An analysis of laminar forced-convection heat-transfer in a horizontal pipe was performed for the case in which the flowing fluid loses heat to the external environment by natural convection and radiation. The temperature difference between the pipe wall and the ambient varies along the pipe. Since the external natural-convection heat-transfer coefficient depends on this temperature difference, it, too, varies along the pipe. The accounting of this variation is a special feature of the analysis. It was found that whereas the pipe Nusselt number is generally insensitive to the variation of the external convection coefficient, a constant-Nusselt-number thermally developed regime does not exist. Radiation tends to lower the pipe Nusselt number, but the maximum effect is only 10%. The wall and bulk temperature distributions are generally more responsive to variable external convection than is the Nusselt number. This responsiveness is diminished when radiation plays an important heat loss role.