Nongray Gas Analyses for Reflecting Walls Utilizing a Flux Technique

A flux formulation for a planar slab of molecular gas radiation bounded by diffuse reflecting walls is developed. While this formulation is limited to the planar geometry, it is useful for studying approximations necessary in modeling nongray radiative heat transfer. The governing equations are derived by considering the history of multiple reflections between the walls. Accurate solutions are obtained by explicitly accounting for a finite number of reflections and approximating the spectral effects of the remaining reflections. Four approximate methods are presented and compared using a single absorption band of H₂O. All four methods reduce to an identical zeroth-order formulation, which accounts for all reflections approximately but does handle nonreflected radiation correctly. A single absorption band of CO₂ is also considered using the best-behaved approximation for higher orders. A zeroth-order formulation is sufficient to predict the radiative transfer accurately for many cases considered. For highly reflecting walls, higher order solutions are necessary for better accuracy. Including all the important bands of H₂O, the radiative source distributions are also obtained for two different temperature and concentration profiles.