The periodic nature of the cardiac cycle induces a pulsatile, unsteady flow within the circulatory system. The pulsatile model of blood flow provides data to analyse the physiological situation in close proximity. The distribution of fatty cholesterol and artery-clogging blood clots in the lumen of the coronary artery is assumed as a porous medium. A mathematical model for pulsatile flow through an stenosed artery filled with porous medium in the presence of transverse static magnetic field has been formulated under the consideration of hematocrit dependent viscosity of blood that governed by Einstein equation. The velocity profile, volume flux, pressure gradient and wall shear stress are obtained and the effects of magnetic number, Darcy number, Womersely number are computed and represented through graphs.