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THE RADIATIVE TRANSFER EQUATION WITH MEAN ABSORPTION COEFFICIENTS

DOI: 10.1615/ICHMT.2004.RAD-4.120
8 pages

J.-F. Ripoll
Center for Turbulence Research, Department of Mechanical Engineering, 488 Escondido, Building 500/500A, Stanford University, CA 94305-3035, USA

A. A. Wray
Center for Turbulence Research NASA Ames Research Center

Abstract

In order to remove the frequency dependence in the radiative transfer equation (RTE), mean absorption coefficients can be introduced and modeled. It will be first shown that the model proposed here for these coefficients is accurate when the frequency dependence is not too strong. The frequency-integrated RTE using these coefficients will be also shown accurate compared to the full RTE. A large range of spectral absorption coefficients, having the form σ = C να, will be tested for a simple 1D slab; α varies between -3, which is the limit value of the model, and 4. The validation of these coefficients allows us to conclude first that the frequency dependence can be modeled in the RTE instead of solving it directly, provided that the spectral coefficient is not too complex or stiff, and that these coefficients will accurately model complex opacities when used in macroscopic radiation models.

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