Radiative exchange between black bodies

The calculation of radiative exchange is simplified if black bodies are considered, because no reflection occurs and the entire incident radiation flow is absorbed. Besides that, the intensity Ls of a black body is only dependent on its temperature. Therefore the intensity is constant on an isothermal surface of a black body. This was a prerequisite for the calculation of view factors in the previous section. 

We will calculate first the direct radiative interchange between two black bodies of arbitrary shape with surfaces Ax and A2 and uniform temperatures 7 and T2, Fig. 5.54. In this case, all radiation flows emitted by one body that do not strike the other body will be ignored. The proportion of the radiation flow emitted by 1 and incident on 2 is given by 

This energy flow is absorbed by black body 2. The radiation flow received and absorbed by black body 1, from body 2, is 

The net radiation flow transferred by direct radiative interchange from 1 to 2 is therefore 

If both bodies are at the same temperature Tx = T2, then no (net) energy flow will be transferred between them hj2 = 0. This then yields 

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Fig. 5.54 Radiation flows 12 and 21 in direct radiative exchange between black bodies 1 and 2...

Consider radiative exchange between a body of area A i and temperature Ti and black surroundings at To. The net interchange is given by... 

Fig. 1.11 Radiative exchange between a body at temperature T and black surroundings at temperature...

The net radiation flow transferred by direct radiative exchange between two black bodies is proportional to the difference of the fourth powers of their thermodynamic temperatures. 

As an introduction, a simple case of radiative exchange will be looked at. A radiator with area A, and at temperature T, is located in surroundings which are at temperature Ts, see Fig. 1.11. The medium between the two shall have no effect on the radiation transfer it shall be completely transparent for radiation, which is a very good approximation for atmospheric air. The surroundings shall behave like a black body, absorbing all radiation, as = 1. 

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