1,3 • RADIATION FROM FLAMES AND GASES 



in which eg..^ is the gas emissivity evaluated at the arithmetic mean of 

 Tg and Tx. Values of a and h, which represent d In ejd In pjj and d In tj 

 d In Tg, respectively, are given in Fig. I,3f for CO2 and H2O. When a 

 mixture of the two gases is present, it is recommended that mean values 

 of a, h, and c be used in Eq. 3-5, the factors for the different gases being 

 weighted in proportion to their emissivities. (A roughly approximate 

 value of (a + 6 — c) suffices, however, since an error of 0.1 in it produces 

 an error of only 2.5 per cent in q/S.) The use of Eq. 3-5 when Tg and Ti 

 do not differ by a factor greater than 2 leads to results of accuracy com- 

 parable to Eq. 3-4, and will usually save time as well by eliminating the 

 necessity for the fairly tedious evaluation of a^i. 



Mean beam length. The preceding expressions were formulated for 

 the case of interchange between a gas hemisphere and a spot on its base, 



0.01 



0.008 



5000 



1000 2000 3000 4000 5000 1000 2000 3000 4000 



Temperature, °R Temperature, °R 



Fig. I,3f. Rate of change of emissivity with T and p^L, for CO2 and H2O. 



i.e. for the case in which the path length L of the radiant beam is the 

 same in all directions. For gas shapes of practical interest, it is found that 

 any shape is approximately representable by an equivalent hemisphere 

 of proper radius, or that there is a mean beam length L which can be 

 used in calculating gas emissivities and absorptivities from Fig. 1, 3a and 

 1, 3c [30,31]. As pL approaches zero, the mean beam length approaches as 

 a limit the value 4a; (ratio of gas volume to bounding area) . For the range 

 of pL encountered in practice, L is always less; 85 per cent of the limiting 

 value is generally a satisfactory approximation [32]. Table 1,3 summarizes 

 the results of tedious graphical or analytical treatment of various shapes. 

 Temperature variation along flow path. If gas radiation occurs in a 

 system in which there is a continuous change in temperature of the gas 

 or surface, or both, along the gas flow path from one end to the other 

 of the interchanger, and if the dimensions transverse to flow are small 

 enough to make radiant exchange in the flow direction relatively un- 



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