Contributed by the Heat Transfer Division for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received by the Heat Transfer Division February 5, 1999; revision received April 16, 2001. Associate Editor: P. Menguc.

The mathematical model for describing a radiation field in a participating medium is the radiative transfer equation (RTE). The dependent variable in the RTE, the spectral radiative intensity, is a function of location, wavelength, and solid angle. This makes it very difficult to be solved, especially for multi-dimensional geometry. Therefore previously the gray medium assumption was usually used to simplify the problem 1,2,3, and combined conductive-radiative heat transfer in multi-dimensional geometry was also studied 4,5,6. In order to incorporate the nongray effects, many approximate methods have been developed. One of them is to apply the picket fence model 7, where the band-distributed radiative properties are...

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