1,2 ■ THE VIEW FACTOR 



by which <j{T\ - Tl) should be multiplied is not e, but e[l + (n/4)]. 

 Eq. 1-4 can be used with small error over an absolute temperature ratio 

 up to 2. 



1,2. The View Factor. Direct Interchange between Surfaces. 



The relations just given were restricted to radiant interchange when a 

 surface Si could "see" nothing but surroundings at T2. The more com- 

 plicated but important case of interchange in a system of several sur- 

 faces at different temperatures and emissivities involves the concept of 

 a geometrical view factor F. F12 is defined as the fraction of the radiation 

 leaving a surface Si in all directions which is intercepted by a surface S2. 

 Evaluation of this factor is as follows: Visualize, on black surface Si of 

 total emissive power Whi, a small surface element dSi radiating in all 

 directions from one side, and on a black surface ^^2 a small surface ele- 

 ment dS2 intercepting some of the radiation from dSi. Let the straight 

 line connecting dSi and dS2 have length r, and let r make angles di and 62 

 with the normals to dSi and ^^§2 respectively. The rate of radiation from 

 dSi to dSi, called dqi-^2, will be proportional to dSi cos di, the apparent 

 area of dSi viewed from dS2 ', to dS2 cos 62, the apparent area of dS2 viewed 

 from dSi] and inversely proportional to the square of the distance sepa- 

 rating the elements. Calling the proportionality constant Jbi, one may 

 write 



, J (iAi cos 01 c? J. 2 cos 02 ,0 -.x 



dgi-^2 = J hi ^ (2-1) 



This equation defines Jbi, the intensity of radiation from a black surface. 



By integration of Eq. 2-1 over a receiving surface filling the field of 

 view of dSi, one obtains WhidSi, the total rate of emission from dSi 

 throughout the hemisphere. The integration gives irJ^idSi, from which 

 one concludes that the emissive power Wb of a black surface is tt times its 

 intensity of radiation Jb- By integration of Eq. 2-1 over finite areas Si 

 and S2 to obtain the rate of radiation from one to the other and dividing 

 the result by SiWhi, one obtains Fu, the desired fraction of the radiation 

 leaving surface Si in all directions which is intercepted by surface S2. 

 Although the discussion has been restricted to black surfaces, it is ap- 

 parent that for a nonblack surface Si the emissivity of which is inde- 

 pendent of angle of emission, F12 calculated by the method above will 

 continue to represent the fractional radiation from Si intercepted by S2 

 (though not necessarily absorbed unless ^2 is black) . 



Important and useful concepts in evaluating F's are that 



S1F12 = S2F21 (2-2) 



(since otherwise there would be a net heat flux between Si and S2 when 



< 507 ) 



