MATHEMATICAL MODELING OF BLOOD FLOW IN ARTERIES USING NANOFLUID DYNAMICS AND FREE FLOW CONDITIONS

Abstract

This study presents a comprehensive mathematical model for analyzing blood flow in arteries using nanofluid dynamics under free-flow boundary conditions. The model incorporates the Navier–Stokes, energy, and nanoparticle concentration equations to describe the influence of nanoparticle volume fraction on velocity, pressure, and wall shear stress (WSS). Blood is treated as an incompressible, laminar nanofluid, and numerical simulations are performed using the finite element method. The results reveal that increasing nanoparticle concentration enhances the effective viscosity, leading to reduced axial velocity and higher wall shear stress. Under free-flow conditions, the model predicts lower wall friction and a more uniform velocity distribution compared to no-slip flow. Validation against the analytical Poiseuille profile and existing literature demonstrates strong agreement, confirming the model’s accuracy. The findings have significant implications for biomedical applications such as targeted drug delivery, arterial disease modeling, and therapeutic nanoparticle transport. The study provides a foundation for extending nanofluid-based hemodynamic analysis to pulsatile and elastic arterial systems in future research.