I • ENGINEERING CALCULATIONS OF RADIANT HEAT EXCHANGE 

 Then 



*Sl5^12 = 0lO2 



(4-4) 



D 



The number of unique view factors F necessary for evaluation of JF by 

 Eq. 4-4 may be determined. By noting that in a p zone system there are 

 2)2 /T's in the determinant D but that (a) D is symmetrical and (b) any 

 row or column of F's adds to 1, it is seen that the number of unique 7^'s 

 necessary is p{p — l)/2. If, in addition, each n of the zones cannot see 

 itself, the number is further reduced by n. 



Eq. 4-4 can be used to make allowance for any degree of complexity 

 of an enclosure, and to approach the true solution to any degree of 

 approximation dependent on the number of zones into which a surface is 

 divided. The guiding principle in deciding upon the number of zones 

 necessary is that any reradiation or reflection must come from a zone 

 small enough so that different parts of its surface do not have a signifi- 

 cantly different view of the various other surfaces. Black source-sink sur- 

 faces need be zoned only according to temperature, but light gray ones 

 may require further subdivision. 



As one of the simpler examples of application of the determinant 

 method, consider a system containing no emitting or absorbing gas. One 

 case may be presented which covers a wide range of practical situations, 

 i.e. the case of an enclosure divided into any number of no-flux zones but 

 only two source-sink zones ;Si and >S2 (an especially justifiable assumption 

 if the emissivities of Si and *S2 are so high as to make reflections from 

 their surfaces relatively unimportant in the over-all heat transfer) . From 

 Eq. 4-4 it may readily be shown that for this case 



1 



Si^nj 



gas free 



kt-^)-m-^) 



+ 



1 



Sl^l2 



gas free, 

 black surfaces 



(4-5) 



( 526 ) 



