A continuous exchange factor method for the analysis of radiative exchange in gray enclosures with absorbing-emitting and isotropically scattering media and diffuse surfaces is developed. In this method two types of exchange function are defined: the direct exchange function and the total exchange function. Certain integral equations relating total exchange functions to direct exchange functions are developed. These integral equations are solved using a Gaussian quadrature integration method. The results obtained based on the present approach are found to be more accurate than those of the zonal method. Unlike the zonal method, in the present approach, there is no need for evaluation of multiple integrations for calculating direct exchange factors.

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