Near black surfaces
The Gebhart method describes the radiative heat transfer in terms of heat coming from one surface and absorbed by another, including all reflections. The Gebhart matrix traces exactly the radiative transfer contribution of each surface to the others.
For two surfaces with high emissivities (close to 1) the Gebhart factor can be simplified by:
Reflections are then not taken into account, but because of the low reflectivity its fraction is relatively small and therefore also the error you make. In that case the relation becomes:
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