A numerical study has been made of the interaction of the thermal radiation with laminar mixed convection for a gray fluid (a gas that may have particulates in suspension) in a vertical square duct. Using the vorticity-velocity method, the three-dimensional Navier-Stokes equations and energy equations were solved simultaneously. The integro-differential radiative transfer equation was solved by the discrete ordinates method. Results are presented for a wide range of governing parameters. The effects are emphasized of thermal buoyancy and radiative transfer on the development of velocity and temperature fields, the friction factor and the Nusselt number. The results show that radiation significantly affects the total Nusselt number Nu(t) and tends to reduce the buoyancy effects. In addition, radiation speeds the development of the temperature field. (C) 2001 Elsevier Science Ltd. All rights reserved.