Losses in channel flows are usually determined using a frictional head loss parameter. Fluid friction is however not the only source of loss in channel flows with heat transfer. For such flow problems, thermal energy degradation, in addition to mechanical energy degradation, add to the total loss in thermodynamic head. To assess the total loss in a channel with combined convection and radiation heat transfer, the conventional frictional head loss parameter is extended in this study. The analysis is applied to a 3D turbulent channel flow and identifies the critical locations in the flow domain where the losses are concentrated. The influence of Boltzmann number is discussed, and the best channel geometry for flows with combined heat transfer modes is also determined.