Mathematical and neural network analysis of peristaltic flow of a second-grade fractional hybrid nanofluid with variable viscosity in bifurcated arteries

The flow behavior of tetra-hybrid nanofluids in a peristaltic wavy bifurcated artery is essential for improving biomedical devices, industrial thermal management, and next-generation fluidic systems. This aims to develop a mathematical model to examine the hemodynamic and thermal behavior of peristaltic non-Newtonian blood flow containing tetra-hybrid nanoparticles (Ag−Au−TiO2−Fe3O4) in a porous bifurcated artery under magnetic effects and variable viscosity, with potential relevance to targeted drug delivery. To capture the non-Newtonian and memory-dependent characteristics of the blood nanofluid system, a fractional second-grade fluid model is employed. The effective thermophysical properties of the tetra-hybrid nanofluid are evaluated using the Yamada–Ota and Xue models. The resulting coupled nonlinear equations governing momentum and energy transport, incorporating viscosity variation, buoyancy forces, Joule heating, and electromagnetic effects, are solved using the homotopy perturbation method, yielding rapidly convergent series solutions. Our graphical results indicate that, in the parent artery, velocity increases under the effects of the magnetic field, viscosity, and fractional parameter but decreases after a certain distance, whereas in the daughter artery, velocity continues to rise under the influence of these factors, highlighting their role in promoting flow regulation and hemodynamic stability. Enhanced viscous and electromagnetic effects reduce the fluid temperature, whereas buoyancy and internal heat generation effects increase it. Increased material resistance lowers the pressure gradient, while the memory-dependent behavior elevates it. Furthermore, the artificial neural network (ANN) model exhibited outstanding predictive performance for both the heat transfer coefficient and wall shear stress, achieving high accuracy and minimal error across different regions of the arterial system. These findings offer valuable insights for enhancing flow regulation, optimizing heat transfer, and contributing to advancements in cardiovascular healthcare applications.