Mathematical Analysis of Bio-nanofluid Flow over a Nonlinear Tapering Artery with Stenosis Conditions Using Cross Fluid Viscosity Model

Non-Newtonian bio-nanofluid flow in tapered arteries is highly helpful in prosthetic blood vessel design, since using grafts with tapered lumen offers advantages in surgery and many other treatments. This study analyzes the way non-Newtonian bio-nanofluid flow through a nonlinear narrowing of an artery, examining its behavior through mathematical modelling along with numerical simulation. Blood behaves as a non-Newtonian bio-nanofluid. The viscosity model of Cross bio-nanofluid provides the ability to examine the qualities of fluid flow under extreme high and low shear rates. Perturbation technique is utilized to tackle the governing differential equations. This technique reveals physical information ascertaining pertinent information about physical quantities such as velocity, wall shear stress, shear stress field, and resistance impedance at the stenosis constriction. Numerical simulation predicts the noteworthy increase in numerous dimensionless parameters. The results obtained from the current investigation demonstrate a positive correlation between escalation of Weissenberg number, regulating factor, resistance impedance and the power law index ( m ). The decline in wall shear stress is observed to occur concomitant with an elevation in the Weissenberg number. To date, no investigation has been undertaken within the extant scholarly literature concerning the potential impact of blood flow on the morphology of a stenosis artery characterized by nonlinear tapering, with due regard to the non-Newtonian qualities of the fluid. A lot of mathematical model in literature are used to investigate different facts in different scenario. The fluidic models like Carreau, Casson, Maxwell, and power law just focus to investigate the behavior of fluid within confined ranges. For example, power law fluid investigates only behavior of fluid in only power law region, but Cross fluid model has capability to investigate the behavior of fluid at very high and very shear rate. That is inspired to investigate the bio-nanofluid by using Cross fluid viscosity model.