I • ENGINEERING CALCULATIONS OF RADIANT HEAT EXCHANGE 



chromatic absorptivity a\, and is given in terms of the monochromatic 

 absorption coefficient k\ by 



ex = 1 - e-^x-^^ (3-1) 



in which c is the soot concentration and L is the path length through the 

 flame. The absorption coefficient k\ varies approximately as an inverse 

 power function of X [18,19,20,21]. Suppose k-K to be representable by fc/X" 

 so that ex is (1 — g-^c^/x")^ ^j^^j jg^ ^.^i^ y^^ represented by KL, called the 

 absorption strength of the flame. A little consideration will show that if 

 KL and the true flame temperature Tf are known, the complete descrip- 

 tion of the thermal radiating characteristics of an isotropic flame can be 

 inferred, including the monochromatic emissivity at any wavelength, the 

 total emissivity €{, the total emissive power of the flame Wf( = ei(xTf), 

 and the effect of flame size and shape on the emission from its envelope. 

 It may be shown [5, Chap. 4; 18] that 2 properly chosen optical measure- 

 ments on the flame suffice to determine these properties. Among the most 

 useful pairs of measurements are: (1) red brightness temperature T^ (de- 

 termined with an optical pyrometer) and total emissive power W{ (de- 

 termined with a total radiation pyrometer; (2) T, for a single and for a 

 doubled flame thickness, the latter by use of a mirror behind the flame; 

 (3) red brightness temperature of the flame alone and of the flame backed 

 by a target of known red emissive power, near that of the flame ; (4) total 

 emissive power of the flame alone and of the flame backed by a target of 

 known total emissive power. The method of interpreting these data is 

 presented elsewhere [5, Chap. 4]. 



The emissivity of luminous flames varies greatly, and the eye is no 

 judge; a flame so bright that nothing on the other side of it can be seen 

 may nevertheless be far from a black body. The total emissivity may 

 vary from a maximum value near unity in a two-foot depth of a natural- 

 gas diffusion flame down to the value due only to infrared radiation from 

 combustion products, in a premixed gas-air flame. (For the latter value, 

 due to CO2 and H2O, see below, this article.) 



Luminosity due to larger particles. Reference here is to the particles 

 from a pulverized coal or well-atomized residual fuel oil flame — particles 

 large compared to the wavelength of radiation of interest and therefore 

 acting simply to block out a beam passing through the flame. It may 

 readily be shown that for such particles the emissivity of the flame sur- 

 face, from the direction in which L is the path length through the flame, 

 is given by 



e, = 1 - e-c.iL (3_2) 



where c is the number of particles per unit volume, and A is the projected 

 area of a particle. This may be applied to a heavy fuel oil flame to esti- 

 mate the degree of atomization necessary to make luminosity of this kind 



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