G • COOLING BY PROTECTIVE FLUID FILMS 



Radial temperature profiles were also measured at six stations along 

 the axis of the porous-wall pipe. The inner temperature of the porous wall 

 was measured at six axial stations by thermocouples of the integrating 

 type. The results of the measured temperature profiles were also used in 

 a comparison with those of the theoretically calculated temperature pro- 

 files. This comparison was given in Fig, G,5g. The results of the present 

 temperature-profile surveys for a fully developed turbulent pipe flow with 

 coolant injection at the wall will be used to develop a semiempirical rela- 

 tion of the heat transfer coefficient for transpiration cooling. The study 

 has not reached the stage at which final results can be presented at this 

 time. 



U 



Experimental points §i = 0.497 [43] 

 Tineoretical curve l\ = 0.497 [7] 

 Theoretical curve ?i = [7] 



10 



12 



14 



Fig. G,6c. Comparison of theoretical and experimental velocity 

 profiles with injection for J = {v^/UyRcx = 1.0. (From [43].) 



Question of Skin Friction and Heat Transfer Coefficient. As 

 pointed out in Art. 4 the rate of change of momentum in the boundary 

 layer due to mass fluid injection at the wall has the same effect as the 

 rise of pressure gradient in the flow direction. Hence it is clear that the 

 increase of fluid injection at the wall increases the thickness of boundary 

 layer and decreases the slope of the velocity profile at the wall in the 

 boundary layer. In the case of laminar boundary layer it is evident that 

 the wall shearing stress and heat transfer from the hot gas to the wall 

 decreases as the injected coolant increases. Since the heat flow from hot 

 gas to the wall can be expressed by the following forms : 



-(a 



= /ii(T'g — Tw) 



(6-1) 



(478) 



