1,3 • RADIATION FROM FLAMES AND GASES 



important, exact allowance for stream temperature variation can be made 

 by conventional graphical integration. Let the heat transfer surface per 

 unit length be designated by P, the local gas and surface temperatures 

 at length x by Tg and Ti, the mass flow rate and heat capacity of the gas 

 by m and Cp, and the local heat transfer rate — by whatever mechanisms, 



0.20 



0.10 



0.05 



j 0.03 

 }J" 0.02 



0.01 



0.005 



2X 10'2 



10'3 



10' 





Tt 



Fig. I,3g. Plot for calculation of mean gas temperature T'^ in countercurrent gas 

 radiant heat exchangers, in terms of arithmetic mean gas and surface temperatures Tg 

 and Ti and gas-temperature change Tgi — T^i- (Cohen [33].) 



and expressible as a function of T^ and Ti — by (g/>S)iocai- Then one may 

 write 



mc,dT, = iq/S):o..iPdx (3-6) 



If the gas temperature at length B is Tg,B, the above yields on integration 



mc,, J T. 



dT. 



{q/S\ 



(3-7) 



Then a plot of the reciprocal of the local transfer rate vs. gas temper- 

 ature yields a curve, the area under which is proportional to the length 

 of the exchanger. This graphical procedure can be avoided, however, by 

 evaluation of suitable mean gas and surface temperatures for use in Eq. 

 3-4 or 3-5 to obtain {q/S),.. Fig. I,3g, from Cohen [33], gives the mean 

 gas temperature for radiation T'^ as a function of the four terminal tem- 

 peratures. The mean surface temperature T[ is that corresponding to the 

 point in the exchanger where the gas temperature is T'^, and may be 

 obtained by an enthalpy balance. 



Rigorous allowance for temperature variations in a gas within the 



(521 > 



