I • ENGINEERING CALCULATIONS OF RADIANT HEAT EXCHANGE 



Flux between gas and surfaces; the factor 3^ig. The treatment of the 

 general problem of radiation in a gas-containing enclosure was not com- 

 pleted by presentation of Eq. 4-3 giving Sm^mn. In addition to the various 

 values of g^et for different pairs of source-sink zones, one is interested in 

 the net transfer between any one of such zones and the gas, which may 

 well be the primary heat source of the system. The net radiant flux from 

 the gas is given by 



?g,net = Qa-l + q^^2 + • • • (4-9) 



and Qe^i is given by 



g.^1 = S,^^,a{Tl - Tt) (4-10) 



The problem is to evaluate JFig. Let aSi be the only original emitter in the 

 system; all other source-sink zones and the gas are kept at absolute zero. 

 S\ radiates at the rate A^iei per unit value of black emissive power at tem- 

 perature Ti. Radiation streaming away from ^2, Sz, . . . , Sr, Ss, • • • 

 is due solely to reflection at S2, S3, ... , and to reflection and/or re- 

 radiation at Sr, Ss, .... Of the total emission Siei, the amount /SiO^n re- 

 turns to and is absorbed by Si, Si^u goes to and is absorbed by >S2, . . . , 

 Si^in is absorbed by Sn- The residue must have been absorbed by the gas 

 since all other surfaces are nonretaining. Then 



Si^u = >Si(ei - J?ii - $Fi2 - • • ■ - ^m) (4-11) 



Since it will have been necessary to evaluate all of these 5's except S^n 

 in fixing the radiant interchange in the system, S^n is the only new factor 

 requiring evaluation to determine SiUrig. Another approach to the problem 

 [5, Chap. 4; 36] yields the following direct formulation: 



Sr.^n, = ^'^ (4-12) 



in which gD„ is obtained by inserting, into the nth column of D 

 (Eq. 4-2), thejerms -^1 +JT1 -|- 12 + • • • + I^ + • ^, -_^2 + 

 (21 + 22 + 2S -\- '■ - + 2R +•••),■■■ , -Sr + (Rl -{- R2 + 

 ' • • -\- RR -\- • • •). Any one of these expressions may be written 



— <S„[1 — (FnlTnl + FnlTnl + " " " + F„RTnR + ' ' ")] 



the parenthetical term of which equals the weighted-mean transmissivity 

 or transmissivity for the total radiation arriving at or leaving Sn (and 

 therefore identifiable with a single subscript, xn) . The complement of t„ is 

 the gas absorptivity and, because it is gray, the gas emissivity Cgn. Note 

 that egi and eg2 differ only because the mean path lengths through the 

 gas to *Si and S2 differ. Eq. 4-12 may of course be shown to be the equiva- 

 lent of Eq. 4-11. 



Temperature of no-jiux zones. Before the use of Eq. 4-11 is discussed, 



< 528 ) 



