Modeling and analysis of magnetic hybrid nanoparticle (Au-Al 2 O 3 /blood) based drug delivery through a bell-shaped occluded artery with joule heating,viscous dissipation and variable viscosity effects

Abstract

The present work deals with the impact of hybrid nanoparticles (Au-Al₂O₃) on the blood flow pattern through a porous cylindrical artery with a bell-shaped stenosis in the presence of an external magnetic field, Joule heating, and viscous dissipation by considering two-dimensional pulsatile blood flow. The temperature-dependent viscosity model is utilized in this study. The blood flow is assumed to be unsteady, laminar, viscous, and incompressible. The mild stenotic presumption normalizes and reduces the bi-directional flow to uni-directional. The Crank-Nicolson scheme is applied to solve the continuity, momentum, and energy equations with appropriate initial and boundary conditions. Transport characteristics are visualized graphically for key dimensionless parameters such as Magnetic number ( $M^2$ ), Darcy number (Da), Grashof number (Gr), viscosity parameter (β₀), Reynolds number (Re), Eckert Number (Ec), Prandtl number (Pr), different concentration of both the nanoparticles (ϕ₁, ϕ₂), and pressure gradient parameter (B₁). The velocity contours for different emerging parameters have also been drawn to assess the overall behaviour of blood flow patterns. The non-dimensional velocity profile is enhanced with increment in values of Da, implying that the medium permeability provides less resistance to the flow. Increasing viscous dissipation (Ec) and Joule heating ( $M^2$ ) parameter simultaneously raise the nanofluid temperature. Hybrid nanoparticles (Au-Al₂O₃/blood) effectively reduce hemodynamic variables such as wall shear stress and resistance (impedance). The present work finds applications in nano-mediated treatment of atherosclerosis and other diseases.