SECTION I 



m I m 



ENGINEERING CALCULATIONS OF 

 RADIANT HEAT EXCHANGE 



HOYT C. HOTTEL 



1,1. Radiating Characteristics of Surfaces. Knowledge on the 

 reader's part of the general nature of thermal radiation and the laws of 

 black body radiation will be assumed in this section (see this volume, 

 Sec. H). Fig. I, la summarizes, for numerical use, the radiating charac- 

 teristics of a black body in the form of a plot of monochromatic emissive 

 power^ TFbx divided by the fifth power of the absolute temperature versus 

 the wavelength-temperature product. The curve may be visualized as an 

 intensity-wavelength distribution at 1° absolute. An extra scale along the 

 top permits a determination of the fraction of the spectral energy found 

 below a given wavelength X. The area under the curve is directly the 

 Stefan-Boltzmann constant (r[0.1713 X IQ-^ BTU/ft^ hr (°R)4; 5.67 X 

 10-5 ergs/cm^ sec (°K)4; 4.88 X 10"^ kg-cal/m^ hr fK)^; 1.00 X 10"^ 

 CHU/ft^ hr (°K)4], for use in the relation 



TFb = (jT^ (1-1) 



where W^ is the total emissive power, throughout a sohd angle of 27r 

 steradians, of a black body or ''perfect" radiator. 



In evaluating radiant heat transfer between surfaces, one could con- 

 sider monochromatic radiation exchange and integrate throughout the 

 spectrum; certain advantages would appear. For most engineering pur- 

 poses, however, it is simpler to formulate total radiation exchange, ex- 

 pressing it in terms of the 4th power temperature law strictly applicable 

 only to the black body or perfect radiator, and to let the more-or-less 

 weak residual temperature function be taken care of by the variable total 

 emissivity, absorptivity, or transmissivity of the pertinent bodies. 



The emissivity e of a surface (more properly the total hemispherical 

 emissivity, to differentiate it from monochromatic emissivity ex and from 

 directional emissivity eg, the ratio of radiating powers in a direction mak- 

 ing the angle d with the normal to the surface) varies with its temper- 

 ature, its degree of roughness or grain size, and, if a metal, its degree of 



^ Emissive power refers to radiation throughout a full hemisphere of 2^7 steradians, 

 and is irJ where J is intensity (see Art. 2). 



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