On the use of mean absorption coefficients in the presence of strong temperature gradients

We compare results obtained by using the Planck and Rosseland mean absorption efficientg with exact multifrequency transport results in a purely absorbing halfspace problem in the presence of strong temperature gradients. We give numerical results for both a prescribed temperature distribution in th...

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Bibliographic Details
Published in:Journal of quantitative spectroscopy & radiative transfer 1981-01, Vol.26 (3), p.199-213
Main Authors: Pomraning, G.C., Prinja, A.K., Shokair, I.R.
Format: Article
Language:English
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Summary:We compare results obtained by using the Planck and Rosseland mean absorption efficientg with exact multifrequency transport results in a purely absorbing halfspace problem in the presence of strong temperature gradients. We give numerical results for both a prescribed temperature distribution in the presence of an Elsasser band absorption coefficient and a self-consistent radiative equilibrium distribution corresponding to a source deep within the halfspace transporting through a picket fence absorption coefficient. This latter problem (the Milne problem) is analyzed using the Wiener-Hopf factorization technique, and an explicit expression is given for the characteristic H-function. We conclude that the use of the Rosseland mean is generally more accurate than the use of the Planck mean, but that the Rosseland mean results can nevertheless be significantly in error.
ISSN:0022-4073
1879-1352
DOI:10.1016/0022-4073(81)90114-X