The cooling problem of the hot internal pipe flow has been investigated. Simultaneous conduction, and radiation in the fully developed inner pipe flow were considered with prescribed azimuthally varying convective heat loss at the pipe wall. A complex, nonlinear integro-differential radiative transfer equation was solved by the discrete ordinates method (or called S-N method). The energy equation was solved by control volume based finite difference technique. A parametric study was performed by varying the conduction-to-radiation parameter, optical thickness, and scattering albedo. The results have shown that initially the radiatively active medium could be more efficiently cooled down compared with the cases otherwise. But even for the case with dominant radiation, as the medium temperature was lowered, the contribution of conduction began to exceed radiation.