Implementation of the Weighted Sum of Gray Gases Model to a Narrow Band : Application and Validity

Abstract

The weighted sum of gray gases model (WSGGM) is applied to narrow bands of water vapor for analyzing radiative heat transfer in nongray media. For a given narrow band, the band mean spectral emissivity is represented by a weighted sum of gray gas emissivities expressed in terms of absorption coefficients, weighting factors, absorbing gas density, and path length. Five types of temperature-versus-narrow band absorption coefficient relation are suggested, and comparisons between the modeled emissivity and that of the original narrow band model are made and shown at a few typical bands. Total and low-resolution spectral intensifies at the boundary are obtained for uniform, parabolic, boundary-layer-type temperature and parabolic concentration profiles using the WSGGM with five gray gases. Results using the Curtis-Godson approximation are compared with the WSGGM computations for each narrow band. The results using the WSGGM show good agreement with the Curtis-Godson approximation results, and especially, two of the WSGGMs with wavenumber-dependent absorption coefficients show highly accurate results with a few percent error in the total wall heat flux. The WSGGMs with wavenumber-independent absorption coefficients are, however, more useful for total spectrum computation, with a slight sacrifice in the accuracy.