Application of Rosseland approximation and solution based on series expansion of the emission power to radiation problems

Yehuda Taitel, J. P. Hartnett

Research output: Contribution to journalArticlepeer-review

Abstract

The nature of errors introduced by the use of approximate methods for determining the radiant heat fluxes in problems of pure radiation and combined convection radiation are examined in detail. Special attention is given to 1) the Rosseland thick approximation and 2) the solution based on a series expansion of the emission power. Results show that no inherent difficulty is introduced due to the fact that the emission power is not an analytic function at the wall. The series-expansion method has been found quite accurate over the complete range of optical thicknesses with the maximum errors occurring at intermediate values of the optical thickness. On the other hand, the Rosseland approximation, which is limited to the optically thick situation, is in general not as accurate as the series-expansion approach. This inaccuracy is in large part due to the fact that the Rosseland approximation is incorrect in the region of the wall, as can be verified by comparing the Rosseland expression with the more correct series-expansion expression in this region. Nevertheless, the thick approximation has been found very useful when applied with care, basically because the errors introduced in the radiant and conductive heat fluxes at the wall cancel each other to yield a reasonably accurate total heat flux.

Original languageEnglish
Pages (from-to)80-89
Number of pages10
JournalAIAA Journal
Volume6
Issue number1
DOIs
StatePublished - Jan 1968
Externally publishedYes

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