The present research discusses the solute transport in a catheterized stenosed artery of sine and cosine-shaped stenosis. The steady blood flow in the artery is governed by the continuity and momentum equations with the catheter radius and stenosis size using appropriate boundary conditions. Herschel–Bulkley (H–B) model is chosen to represent the blood rheology as it is suitable for the very narrow flow region of the catheterized stenosed artery. The velocity profile solution is obtained through Simpson's 3/8 rule in evaluating the integrals and the Regula-Falsi method in solving for the plug flow radius. The mean concentration and diffusion coefficient are obtained by applying the Generalized Dispersion Model (GDM) to the convective-diffusion equation, which is then solved analytically. The impact of the radius of the catheter and stenosis height on the diffusion coefficient and mean concentration are investigated by plotting the graphical solutions. Analysis shows that the rise in either catheter radius and stenosis height decreases the diffusion coefficient, further increasing the solute mean concentration. In addition, the artery with sine stenosis is affected more by diffusion coefficient decrease than the cosine stenosis. The mean concentration is also more affected for the sine stenosis as the catheter radius and stenosis height increase. Studying the influences of stenosis height and catheter radius on blood flow can improve clinical outcomes, device design, diagnosis and treatment methods, and numerous other aspects of medical practice.