The interaction between convection and axial heat conduction along a pipe is analysed assuming third kind boundary conditions at the outer face of the duct. Wall thickness is assumed to be either uniform or having periodic step variations in the axial direction. Axial heat conduction is found to have a definite influence on the heat flux and the Nusselt number distributions. However, the overall heat flux can accurately be predicted by ordinary methods disregarding axial conduction in the wall.