I • ENGINEERING CALCULATIONS OF RADIANT HEAT EXCHANGE 



For this system all direct view factors can be expressed in terms of the 

 single one Frx as follows : 



\R = SlFlRTlR = SrFritir 



TT = SiFnni = Si(l - FiR)Tu = (Si - SrFri)^ 



RR = SrFrrTrr = Sr{1 — FriJTrr 



Substitution of these values in Eq, 4-17 and replacement of t by 1 — e^ 

 gives 



Tu = en 1 + 



Sr 



Si 



eii/egfl — eii , en _ 1 

 1 — €ii 1 — en Fri 



{Sr/Si)F%, 



Fri + eRRil - Fri) 



(en + eRR — 2eRi + e|i — eneRR) (4-19) 



in which double-subscript e's refer to an evaluation of gas emissivity based 

 on a path length specific to the two surface elements mentioned. The 

 problem, simple as it appeared to be, has a solution rather formidable 

 for engineering use. If the various gas emissivities are assumed to be alike 

 or if each one is replaced by their average value, called eg, it will be noted 

 that the second term on the right of Eq. 4-19 will vanish, giving 



>S 



R 



Fi. = e, I 1 + ^ i (4-20) 



1 - e^Fj 



Some practical consequences of Eq. 4-18 and 4-20 are these: increasing 

 the flame emissivity increases the heat transmission, but not proportion- 

 ately; decreasing surface emissivity ei (and absorptivity) from one, when 

 the flame is very transparent, produces but little effect on the heat trans- 

 mission; but decreasing ei from one, when the flame is substantially 

 opaque (eg = 1), produces a proportional decrease in heat transmission. 

 The Hmitations on the vahdity of Eq. 4-18 and 4-20 must be borne in 

 mind. They are restricted to a one-zone sink, a one-zone refractory or 

 no-flux surface, and a gray gas. The first two assumptions are rigorously 

 justifiable only when each element of Si (or Sr) shares its "view" of its 

 own zone and of Sr (or ^i) in the same ratio as every other element; and 

 this in turn is true only when the two kinds of surfaces are intimately 

 mixed in the same ratio on all parts of the enclosure, forming what one 

 might call a "speckled" enclosure. Under those circumstances, the as- 

 sumption made in going from Eq. 4-19 to 4-20, that the various Cg's are 

 representable by an average value, becomes valid; and Fri becomes *Si/ 



( 530 ) 



