We study a steady-state free (or mixed) convection model in 2 or 3 dimensions of space, taking into account radiative thermal transfer of grey bodies separated by a non participating media. The existence of a weak solution is proved and the uniqueness is obtained when the viscosity and the thermal conductivity of the fluid are large enough. Then, we discretize the model using classical finite element schemes and we prove in detail the existence, uniqueness and the convergence of the discrete solution (when the viscosity and the thermal conductivity are large enough and the step size is small enough).