I • ENGINEERING CALCULATIONS OF RADIANT HEAT EXCHANGE 



as the surfaces, are assumed gray. A gray gas is one which exhibits, for 

 radiation from whatever source, an absorptivity a equal to its emissivity e. 

 Its emissivity and absorptivity vary, however, with path length. If the 

 gas transmissivity r, equal to 1 — a, is established for radiation from one 

 zone to another, the transmissivity for twice the mean beam length be- 

 tween zones is r^, a conclusion which can be true only for a gray gas which 

 does not produce a change in quality of the radiation transmitted by it. 

 (2) Such reflection as occurs, whether at a source-sink or at a no-flux 

 surface, must be diffuse reflection, a term describing reflection which, like 

 black radiation, obeys the cosine principle that appeared in Eq. 2-1 ; and 

 emission from any surface must likewise obey the cosine principle. Non- 

 metallic and oxidized metallic surfaces do not depart greatly from this 

 characteristic. (3) A zone of the no-flux surfaces, or those of the source- 

 sink surfaces which are not black, must be chosen small enough so that 

 the intensity of radiation leaving the zone in consequence of irradiation 

 by some other zone is uniform over the zone. This completes the assump- 

 tions. The additional nomenclature needed is the representation of trans- 

 mittance from one zone through the gas to another zone by t with ap- 

 propriate subscripts to indicate the two zones involved. 



Flux between gray source-sink surfaces; the factor 3^i2. The net flux 

 between *Si and S2 occurs by a complex process involving multiple reflec- 

 tion from all source-sink surfaces as well as both reflection and reradiation 

 from the no-flux surfaces; and one might at first consider the contribution 

 of Sr, Ss, ... to the net flux between Si and *S2 impossible to disen- 

 tangle, since the equilibrium temperature of Sr, for example, depends on 

 contributions from Sz, S4, . . . as well as from Si and S2. The new con- 

 cept necessary here is that the refractory zone Sr can be thought of as 

 having a partial emissive power due to the presence of each of the source- 

 sink zones and the gas, and a total emissive power equal to their sum. 

 Thus the term qi^2 represents net flux between Si and ^2 consequent 

 solely on their respective emission rates and includes, in addition to direct 

 interchange SiFueie2cr{Tf — T'2)ti2, the contributions due to multiple re- 

 flection at all surfaces, as well as such contributions by reradiation from 

 the no-flux surfaces as are consequent on their partial emissive powers 

 due to the existence of Si and *S2 alone as net radiators in the system. 

 This is the necessary meaning of gi-2 if it is to become zero when Ti = T2. 

 It is apparent that gi^2 must take a form equal to cr{Tf — T^) multiplied 

 by some factor which depends on the geometry of the whole enclosure, 

 the emissivity of its source-sink surfaces and the transmittance of the gas, 

 and that it can be expressed in the form 



qi^2 = Si^u<7{Tt - TI) ^ S2^2i<r{Tt - Tt) (4-1) 



The problem is to evaluate the new factor JF, called the over-all exchange 



< 524) 



