Heat Transfer: Black Body Radiation

Blackbody Radiation Heat Transfer 
The heat emitted by a blackbody (per unit time) at an absolute temperature of T is given by the StefanBoltzmann Law of thermal radiation, 
where has units of Watts, A is the total
radiating area of the blackbody, and s is
the StefanBoltzmann
constant.
A small blackbody at absolute temperature T enclosed by a much larger blackbody at absolute temperature T_{e} 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 StefanBoltzmann 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 T_{e}. 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 T_{e} is given by, 
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