engineering fundamentals Radiation: Blackbodies
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Blackbody Radiation Heat Transfer
The heat emitted by a blackbody (per unit time) at an absolute temperature of T is given by the Stefan-Boltzmann Law of thermal radiation,
where has units of Watts, A is the total radiating area of the blackbody, and s is the Stefan-Boltzmann constant.

A small blackbody at absolute temperature T enclosed by a much larger blackbody at absolute temperature Te will transfer a net heat flow of,

Why is this a "net" heat flow? The small blackbody still emits a total heat flow given by the Stefan-Boltzmann law. However, the small blackbody also receives and absorbs all the thermal energy emitted by the large enclosing blackbody, which is a function of its temperature Te. The difference in these two heat flows is the net heat flow lost by the small blackbody.
Gray Body Radiation Heat Transfer
Bodies that emit less thermal radiation than a blackbody have surface emissivities e less than 1. If the surface emissivity is independent of wavelength, then the body is called a "gray" body, in that no particular wavelength (or color) is favored.

The net heat transfer from a small gray body at absolute temperature T with surface emissivity e to a much larger enclosing gray (or black) body at absolute temperature Te is given by,

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