A novel fractional hybrid nanofluid model for blood flow in a stenosed artery with a peripheral plasma layer: Narrowing the gap between Bingham’s model and experiments

Abstract

Understanding blood flow is crucial for improving drug delivery, cardiovascular health, and treatments. This study introduces a novel fractional model for blood flow in stenosed arteries using a ${\mathrm{TiO}}_2$-$\mathrm{Au}$ hybrid nanofluid within a two-fluid framework. Red blood cells are modeled as a non-Newtonian Bingham fluid, while plasma is treated as a Newtonian fluid. The formulation incorporates a fractional-order momentum equation, a dual-phase lag fractional energy equation, considering phase lags, a magnetic field, porosity, and thermal radiation. The use of fractional calculus in combination with the two-phase flow approach is intended to capture the complex rheological behavior of blood, including memory effects and non-local characteristics that are often neglected in traditional models. This approach aims to enhance the accuracy of the classical Bingham model and bridge the noticeable gap between its predictions and experimental results. Finite difference methods with Caputo L1 fractional derivatives solve the dimensionless equations. Key parameters analyzed include the Hartmann number, thermal radiation, Darcy number, and fractional orders (${\alpha }_1$, ${\alpha }_2$, $\beta$). Results reveal their impact on velocity, temperature, flow rate, wall shear stress, and the Nusselt number. It is found that the fractional Bingham model with plasma outperforms classical models across all degrees of stenosis when compared to experimental data, most notably in mild stenosis, with only a 0.3% error in time-averaged velocity. For the fractional Bingham model, a fractional order of ${\alpha }_1$ = 0.6 aligns best with experimental results across all three stenosis cases, while the hybrid nanofluid enhances both flow and heat transfer. These findings offer insights for biomedical applications, including therapeutic interventions and device design.