotic region. Stenosis has been considered to be a porous material. The impact of both the Reynolds number and the degree of stenosis on the blood's flow patterns investigated. The result obtained is very sensitive to the values of the initial conditions and this helps to explain the condition of hypertension.