A distributed source model to predict fan tone noise levels of an installed turbofan aero-engine is extended to include the refraction effects caused by the fuselage boundary layer. The model is a simple representation of an installed turbofan, where fan tones are represented in terms of spinning modes radiated from a semi-infinite circular duct, and the aircraft's fuselage is represented by an infinitely long, rigid cylinder. The distributed source is a disk, formed by integrating infinitesimal volume sources located on the intake duct termination. The cylinder is located adjacent to the disk. There is uniform axial flow, aligned with the axis of the cylinder, everywhere except close to the cylinder where there is a constant thickness boundary layer. The aim is to predict the near-field acoustic pressure, and in particular, to predict the pressure on the cylindrical fuselage which is relevant to assess cabin noise. Thus no far-field approximations are included in the modelling. The effect of the boundary layer is quantified by calculating the area-averaged mean square pressure over the cylinder's surface with and without the boundary layer included in the prediction model. The sound propagation through the boundary layer is calculated by solving the Pridmore-Brown equation. Results from the theoretical method show that the boundary layer has a significant effect on the predicted sound pressure levels on the cylindrical fuselage, owing to sound radiation of fan tones from an installed turbofan aero-engine.