A numerical analysis of flow and convection-dominated diffusion processes in an axi-symmetric tube with a local constriction simulating a stenosed artery is carried out. The primary aim of this study is to demonstrate the effect of wall shear stress and recirculating flow on the concentration distribution in the vessel lumen and on wall mass transfer. The applied physical parameters describe the convective-diffusive transport of oxygen in the human abdominal aorta. The flow dynamics is described applying the incompressible Navier-Stokes equations for Newtonian fluids, the mass transport is modelled by the convection diffusion equation. For the solute flux at the wall a model with shear-dependent permeability and a model with constant wall permeability are compared. The results demonstrate a strong influence of the mural permeability characteristics on the shape of the flux and interfacial concentration profiles along the wall. The numerical solution of the flow equations and the coupled mass transport equation uses the finite element method. The application of a streamline upwind procedure for the transport equation and a special subelement technique enable a stable solution in the convection-dominated diffusion process. The analysis illustrates an essential influence of the flow patterns on the mass transport. In the reversed flow region downstream of the stenosis the oxygen concentration is decreased to 75% of the inlet concentration value.