This study was conducted with the aim of investigating the Newtonian nanofluid flow in a catheterized tapered artery through using a completely consistent couple stress theory. In the process of carrying out this study, the slip condition at the arterial wall and the catheter, as well as, the permeability was taken into account. Further, the velocity, temperature, and concentration profiles were analytically modeled and the effect of the length scale on these profiles was well presented through the way it influences small-scale flows. The effect of the slip condition at the artery and catheter walls on the velocity was also investigated and revealed that any increase in the velocity leads to an increase in the slip velocity. Furthermore, the effect of other parameters such as the catheter diameter, shape, and height of the stenosis on these profiles was explored for all three artery geometries, i.e., diverging tapered artery, converging tapered artery, and non-tapered artery, respectively. The findings suggested that any increase in the catheter diameter and stenosis height can decrease the velocity and nanoparticle concentration profiles, while the temperature profile increases. It was also found that by increasing the stenosis shape parameter the velocity and concentration profiles increase and temperature decreases.