Numerical study of the unsteady flow of non-Newtonian fluid through differently shaped arterial stenoses

The problem of non-Newtonian and nonlinear pulsatile flow through an irregularly stenosed arterial segment is solved numerically where the non-Newtonian rheology of the flowing blood is characterized by the generalized Power-law model where both the shear-thinning and shear-thickening models of the streaming blood are taken into account. The combined influence of an asymmetric shape and surface irregularities (roughness) of the constriction has been explored in a study of blood flow with 48% areal occlusion. The vascular wall deformability is taken to be anisotropic, linear, viscoelastic, incompressible circular cylindrical membrane shell. The effect of the surrounding connective tissues on the motion of the arterial wall is also paid due attention. Results are obtained for a smooth stenosis model and also for a stenosis model represented by the cosine curve. The present analytical treatment has the potential to calculate the rate of flow, the resistive impedance and the wall shear stress without excessive computational complexity by exploiting the appropriate physiologically realistic prescribed conditions in nonuniform nonstaggered grids, and to estimate the effects of surface roughness as well as asymmetry of stenosis shape for both shear-thinning and shear-thickening models of Power-law fluid, representing the streaming blood through graphical representations in order to validate the applicability of the present improved mathematical model.