Abstract
The present paper presents a general formulation of the radiative heat flux and its divergence for multi-dimensional radiative problems involving nongray absorbing-emitting gases. The expressions obtained are in terms of total band absorptance rather than the spectral absorption coefficient. Thus the frequency integration is eliminated, and the expressions are more compact. They avoid the necessity of detailed spectral absorption coefficient data for radiative transfer computations. Also presented is the bulk radiative exchange approximation together with its refinement. It is proposed to circumvent the mathematical complexity inherently imbedded in nongray multidimensional problems. The approximation, which is valid in the optically thin and thick limits, is found to be general and useful, not only because of its simplicity, but also because of its accuracy in all optical conditions.
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