Heat Exchange between Nonblackbodies

The calculation of the radiation heat transfer between black surfaces is relatively easy because all the radiant energy which strikes a surface is absorbed. The main problem is one of determining the geometric shape factor, but once this is accomplished, the calculation of the heat exchange is very simple. When nonblackbodies are involved, the situation is much more complex, for all the energy striking a surface will not be absorbed part will be reflected back to another heat-transfer surface, and part may be reflected out of the system entirely. The problem can become complicated because the radiant energy can be reflected back and forth between the heat-transfer surfaces several times. The analysis of the problem must take into consideration these multiple reflections if correct conclusions are to be drawn. 

We shall assume that all surfaces considered in our analysis are diffuse and uniform in temperature and that the reflective and emissive properties are constant over all the surface. Two new terms may be defined  

In addition to the assumptions stated above, we shall also assume that the radiosity and irradiation are uniform over each surface. This assumption is not strictly correct, even for ideal gray diffuse surfaces, but the problems become exceedingly complex when this analytical restriction is not imposed. Sparrow and Cess [10] give a discussion of such problems. The radiosity is the sum of 

The net energy leaving the surface is the difference between the radiosity and the irradiation  

At this point we introduce a very useful interpretation for Eq. (8-38). If the denominator of the right side is considered as the surface resistance to radiation heat transfer, the numerator as a potential difference, and the heat flow as the current, then a network element could be drawn as in Fig. 8-24 to represent the physical situation. This is the first step in the network method of analysis originated by Oppenheim 120]. 

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