G,4 • TRANSPIRATION-COOLED BOUNDARY LAYER 



the reciprocal of the square root of the distance from the leading edge 

 of a flat plate. However, the velocity and temperature profiles obtained 

 by this method are quite accurate. They can be used in a laminar bound- 

 ary layer stability analysis. 



The equations of the laminar boundary layer for steady state flow of 

 a viscous compressible fluid with heat transfer may be obtained from 

 Vol. IV as 



Momentum equation: 



du , du d 



pu~ + pv— = — 



dx ay ay 



(^S 



dp 

 dx 



Continuity equation: 



Energy equation: 



d{pu) _^ d{pv) ^ Q 



dx 



dy 



( dT . dT\ d A dT\ , ( 



dliV dp 



dy) dx 



(4-14) 



(4-15) 



(4-16) 



The boundary conditions are: when y = 0, 



and when y = ^ , 



u = Q) V = v,,{x); T = T^ 



u = u.; P = 0; T = T.; ^ = 

 ' dy ' ' dy 



(4-17) 



Incompressible boundary layer with constant fluid properties. In the 

 case of incompressible laminar boundary layer flow with constant fluid 

 properties (p = constant and /x = constant) [15], the last two terms in 

 Eq. 4-16 can be neglected. When the velocity outside the boundary layer 

 is assumed to be proportional to a power of distance along the wall 

 from the stagnation point (We = ex™), the transformation methods of 

 Schlichting [16] and of Falkner and Skan [17] can be applied. With the 

 following changes in variables: 



(4-18) 



where u = d^p/dy, v = —d^p/dx and m is the Euler number, the momen- 

 tum equation (Eq. 4-14) and the energy equation (Eq. 4-16) are trans- 



(447 ) 



