1,6 • APPLICATION OF PRINCIPLES 



make allowance for grayness of a refractory surface. In this case *S2 is 

 truly a no-flux surface, with S^UiT^ - To) = h^S^iT, - T^). Then Eq. 

 6-5 can be readily solved for T^. If this is put into Eq. 6-4a and 6-4b and 

 the radiation terms of those two equations are added, one obtains 



yg. net loss ^1, net gain 



by radiation by radiatiot 



^1^1. + — j — ^ — —] <^t - n) (6-6) 



+ 



*Si3^i2 82^ 



The bracket, allowing as it does for the radiation from gas to Si with the 

 aid of S2, is like the term ^lO^ig for the system, gas-*Si->Sie (with ^2 repre- 

 senting Sr) except that it now allows for the grayness of S2. If, in Eq. 6-6, 

 S2 is assumed to be a white surface (p2 = 1), it may be shown that the 

 bracketed term reduces to the »Si?Fig of Eq. 6-1. 



Estimation of heat transfer in a combustion chamber. Although rela- 

 tions have been presented for evaluating radiant heat transmission in 

 chambers filled with the combustion products of fuels, those relations 

 have been restricted to idealized cases in which the gas temperature was 

 uniform or was changing in one dimension along a flow path long com- 

 pared to the transverse dimensions. Plainly, the average combustion 

 chamber, in which combustion and mixing are occurring simultaneously 

 and in a complicated flow path which involves recirculation as well, is far 

 from typical of the idealized systems discussed. Those systems can never- 

 theless provide an indication of the performance to be expected and can 

 in many cases be used for quantitative prediction. The simplest case to 

 discuss is the limiting one in which all dimensions of the chamber are of 

 the same order of magnitude, and in which the mixing energy provided 

 in the incoming fuel and air produces a turbulent gas mixture uniform in 

 temperature throughout and equal to the temperature of the gas leaving 

 the chamber. Assume the problem to be the determination of heat trans- 

 fer in the chamber, given the mean radiating temperature Ti of the stock 

 or heat sink, the chamber dimensions, and the fuel and air rates. Let the 

 unknown mean gas temperature (and exit temperature) be Tg. Then the 

 net heat transfer rate from the gas is given by 



g.net = Si^i,a{TI - Tt) + hiS[iT, - Ti) H- Vn&niT, - To) (6-7) 



The sink area S[ at which convection heat transfer occurs is indicated as 

 possibly different from the area ;Si at which gas radiation occurs, because 

 heat sink surfaces such as a row of tubes covering the gas outlet from the 

 chamber, and therefore receiving by convection no heat which affects the 

 mean gas temperature in the chamber, should be included in &x but not 

 in &[. Convection from gas to S>r has been assumed equal to the loss 

 through Sr, which replaces it in the equation. With the outside air tem- 

 perature To known, Eq. 6-7 expresses a relation between two unknowns, 



< 537 ) 



