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 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 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 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, |