A frequent cardiovascular condition that reduces blood flow is arterial stenosis. Tangent stress pressure, produced by a stenotic blood artery, diminishes the arterial side and results in an aneurysm. We explored the dynamics of entropy generation in blood stream via arteries observing mild overlapping stenosis, using a Prandtl fluid and focusing on the eccentric placement of catheters to enhance patient comfort. The governing equations assume conditions of mild stenosis and low Reynolds number, and applied the homotopy perturbation method. Several critical physical aspects are characterized, including velocity, temperature, impedance, entropy generation, wall shear stress, the Bejan number, and flow streamlines. The results show that a rise in the catheter radius tends to elevate impedance levels, whereas an increase in eccentricity, amplitude ratio, and inner cylinder speed leads to a decrease. These behaviors may serve to optimize catheter placement to minimize patient discomfort during medical interventions.