1,4 • RADIANT EXCHANGE 



Black source-sink surfaces; the factor F12. Further to indicate the tech- 

 nique of application of the determinant method, let Eq. 4-4 be used to 

 determine the interchange factor when all source-sink surfaces are black. 

 The interchange factor for this case has been designated by F, to indicate 

 that it covers a more complex situation than F but a less general one 

 than fF. Let the problem be to evaluate F12. Setting into Eq. 4-4 the con- 

 dition that ei = €2 = es . . . = 1 or that pi = P2 = Ps • • • =0, one can 

 eliminate all rows and columns containing reference to any source-sink 

 surface except 1 and 2 as follows. 



Cancel Si/pi out of the numerator and multiply the denominator first 

 columnbypi/^Siwhich, being zero, makes the first column —1,0, 0,0, . . . 

 and reduces the order of D by one. Similarly, multiply the second column 

 of the numerator and the second column of the new denominator by P3/S3, 

 making them become 0, — 1, 0, 0, . . . each. Similarly, eliminate all terms 

 containing numbers other than 1 and 2. One thus obtains 



S1F12 = 



(4-6) 



If there is but one refractory zone, all rows and columns mentioning 

 others may be crossed out, and Eq. 4-6 yields 



*Sii^i2 = 12 4- 



-^ , (IR)(2R) 



Ar - RR 



(4-7) 



This simple result, an approximation because all no-flux surfaces are 

 assumed to be in equilibrium at a common temperature, is often adequate 

 for estimating the transfer between Si and ^2. 



If no emitting or absorbing gas is present in the system, Eq. 4-7 yields 



Tp , FirFr2 



"^ -^ 12 -t- ■, _ ET 



gas free •*• " R^ 



(4-8) 



The factor F12 for systems containing no interfering gas has been deter- 

 mined exactly for a few geometrically simple cases [35]. If Si and S2 are 

 equal parallel disks, squares, or rectangles connected by nonconducting 

 but reradiating walls, F12 is given by Fig. 1, 2b, lines 5 to 8. 



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