I • ENGINEERING CALCULATIONS OF RADIANT HEAT EXCHANGE 

 gg. net and Tg. The other relation is an energy balance, such as 



gg.net = i - mCpiTg - To) (6-8) 



where i represents the hourly enthalpy of the entering fuel, air, and re- 

 circulated flue gas, if any, above a base temperature To (water as vapor) ; 

 and Cp represents the heat capacity (mean value between Tg and To) of the 

 gas leaving the chamber, at hourly mass rate m. Eq. 6-7 and 6-8 may be 

 solved, usually by trial and error, to give gg, ^et and Tg. The limitation on 

 Qg, that it does not include gas convection at area S — S', must be borne 

 in mind. 



The pair of equations just discussed applies strictly to one of two 

 limiting combustion chamber types — that one in which the assignment 

 of a mean flame temperature equal to the temperature of the gases leaving 

 is justifiable. The method consequently predicts the minimum heat trans- 

 fer of which the system is capable. Better agreement between predicted 

 and experimental results is obtained on some furnaces when the assump- 

 tion is made that flame temperature and exit gas temperature are not 

 the same but differ by a constant amount. In a number of furnace tests 

 used to determine what value of this difference produces agreement be- 

 tween experiment and the equations recommended, the difference was 

 found to be about 300°F. 



The other extreme in chamber types is that one in which combustion 

 occurs substantially instantaneously at the burners (through complete 

 premixing of fuel and air); the temperature attained is that generally 

 known as theoretical flame temperature or adiabatic combustion tem- 

 perature; and the temperature falls continuously as the gases flow from 

 burner to outlet. When such a chamber is long compared to its cross sec- 

 tion normal to the direction of gas flow, Eq. 6-7 may be considered as 

 applying to a differential length, and the remarks in connection with 

 Eq. 3-6 are applicable. One must, however, be prepared to examine the 

 validity of the assumption that radiant flux in the gas flow direction is of 

 secondary significance. Allowance for the improbability of attainment of 

 adiabatic flame temperature at the hot end of the chamber may be made, 

 though somewhat arbitrarily, by use of what Heiligenstadt [4-5] calls a 

 pyrometric efficiency, the factor by which to reduce the adiabatic flame 

 temperature to obtain the true value. If the gases are assumed constant 

 at this temperature from burner inlet until, by the calculation method 

 just outlined, they have lost enough heat to equal the difference between 

 their entering enthalpy and that at their assumed temperature, and they 

 are allowed thereafter to cool in step with their heat transfer rate, better 

 agreement with experimental data can of course be obtained — provided 

 there is knowledge of what to use for the pyrometric efficiency. It varies 

 primarily with burner and chamber design and fuel type. A value of about 

 0.75 has been used in application to steel reheating furnaces. The chief 



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