1,4 • RADIANT EXCHANGE 



the problem of interchange in a gray-gas-containing system requires one 

 more item for completion. Near the beginning of Art. 4, the concept of 

 partial emissive powers of a no-flux surface due to the separate effects 

 of the various sources and sinks was presented. This leads to an evalu- 

 ation of the equilibrium temperature of a no-flux surface. It may be 

 shown [5, Chap. 4; 36] that 



^ R 



iD^Tt + 2D«T^ + 



+ nD«n + 



+ .^RTt 



D 



(4-13) 



Since the sum of the D^'s in the numerator can be shown to equal D, 

 Eq. 4-13 states that T% is a weighted mean of the fourth powers of the 

 various original emitters present, including all source-sink surfaces and 

 the gas — as it must of course be. Application of this relation to determine 

 the equilibrium refractory temperature in a simple system consisting of 

 a gray gas enclosed by a single heat-sink zone Si and a single no-flux 

 zone Sr, with all values of eg taken to be the same, yields 



^ R — ^ e 



(Tt - T\) 



1 



(4-14) 



1 + 



FriI 



1^\/1__ 



61 JKFriI 



■ + ^ + 1 



; Ol 



When /Si is black, the last term in the denominator drops out. 



Application of the factor Jig. Returning now to the use of 3^ig, con- 

 sider the same simple system just used in illustrating the calculation of 

 Tr. From Eq. 4-11 



Si^ig = »Siei — Si^ii 



= s 



or 



oiS^ig 



1 



11 + IR'/iRR - Sr) 



(4-15) 



(4-16) 



When €i becomes 1, ^u by definition becomes i^ig and, from Eq. 4-16, 



and 



SiFig — Si 



Si 



Si^u 



11 +-^=^ 

 {RR 



TR' 



Sr) 



- - 1 

 ei 



SiFig 



(4-17) 



(4-18) 



< 529 ) 



