Hemodynamics is the dynamics of blood flow. The circulatory system is controlled by homeostatic mechanisms, such as hydraulic circuits are controlled by control systems. Hemodynamic response continuously monitors and adjusts to conditions in the body and its environment. Thus hemodynamics explains the physical laws that govern the flow of blood in the blood vessels. In blood, the concentration of red blood cells varies with the arterial diameter. In the case of narrow arteries, red blood cells concentrate around the centre of the artery and there exists a cell-free plasma layer near the arterial wall due to Fahraeus-Lindqvist effect. Due to non-uniformity of the fluid in the narrow arteries, it is preferable to consider the two-phase model of the blood flow. This research area focuses on the heat transfer effects on the two-phase model of blood flow when it flows through the stenosed artery under an external pressure gradient. Blood is considered as a non-Newtonian fluid with uniformly distributed magnetic particles. Both the blood and magnetic particles are moving with distinct velocities. Effects of pertinent parameters on blood velocity and particle velocity will be shown graphically