G,4 • TRANSPIRATION-COOLED BOUNDARY LAYER 



density and viscosity of the fluid are assumed to be constant, (2) the 

 flow is assumed to be laminar, and the fluid along the wall and the coolant 

 flowing through the pores are assumed homogeneous, and (3) the wall 

 temperature in the direction of flow is constant. 



In accordance with the above assumptions, Eq. 4-1 and 4-2 can be 

 simplified considerably by dropping both the second terms on the left- 

 hand side and taking out p, n, and Cp from the integrals. Furthermore, 

 both Me and Te are equal to the constant quantities U and T^ in the free 

 stream. The term giving the heat produced through internal friction in 

 Eq. 4-2 can be neglected because it is comparatively small at the low 

 speed considered here. 



Fig. G,4a. Boundary layer along a porous transpiration-cooled wall. 



In order to solve these two simplified momentum and energy equa- 

 tions for the boundary layer, polynomials of the fourth degree as approxi- 

 mations of the velocity and temperature profiles are assumed. The coef- 

 ficients of the fourth degree polynomials are calculated from the boundary 

 conditions used by Pohlhausen, except that at the wall the velocity per- 

 pendicular to the main flow is equal to the injection velocity v^ instead 

 of zero value. The results are, for velocity profile, 



u 

 U 





1 +x 



and for temperature profile, 



(4-3) 



T - T^ 

 T — T 





2\h 

 1 +X;, 



(4-4) 



< 439 ) 



