Radiative Calculations for Non-Gray Media with Heat Sourcesby using the Spectral Line-Based Weighted Sum of Gray Gases Model

Some solutions are presented to show the ability of the spectral line-based weighted sum of gray gases approach to solve the radiative transfer equation in absorbing-emitting non-gray media. The medium contains heat sources and is atradiative equilibrium state which occurs in high temperature systems. The non-gray gaseous medium is divided into a number of gray gases, and the radiative transfer equation is solved for each gray gas by the discrete ordinate method. The intensities are found by a summation over all gray gases, and the temperature field is updated by an iterative procedure. The updated coefficients obtained from high-temperature molecular spectroscopic database (2010thedition) are employed in the spectral line-based weighted sum of gray gases model. The method is verified through comparison with a benchmark problem for the case of a specified temperature distribution, and also for thecase of a variable temperature distribution (radiative equilibrium). Several examples are taken into account to show the ability and performance of proposed procedure for the radiative equilibrium calculations in media with heat sources and different boundary conditions (constant temperature and insulated walls).