Elmer is capable of solving axisymmetric and 3D radiation problems. The attached figure shows temperature distribution in an axisymmetric closure with a heater placed inside a cylindrical object. The heat is transferred by conduction inside the object and diffuse gray radiation between the inner walls. The two closures are treated separately. ElmerSolver used a fully implicit Newton iteration to solve the heat equation with the nonlinear boundary condition.
The files needed for reproducing the example may be found in radiation.tar.gz.