Unsteady mathematical analysis of non-Newtonian blood flow models in a double stenosed artery

Abstract

The simultaneous effect of pulsatile blood flow and double stenoses with different severities, lengths, and interspacing on mass transport using the Newtonian as well as the non-Newtonian power-law models of blood flow are considered in this thesis. These models are important from a physiological perspective as their effects on certain blood flow characteristics that are clinically significant can be analysed. The effect of some essential issues like the diffusivity of mass and the rate of absorption at the lumen-tissue interface are also studied to investigate the effectiveness of solute delivery. The flow is considered two-dimensional, unsteady and axisymmetric in the cylindrical polar coordinate system, while the transport of mass is modelled as an unsteady convection-diffusion equation. A numerical technique in the form of finite-difference approximations in staggered grids, widely known as the Marker and Cell (MAC) method has been used to tackle the coupled system of non-linear partial differential equations. Simultaneous effects of pulsatile flow conditions and double stenoses show an increase in the pressure drop across the stenosis length, as well as in the transport of mass at the throat and mass flux at the artery wall. The delivery of solute is observed to be more effective in the non-Newtonian model. In this study, another concern is on the effect of catheter’s eccentricity on blood flow and heat transfer characteristics using the Carreau model. The perturbation method which is an approximate analytical technique, has been applied to the catheter problem. The accuracy of results is confirmed in the limiting cases, where the existing solutions in the literature are recovered as special cases. The position of the catheter’s eccentricity in Carreau fluid leads to a reduction in the number and size of the circulating bolus zone which agree with physiological observations that the risks and complications associated with catheterization are alleviated when the eccentric position of the catheter is considered. The results of the simulation could provide insights towards the detection of aggregation sites, allowing the treatment of disease to be initiated quickly before it becomes clinically significant.