Approximate solution methods for spectral radiative transfer in high refractive index layers

Abstract

Abstract--Some ceramic materials for high temperature applications are partially transparent for radiative transfer. The refractive indices of these materials can be substantially greater than one which influences internal radiative emission and reflections. Heat transfer behavior of single and laminated layers has been obtained in the literature by numerical solutions of the radiative transfer equations coupled with heat conduction and heating al the boundaries by convection and radiation. Two-flux and diffusion methods are investigated here to obtain approximate solutions using a simpler formulation than required for exact numerical solutions. Isotropic scattering is included. The two-flux method for a single layer yields excellent results for gray and two band spectral calculations. The diffusion method yields a good approximalion for spectral behavior in laminated multiple layers if the overall oplical thickness is larger than about ten. A hybrid spectral rnodcl is developed using Ihe two-flux method in the optically thin bands, and radiative diffusion in bands that are optically thick.

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