The radiation transfer part is treated by the application of a random statistical narrow-band model and the Curtis-Godson approximation. An implicit finite-difference technique, developed for this study is used to solve the mass, momentum and energy conservation equations in a coupled manner. Excellent agreement between our finite-difference solutions and those of other authors are obtained for pure natural convection, pure forced convection and mixed convection without radiation. The investigation of the boundary conditions at infinity shows that the radiation penetration length at atmospheric pressure is of the order of one pure H2O equivalent metre, which is one order of magnitude larger than the boundary layer thickness for mixed convection without fluid radiation. Comparison of results with and without radiation in various conditions shows that fluid radiation enhances the effect of buoyancy forces, increases temperature, velocity, and conductive heat transfer at the wall, but decreases the wall radiative heat flux. A dimensionless parameter R is introduced in order to enable a crude estimation of wall conductive flux enhancement due to radiation.