Non-grey radiative heat transfer in the picket-fence approximation

The radiative heat transfer between parallel plates separated by an absorbing gas with a “picket-fence” absorption coefficient is treated by a variational technique. For the heat transfer, a simple rational algebraic expression is obtained and the variational results are found in excellent agreement with the numerically “exact” results reported recently by Reithet al.(⁸) An expression for the extrapolation distance is also deduced and the results are compared with the values reported earlier by Bond and Siewert.(⁵)