I • ENGINEERING CALCULATIONS OF RADIANT HEAT EXCHANGE 



and color are more important than their chemical composition [3]. (3) The 

 emissivities of most nonmetals are above 0.8 at low temperatures and in 

 the range 0.3 to 0.8 at furnace refractory temperatures. (4) Iron and 

 steel vary widely with the degree of oxidation and roughness: clean me- 

 tallic surfaces have an emissivity of 0.05 to 0.45 at low temperatures and 

 of 0.4 to 0.7 at high temperatures; oxidized and/or rough surfaces, 0.6 to 

 0.95 at low temperatures and 0.9 to 0.95 at high temperatures. (5) In- 

 conel, nichrome, and type 310 stainless steel all show a marked increase in 

 emissivity when maintained at temperatures above 1500°F [4]. Table 1,1, 

 abstracted from a more comprehensive table appearing elsewhere with a 

 bibliography [5, Chap. 4], gives the emissivities of various surfaces and 

 emphasizes the large variation possible in a single material. Although the 

 values in the table apply strictly to normal radiation from a surface (with 

 few exceptions), they may be used with small error for hemispherical 

 emissivity. Well-polished metal surfaces have a hemispherical emissivity 

 15 to 20 per cent higher, and well-polished nonmetals about 7 per cent 

 less, than the normal value [6]. 



The absorptivity a of a surface depends on the factors affecting emis- 

 sivity and, in addition, especially on the quality of the incident radiation, 

 i.e. on its temperature. One may assign two subscripts to a, the first to 

 indicate the receiver and the second, the emitter of the radiation; more 

 specifically, to indicate their respective temperatures. As seen in Sec. G, 

 according to Kirchhoff's law, the emissivity of a surface at temperature 

 Tx is equal to the absorptivity q:i,i which the surface exhibits for black 

 radiation from a source at the same temperature, i.e. a surface of low 

 radiating power is also a poor absorber (or good reflector or transmitter) 

 of radiation from a source at its own temperature. If the monochromatic 

 absorptivity ax varies considerably with wavelength and much less with 

 temperature (which is generally the case for nonmetals), it follows that 

 the total absorptivity a;i,2 will vary more with T2 than with Ti. Data of 

 Sieber [7] on 0:1,2 at Tx = 70°F for a large group of nonmetals appear in 

 Fig. I, lb, indicating a decrease, with increase in T2, from 0.8-0.95 at 

 500°R to 0.1-0.9 at 5000°R. The absorptivity of metallic conductors, on 

 the other hand, increases approximately linearly with -s/TxT^. 



If a\ is a constant independent of X, the surface is called gratj, and its 

 total absorptivity a will be independent of the spectral-energy distribu- 

 tion of the incident radiation; then 0:1,2 = ai.i = ci, i.e. emissivity e may 

 be used in substitution for a even though the temperatures of the incident 

 radiation and the receiver are not the same. 



Radiant interchange between a small nongray body of area Sx and 

 temperature Tx in black surroundings at To is plainly given by 



gi^2 = c7^i(eiT,* - ax.^Tl) (1-2) 



It has been seen that over a moderate temperature range 0:1,2 can be 



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