USE OF THE 2-D COLLAPSED DIMENSION METHOD IN GRAY ENCLOSURES WITH ABSORBING-EMITTING-ISOTROPIC SCATTERING MEDIA IN RADIATIVE EQUILIBRIUM

Abstract

A Cartesian-based method is proposed for combustion-radiation problems in gray enclosures having one ordinate symmetry and containing absorbing-emitting media with isotropic scattering. This method collapses the 3-D radiative information of the problem into its 2-D solution plane and is shown to be applicable for all ranges of optical thicknesses, including the optically very thin case, while maintaining near-analytic accuracy over most of this range. To accomplish this task, the collapsed dimension method makes use of effective intensity rays, each of which contains the information of the conglomerate of all the conventional intensity rays focused on the same point and contained in a plane that is both inclined at the same angle as the ray and is also normal to the solution plane. This novel procedure thus eliminates the use of solid angles and reduces both the complexity and the computational expense involved in the solution of such problems. The method is shown to be applicable to gray wall problems enclosing gray absorbing-emitting isotropic scattering media in radiative equilibrium.