Radiation Network for an Absorbing and Transmitting Medium

The foregoing discussions have shown the methods that may be used to calculate radiation heat transfer between surfaces separated by a completely transparent medium. The radiation-network method is used to great advantage in these types of problems. 

Returning to the analysis, we note that the medium can emit and transmit radiation from one surface, to the other. Our task is to determine the network elements to use in describing these two types of exchange processes. The transmitted energy may be analyzed as follows. The energy leaving surface 1 which is transmitted through the medium and arrives at surface 2 is 

Now consider the exchange process between surface 1 and the transmitting medium. Since we have assumed that this medium is nonreflecting, the energy leaving the medium (other than the transmitted energy, which we have already considered) is precisely that energy which is emitted by the medium 

And of the energy leaving the medium, the amount which reaches surface I is 

Of that energy which leaves surface 1, the quantity which reaches the transparent medium is 

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