Mathematical Modelling of Pulsatile Flow of Non-Newtonian Fluid Through a Constricted Artery

Abstract

The research work explores blood flow into a stenosed artery, or one with abnormal growth within it. At the throats and at the critical height of the stenosis, mathematical and computational models have been developed to calculate the various associated parameters such as flow rate, pressure gradient, impedance, and wall shear stress. Modeling blood as a power law fluid showed the dependency of these quantities on temporal and spatial variables, as well as the frequency of the flow oscillation in time and the key parameters of the flow mechanism. The exponential curve is the geometry of the stenosis studied in this analysis. Analytical expressions for axial velocity, volumetric flow rate, pressure gradient, blood flow resistance, and shear stress have been computed and simulated in ANSYS to generate useful results with respect to variation of flow parameters with power law indices and also for comparison between Newtonian and NonNewtonian models of blood. Upon investigation, it was found that wall shear stress (WSS) increases with stenosis depth and therefore, plays a crucial role in affecting other flow parameters. At power law index 0.6, the highest shear stress and flow velocity were encountered at approximately 7 Pa and 0.5 m/s respectively.