G • COOLING BY PROTECTIVE FLUID FILMS 



cate that the heat transfer coefficient decreases with the increase of cool- 

 ant injection. Thus there is a definite direct relationship between the 

 friction coefficient and the heat transfer coefficient. On the other hand, 

 the results obtained here indicate that in a pipe flow the effect of fluid 

 injection at the wall is to accelerate the main stream velocity. Hence the 

 velocity gradient at the wall, which determines the wall friction, increases. 

 This phenomenon indicates that the analogue between the heat transfer 

 and the momentum transfer does not exist in porous-wall cooling of pipe 

 flow. 



0.12 





Fig. G,5e. Temperature difference ratio for various coolant 

 parameters {{l/PrRe){\/D) = 0.075). (From [32].) 



Approximate Solution of Turbulent Pipe Flow with Coolant 

 Injection at Wall. In the present treatment an approximate analysis 

 for determining the effect of transpiration cooling on a fully developed 

 turbulent flow in a circular pipe is given [35]. In order to simplify the 

 analysis it is assumed that: (1) the fluid is incompressible, i.e. the fluid 

 properties remain constant, (2) the fluid flowing in the axial direction 

 and the fluid flowing through the porous wall are assumed homogeneous, 



(3) the fluid flowing through the porous wall is uniform throughout, and 



(4) the wall temperature is constant. 



If a curvilinear coordinate system is introduced with the origin at the 

 center of the cross section of a circular pipe where x is taken in the direc- 

 tion of the flow and r in the radial direction and (p is the azimuthal angle, 

 then with axial symmetry of flow the Reynolds equations for the time- 



(470 > 



