G • COOLING BY PROTECTIVE FLUID FILMS 

 the equation 



i: 



durdr 



Ti 



I urdr 

 Jo 



The heat transfer coefficient is then defined by 



q = h(Tu - T^) 

 where heat flow per unit area at the wall is 



=-ex 



- I (Ti - TJ 



\^'7/.;=l 



(5-40) 



(5-41) 



(5-42) 



In nondimensional form, the heat transfer coefficient or Nusselt number 



Nu is 



hD 



Nu = 



k 





+ ^i 





■4^'-^ M[{1) 



"4^'-^M^(l) + 



(5-43) 



The temperature distribution given in Eq. 5-30 may be used to deter- 

 mine the amount of coolant required to cool the wall to a predesignated 

 temperature. From the condition of heat balance at the wall, one obtains 



'>m. 



dx = -pv^Cp{T^ - To)l 



(5-44) 



Upon substitution of Eq. 5-30 into the above equation, one obtains the 

 temperature difference ratio as follows : 



Ti 



= 4PrX 



4Pr\ 



+ 



A^M'M 



1 - 



^2 



l-O + ^rJ)' 



4PrX 



(5-45) 



4PrX 



where 



M'jil) = 





In Fig. G,5d the heat transfer coefficient or Nusselt number is plotted 

 against the coolant Reynolds number. It indicates that the Nusselt num- 



< 468 ) 



