An unsteady two-fluid model of blood flow through a tapered arterial stenosis with variable viscosity in the presence of variable magnetic field has been analysed in the present paper. In this article, blood in the core region is assumed to obey the law of Jeffrey fluid and plasma in the peripheral layer is assumed to be Newtonian. The values for velocity, wall shear stress, flow rate and flow resistance are numerically computed by employing finite-difference method in solving the governing equations. A comparison study between the velocity profiles obtained by the present study and the experimental data represented graphically shows that that the rheology of blood obeys the law of Jeffrey fluid rather than that of Newtonian fluid. The effects of parameters such as taper angle, radially variable viscosity, hematocrit, Jeffrey parameter, magnetic field and plasma layer thickness on physiologically important parameters such as wall shear stress distribution and flow resistance have been investigated. The results in the case of radially variable magnetic field and constant magnetic field are compared to observe the effect of magnetic field in driving the blood flow. It is observed that increase in hematocrit increases the wall shear stress. The values of wall shear stress and flow resistance are obtained at various time instances and compared. It is pertinent to note that the magnitudes of flow resistance are higher in the case of converging tapered than non-tapered and diverging tapered artery.

The present article deals with a four-layered mathematical model for blood flow through an artery with mild stenosis. The four-layered model comprises a cell-rich core of suspension of all the erythrocytes described as a non-Newtonian (Jeffrey) fluid, a peripheral zone of cell-free plasma (Newtonian fluid) and the stenosed artery with porous wall consisting of a thin transition (Brinkman) layer followed by Darcy region. Analytical expressions have been obtained for velocity profiles in all the four regions, total volumetric flow rate, wall shear stress and flow impedance. MATLAB software is employed to compute numerical values of the pressure gradient. The influences of different parameters such as variable core fluid viscosity, hematocrit, thickness of the plasma layer, Brinkman and Darcy layer thickness, Darcy number, Jeffrey fluid parameter, and size and shape parameters of stenosis on the physiologically vital flow characteristics, specifically velocityprofile, volume flow rate, wall shear stress and flow impedance, have been examined. It is observed that the wall shear stress and resistive impedance decrease with the increase of plasma layer thickness, Jeffrey fluid parameter, Darcy number and Darcy slip parameter, and increase with the rise of hematocrit. The results in the case of variable core viscosity and constant core viscosity are compared to investigate the impact of variable core viscosity in managing the flow of blood.