G • COOLING BY PROTECTIVE FLUID FILMS 



Fig. G,4g presents the ratio of skin friction coefficient with fluid in- 

 jection to the skin friction with zero fluid injection at the same Reynolds 

 number and wall-to-free-stream mass flow ratio for both suction and in- 

 jection. Fig. G,4h represents analogous plots of the heat transfer coef- 

 ficient ratio. It can be seen that the theoretical curves give good quali- 

 tative agreement with the experimental data [30]. 



G,5. Heat Transfer in Transpiration-Cooled Pipe Flow. 



Laminar Pipe Flow with Coolant Injection at Wall [31,82]. In 

 Art. 4 the problem of heat transfer in a transpiration-cooled boundary 



t t t I t t t t t t 



X = vw 



A = VwR/v -f- A for injection 



Re = UmD/v — A for suction 



To Vw 



1 I t t I I I i 



Ti \r 



Tw 



t f t 1 t t i t t f 



X — To Vw 



Fig. G,5a. Velocity and temperature distribution along a porous circular pipe. 



layer has been treated to a great extent in the case of a laminar flow over 

 a porous plate. For flows in a conduit, such as the combustion chambers, 

 afterburners of jet motors, and the nozzles of rocket motors, it is not 

 exactly clear whether the results obtained from the transpiration-cooled 

 boundary layer can be directly applied. Because of the unclarified status 

 it is desirable to obtain the basic phenomena of the nonisothermal fully 

 developed flow through a porous-wall pipe with coolant injection. 



The problem of heat transfer of a steady laminar flow in a circular 

 pipe has been studied (Graetz [33] and Nusselt [54]) since the latter part 

 of the last century. In these studies it was assumed that the wall temper- 

 ature is constant and changes discontinuously at a; = (see Fig. G,5a). 

 The physical properties of the fluid are independent of temperature and 

 the Poiseuille velocity distribution is maintained throughout the motion. 



< 460 ) 



