G • COOLING BY PROTECTIVE FLUID FILMS 



Upon substitution of the term of the velocity gradient from Eq. 5-56 

 into Eq. 5-62 it may be integrated to give 



T = [e-/o^^f)'^f]/o [JU("<^f] k{^)d^ + r^e-JU(«^f (5. 



63) 



where 



He. 



+ Kiii - nr 1 - 



^^M'^'T^-^^W 



h{^) = 



4:A f u 



_gin_ 



2— fs 



Wo 



(5-64) 



The term {u^/u^{2/PrRe) is due to heat transfer by molecular conduc- 

 tivity which is negligibly small in comparison with the eddy heat trans- 

 fer term except very close to the wall. The empirical constant K\ may be 

 determined from the measured temperature profiles. 



In Fig. G,5g the effect of coolant injection on the temperature dis- 

 tribution of a fully developed turbulent flow in a circular pipe was shown. 

 The comparison between the theoretical curve calculated from Eq. 5-63 



r 

 R 



0.8 



0.6 



0.4 



0.2 



1.0 



0.2 0.4 0.6 



T/T, 



0.8 1.0 



Fig. G,5g. Effect of coolant injection on the temperature 

 distribution in turbulent pipe flow. (From [35].) 



(474) 



