G • COOLING BY PROTECTIVE FLUID FILMS 



A balance between the heat flow to the wall from the hot fluid and 

 the heat absorbed by the coolant at the wall yields 





1 + TO 



Pr^ 



u 



(de/drj). 



(4-27) 



For a predesignated wall temperature and given Prandtl number, Euler 

 number, and Reynolds number, the amount of coolant required can be 

 determined from Eq. 4-27 provided that the temperatures of the hot fluid 

 and of the coolant are known. In Fig. G,4d the ratio of the temperature 

 difference, (Te —T\)/(T^ — To), is plotted against the coolant mass flow 

 ratio {Q/W) -y/Rex for Pr = 0.7. It is seen that the influence of the 



> 



12 



14 



T — T 



I w — To 



Fig. G,4d. Temperature ratio vs. mass flow ratio for 

 favorable, zero, and adverse pressure gradients. 



pressure gradient on the coolant discharge and the wall temperature is 

 appreciable. For a favorable pressure gradient (m = 1) the heat trans- 

 fer to the wall is increased almost twice the value of the flat plate case 

 (w = 0). On the other hand, the heat transfer to the wall is diminished 

 by 25 per cent of the flat plate value with a small adverse pressure gradi- 

 ent. The wall skin friction behaves in a similar manner but it will be more 

 sensitive to change with the pressure gradient than the heat transfer to 

 the wall. Furthermore, the displacement and momentum thicknesses are 

 reduced to approximately one third of their flat plate values in the favor- 

 able pressure gradient, but the thermal boundary layer thickness is 

 changed only slightly in this case. 



Calculations of 58 velocity and temperature distributions were made 

 for air which include the simultaneous effects of pressure gradients in the 



( 450 ) 



