The paper investigates blood flow into an artery that is stenosed or has abnormal growth inside of it. In order to compute the different associated parameters, including flow rate, gradient of pressure, WSS and impedance, Models in mathematics and computation have been created at a critical level and at the stenosis's throats. Blood's dependence on spatial and temporal variables, the flow's oscillation frequency over time, and important the flow of mechanism's parameters were all demonstrated by modeling it as a power law fluid. The stenosis's geometry under investigation in this study is the exponential curve. Axial velocity, pressure gradient, flow rate in volume, resistance to blood flow, and shear stress, analytical expressions have been calculated and simulated in in this research in a stenosed artery under velocity slip conditions using a harmonic pulsatile flow model to produce insightful results regarding Power law indices and the change in flow parameters and to compare blood models that are Newtonian and those that are not. Examination indicated that wall shear stress (WSS), which is a critical factor influencing other flow parameters, increases with stenosis depth. The maximum flow velocity and shear stress occurred at essentially \(0.5\quad {\text{m}}/{\text{s}}\) and \(7\,{\text{Pa}}\) , respectively, at power law index \(\left( {q = 0.5} \right)\) .