This research presents a numerical simulation of an unsteady two-dimensional channel flow of Newtonian and some non-Newtonian fluids using the finite-volume method. The walls of the geometry oscillate sinusoidally with time. We have used the Cartesian curvilinear coordinates to handle complex geometries, i.e., arterial stents and bulges and the governing Navier-Stokes equations have been modified accordingly. Physiological pulsatile flow has been used at the inlet to characterize four different non-Newtonian models, i.e., the (i) Carreau, (ii) Cross, (iii) Modified Casson, and (iv) Quemada. We have presented the numerical results in terms of wall shear stress (WSS), pressure distribution as well as the streamlines and discussed the hemodynamic behaviors for laminar and laminar to turbulent transitional flow conditions. An increase of wall shear stress and a decrease in wall pressure are significantly observed at the stenosis throat for high Reynolds number and highly stenosed arteries. Likewise, the flow recirculation also increases if the narrowing level and the Reynolds number increases in the dilated region which eventually leads the stream to experience a transition to turbulence at Re = 750. The results for the fluid flow through an aneurysm just after a stenosis with oscillating wall are novel in the literature.

Mixed convection laminar two-dimensional boundary-layer flow of non-Newtonian pseudo-plastic fluids is investigated from a horizontal circular cylinder with uniform surface heat flux using a modified power-law viscosity model, that contains no unrealistic limits of zero or infinite viscosity; consequently, no irremovable singularities are introduced into boundary-layer formulations for such fluids.. The governing boundary layer equations are transformed into a non-dimensional form and the resulting nonlinear systems of partial differential equations are solved numerically applying marching order implicit finite difference method with double sweep technique. Numerical results are presented for the case of shear-thinning fluids in terms of the fluid temperature distributions, rate of heat transfer in terms of the local Nusselt number.