One of the current challenges of the coronary angioplasty technique for treating atherosclerosis in the artery is to target the desired area using nanoparticles. This study aims to investigate the hybrid Au-Fe₃O₄/blood nanofluid flow that passes through a narrowed section of a stenotic artery. The behavior of the Au-Fe₃O₄/blood flow in the stenosis region is mathematically examined, taking into account an inclined magnetic field and temperature-dependent thermal conductivity. Additionally, this work analyses the effect of nanolayers on nanofluid flow in the presence of a catheter with a balloon (angioplasty) on its wall. Tube and balloon catheter models are considered individually to compare the results of flow characteristics and heat transmission. Channel boundaries comprise wall properties with thermal slip and second-order velocity slip conditions. A similarity transformation procedure is used to convert the governing equations into highly nonlinear normal differential equations, which are analytically computed using the homotopy perturbation technique. The obtained results reveal an increased velocity profile due to the magnetic force, while an inverse trend occurs due to the thermal conductivity of the nanofluid. Furthermore, interfacial nanolayers of nanoparticles significantly alter the blood temperature to prevent and manage cardiovascular diseases. This rheological model may be useful for cancer diagnosis, tumor-selective photothermal therapy, medical simulation devices, and other applications.