I • ENGINEERING CALCULATIONS OF RADIANT HEAT EXCHANGE 



in Art. 5 indicated, the no-flux surface must be treated as a source-sink 

 type surface S2. Three S^'s are necessary for a complete solution. Based 

 on the simplifying assumption that the r's between zone pairs are all 

 ahke, Eq. 4-12 and 5-8 yield 



Ci *Si *S2 \p2Tx / '^1^15 



x{l - T,) — ^ — ^-— ^ ^ (b-2) 



Pi 1 1 



Tx Tx 



\Pl / \P2 ''/ 



Si SiFyiTj: 



9?2g is obtained from the above by the interchange of subscripts 1 and 2 . 

 Si^i2 is obtained from Eq. 4-4 and 5-6, which yield 



€1 ^2 



e a: _ ' Pi P2 



Olffl2 = 



1_J i_J A_.. 1_, 



Pi / I \P2 / , \Pl / \P2 



>Si >Sir 12T1 



n — ^ — — 



Pi / I \P2 / I \Pl / \P2 



>S2 ^1 S1F12 



These three S^'s are for use in the heat transfer equations 



q,^i = Si^i,a{Tl - Tt) + hrSr{T, - Ti) (6-4a) 



g.^2 = S2^2ATt - Ti) + h2S2{T, - 7^2) (6-4b) 



?2^i = Sr^MTI - Tt) (6-4c) 



(The difference between 3^j_>y and 'Sfx^y is here ignored for simplicity 

 of treatment.) If surface ^2 is losing heat to the outside at a rate 

 S'iU{T2 — To), a heat balance on S2 yields 



gg^2 = 52;=^! + S2U{T2 " T q) 



or 



S.^2ATt - r.1) = Sx^MT'. - Tt) + S2U{T2 - To) - /^-SoCT, - T2) 



(6-5) 



Assuming the source temperature Tg and the primary sink temperature 

 Ti to be known, Eq. 6-5 permits a solution for the unknown refractory 

 temperature T2 (but trial-and-error because mixed in first and fourth 

 powers). 



The other application mentioned for this system of equations was to 



( 536 ) 



