I • ENGINEERING CALCULATIONS OF RADIANT HEAT EXCHANGE 



Although Eq. 5-5 or 5-6 can in principle be used to handle an en- 

 closure of any degree of complexity as to zoning, and filled with gas of 

 radiating characteristics producing any shape of curve of eg vs. pj^, a little 

 consideration shows what an enormous amount of effort is involved if 

 these expressions for CF contain many terms. A simplification is mandatory 

 and, fortunately, feasible. If wall reflectivities are not very large, a beam 

 of radiation from the gas is rapidly attenuated in its succession of reflec- 

 tions and transmissions, and the fitting of the €g — pju curve is important 

 only for a few units of yjj. The transmittance r given by Eq. 5-4 can be 

 made to equal true transmittance at and at two integral multiples of 

 PgL by assuming the gas gray throughout the energy fraction x and clear 

 throughout the fraction y-\-z-\-'--=\— x, i.e. by assuming that 

 all the r's but Tx are zero and that an asymptotic transmissivity of 1 — a; 

 is approached as pgL = oo . An examination of Eq. 5-5 now indicates that, 

 since all values of i?ig on the right-hand side except the first are for non- 

 absorbing gas and therefore are zero. 



ig = .T^Jig] (5-8) 



J based on 



use of Tx 



For source-sink surface interchange, Eq. 5-6 yields 



iFi2 = x^rA ^ + (1 - rc)Ji2l ^ (5-9) 



Jbased on Jbased on 



use of Tx clear gas, 



r=l 



There remains only the evaluation of x and Tx from a gas radiation 

 plot such as Fig. 1, 3a. Let the objective be to fit the eg, pjj curve at 1 and 

 2 units of pjj, and call the corresponding e's read from the plot, eg and e2.g. 

 From Eq. 5-4 



1 — eg = Tg = XTx + (1 — x) 

 and 



1 — e2.B = T2.g = XtI -\- {I - x) 



Solution of these gives 



x = H — (5-10) 



^eg — eo.g 



and 



r, = 1 - !? = 1 - ^'^ ~ ^'-^ (5-11) 



X Cg 



Recapitulating, fFig equals x times a value of 3^ig from Eq. 4-12 (or Eq. 

 4-18 and 4-20) using a transmissivity of 1 — {ejx) or an emissivity of 

 ejx, with x defined by Eq. 5-10. 



The determination of x and r^ from values of eg at IpgL and 2jpjj is 

 recommended when *Si has a low reflectivity and/or when yjj is large; 

 but a small enclosure with heat-sink zones of high reflectivity may make 



< 534) 



