A general analysis including arbitrary thermal boundary conditions has been made for the energy transport in a circular tube in which a highly rarefied gas is flowing. Thermal radiation acts simultaneously with the free-molecule convection. Detailed consideration was given to the eases of uniform wall temperature, uniform wall heat flux, and the adiabatic wall. It was found that at all temperature levels except those well below room temperature, the results corresponding to combined convective and radiative transport differ little from those for purely radiative transport. Whenever results for the purely radiative transport differed appreciably from those of the purely convective transport, the radiation appeared to be the dominant mode in the simultaneous transport process.