A numerical calculation has been performed for the simultaneously developing laminar mixed convection flow and heat transfer for a gray fluid in an inclined square duct with radiation effects. The discrete ordinates method is employed to solve the radiative transfer equation. The coupled momentum and energy equations are solved by the Du Fort-Frankel numerical scheme. In this paper, the major independent parameters are the modified Rayleigh number, mixed convection parameter, conduction-to-radiation parameter, optical thickness, single scattering albedo and wall emissivity. The influences of these parameters on the developments of velocity, temperature, friction factor and Nusselt number are investigated in detail. The axial variations of the fRe and Nu are characterized by a decay near the entrance due to the entrance effect, but the decay is attenuated by the onset of secondary flow. The results for axial distributions of Nusselt number indicate that heat transfer is enhanced by the presence of radiation, but the thermal buoyancy effect is reduced. In addition, the influences are more significant when the conduction-to-radiation parameter and single scattering albedo decrease or the optical thickness and wall emissivity increase.

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