There are a few theories about the types of fluid of the blood and one of them is that if the blood vessel does not contain a big amount of red blood cells, the blood is known as Power-law fluid. Power-law fluid has a shear rate depending on the obvious viscosity that categorizes non-Newtonian fluid in several types. In blood, the core region is modelled as a non-Newtonian fluid which is located at the centre of the blood vessel. By using the integration method, the velocity for the proposed mathematical model based on three different circumstances including the Power-law fluid for solute dispersion in blood flow with FHD effect, inclined artery and cholesterol stenosed artery are determined. The three circumstances which are considered for obtaining the velocity are done separately with the help of the given boundary conditions.