I • ENGINEERING CALCULATIONS OF RADIANT HEAT EXCHANGE 



true. For a real gas, with its characteristic absorption in certain spectral 

 regions, the absorbable wavelengths are filtered out after a number of 

 passages through the gas, and the transmittance of the gas for the re- 

 mainder of the radiation approaches 1. The gray gas assumption thus 

 leads to prediction of too large an interchange between gas and sinks, 

 and too small an interchange between the source-sink surfaces. In ob- 

 taining a value of *Si?Fig applicable to a real gas, it is desirable to retain 

 the mechanics of gray gas formulation. Fortunately, this is possible. 



For a gray gas the transmittance for the absorption path length repre- 

 sented by 'pjj is e-'^pg^, where k is the absorption coefficient of the gas, 

 a constant independent of wavelength and therefore applicable to the 

 integrated spectrum; and the absorptivity and emissivity equal 1 — e~^^i^^. 

 The relation of transmittance to pJj for a real gas can be represented to 

 any desired degree of accuracy by 



J = a;e-fc-p^ + ye-''yP^ + ze'^'^^ + • • • (5-1) 



and the emissivity relation by 



e = a;(l - e-^^^^) + y{\ - e-*"^^) + z{l - e"*'"-^) + • • • (5-2) 



with kx representing the absorption coefficient applicable to fraction x of 

 the total energy spectrum of the gas, and with the condition 



x + y + z+ - ■ ■ =1 (5-3) 



Representing e-^^p^ by Tx, Eq, 5-1 yields for the transmittance T„g of n 

 layers of gas each of absorption path length 'pjb: 



r„g = XTl + ijt; + 2r? + ■ • • (5-4) 



The components of which the total real-gas transmittance is composed 

 are thus a series of gray body transmittances, each used with a weighting 

 factor, X, y, . . . . 



Consider now an enclosure of surfaces which aid in the transmission 

 of radiation from the gas to Si only by the process of reflection at the 

 other surfaces, i.e. a system of gray source-sink surfaces and completely 

 reflecting, or white, no-flux surfaces. A little consideration will show that 

 the real-gas solution for *Si3^ig is obtainable as the weighted sum of a num- 

 ber of gray gas solutions, using successively Tx, Ty, and t^ for the gas trans- 

 missivity and weighting each solution by the factors x, y, z, etc. ; or 



^u = a:5iJ + y^u] + • • • (5-5) 



J based on J based on 



use of Tx use of t„ 



and similarly 



0^12 = x^i2\ , + y^ii\ , + • • • (5-6) 



J based on J based on 



use of 7x use of t„ 



< 532 ) 



