G,4 • TRANSPIRATION-COOLED BOUNDARY LAYER 



assumptions made in the present article are: (1) the inverse proportion 

 between the mass density and the temperature inside the boundary layer 

 is used, and the viscosity is assumed to be proportional to both the square 

 root and three-fourths power of the temperature ; (2) the flow is assumed 

 to be laminar, and the fluid flowing along the wall and the coolant flow- 

 ing through the pores are assumed homogeneous; (3) the Prandtl number 

 is assumed to be equal to unity; and (4) the wall temperature in the 

 direction of flow is constant. 



1.0 



0.8 



hi 

 h 



0.6 



0.4 



0.2 



0.002 0.004 0.006 0.008 0.010 



Q. 

 W 



Fig. G,4c. Ratio of heat transfer coefficient with and without 

 transpiration-cooled plate vs. mass flow ratio. 



Crocco [10] has shown that, for a Prandtl number equal to unity, the 

 equation of motion in the boundary layer of a flat plate in steady com- 

 pressible flow and the corresponding energy equation can be satisfied by 

 equating the temperature T to a certain parabolic function of the ve- 

 locity u only. This relation between T and u is 





7\ 



-S-) 



U^ 2 U 



i'-i) 



(4-9) 



With the aid of Eq. 4-9 the variation of mass density and viscosity inside 

 the boundary layer can then be expressed as a function of the velocity u 

 only. As in the case of incompressible flow a polynomial of the fourth 

 degree as an approximation to the velocity profile is assumed and its 



< 443 ) 



