Free convection with radiative thermal transfer of grey bodies. Analysis and approximation by finite element methods

We study a steady-state free (or mixed) convection model in two- or three-d imensions of space, taking into account radiative thermal transfer of grey bodies separated by a nonparticipating media. The existence of a weak solut ion is proved and the uniqueness is obtained when the viscosity and thermal conductivity of the fluid are large enough. Then, we discretize the model using classical finite element schemes and prove in detail the existence, u niqueness and the convergence of the discrete solution (when the viscosity and the thermal conductivity are large enough and the step size is small en ough).