The discrete ordinates method (DOM/Sn) is implemented to investigate the high order scattering effects of absorbing–emitting–scattering grey gas media inside the three-dimensional cubical and rectangular furnaces. To validate the numerical method, the furnaces are considered first to be filled with non-scattering grey gases, and the results of the higher order approximations of the DOM show an excellent agreement compared with those available in the literature. The DOM is then extended to apply in the scattering media inside the furnaces, and the results of various scattering approaches such as out-scattering, iso-scattering, linear aniso-scattering and nonlinear aniso-scattering are obtained and presented in this paper
