Discrete-ordinates method in radiative heat transfer

About 50 years ago, Chandrasekhar developed the discrete-ordinates method for analyzing radiation heat transfer within a plane-parallel medium. The effects of absorption, multiple scattering, and collimated incidence were considered. Since then, the numerical method has been utilized to study radiative heat transfer in one- and multi-dimensional rectangular, spherical and cylindrical geometries. In this article, the formulation of the discrete-ordinates method is described for computing radiative transfer in a one-dimensional (1D) slab and two-dimensional (2D) rectangular geometries, including the effects of absorbing, emitting and scattering constituents. Both the strengths and the weaknesses of this numerical approach are addressed. The accuracy of available results obtained by utilizing the discrete-ordinates method is compared with other methods of solution for several representative cases. It is evident that major advances have been made related to the development and application of the discrete-ordinates method in multi-dimensional systems. However, much more work remains to be done with the development of this classical technique, including, among others, a more effective treatment of nongray radiative properties of molecular gases and turbulence, as well as a removal of false scattering.