Mathematical modelling of human blood flow with nanofluids facilitates rapid hypothesis development (the accelerated formulation and testing of scientific ideas or assumptions about how a system behaves, in this case, human blood flow with nanofluids) and cost reduction in biomedical research. This study employs the finite-element method (FEM) to examine the effects of bioconvection and biomagnetic field on pulsatile, non-Newtonian blood flow and heat transfer in the presence of gold nanoparticles (Au-NPs) within a bifurcated artery with aneurysms. The blood is treated as a non-Newtonian, axisymmetric, laminar, incompressible and unstable fluid. The physical model includes a bifurcated artery with aneurysms containing a heated inlet and thermally insulated outlets. The rest are considered cold. Simulations are conducted using Prandtl number ( \(Pr = 21\) ), Reynolds number ( \(Re = 100, 200, 300, 400, 500\) ), power-law index ( \(n = 0.6, 0.8, 1.0\) ), magnetic number ( \(M_{\textrm{nf}} = 0, 1, 2, 3, 4, 5\) ) and volume fraction ( \(\phi = 0.0, 0.01, 0.02, 0.03, 0.04\) ). The study aims to analyse flow phenomena using visual representations of velocity and temperature distributions, streamlines and isotherms. Calculations of the local Nusselt number (Nu), wall shear stress (WSS) and average Nusselt number ( \(\overline{Nu}\) ) are performed. Results indicate that the introduction of a magnetic field decreases the downstream recirculation area and increases vortex size near the magnetic source as \(M_{\textrm{nf}}\) increases. Higher \(M_{\textrm{nf}}\) values also improve temperature distribution and heat mixing. The average Nusselt number ( \(\overline{Nu}\) ) inversely correlates with the power-law index (n) and directly correlates with Re and \(M_{\textrm{nf}}\) . Local Nu and WSS in the artery vary due to flow disturbances and aneurysm size, influencing the overall hemodynamic characteristics. The addition of Au-NPs to the blood significantly enhances heat transfer, with higher Re and increasing n from 0.6 to 1.0 boosting \(\overline{Nu}\) by \(22.752\%\) . Conversely, increasing n from 0.6 to 1.0 decreases \(\overline{Nu}\) by \(7.201\%\) due to \(M_{\textrm{nf}}\) . These findings are significant for nanodrug dispersion in magnet-targeted therapy for aneurysmal bifurcation arterial disease.
