and in which u^ = u/ue, p^ = p/pe, h^ = h/K, and g^ = 2 y/x/pefj^u^ • r. 

 Subscript e indicates conditions at the outer edge of the boundary layer, 

 and the primes denote differentiation with respect to u^. 



Inspection of Eq. 3-8 and 3-9 shows that the momentum equation 

 (Eq. 3-8) is nonhnear, and besides, according to Eq. 3-lOa and 3-lOb, 

 the boundary conditions are on opposite sides of the boundary layer. 

 Hence the solution of Eq. 3-8 is expected to be somewhat troublesome. 

 On the other hand, the energy equation (Eq. 3-9) is linear and first order 

 in Ai/Pr as a function of u^, so that the solution of Eq. 3-9 is readily 



K 

 Pr 



= exp 



ff*(0) 



(1 - Pr) 



dg. 



U;(o) 



9* \\Pr(0) 

 exp 



ff*(0) 



(i_p.)f]d«.) 



(3-11) 



assuming that the shear distribution is known from the momentum 

 equation. Further integration gives 



h^iu^) = h^{0) + 



Km 



Pr(0) 



Pr • exp 



ff*(0) 



(1 



T^ / Pr • exp 



Ale /O 



Pr) 

 dg^ 



dg^ 



du. 



(1 - Pr) 



or 



where 



S{u^) 

 and 

 R{u^) 



exp 



h^{u^) = /i*(0) -t- 



(1 - Pr) ^ 



du^ \ du 



^SK)-gK(«,) 



Pr • exp 



Pr • exp 



ff*{0) 



(1 - Pr) "'=^* 



dg^ 



9* 



du^ 



(3-12) 

 (3-13) 



(3-14) 



g*(0) 



exp 



(1 



9* 



(1 - Pr) ^ 

 LJg*iO) 9* 



Now, /i^(l) = 1. Hence from Eq. 3-13, 



Pr(0) 



KiO) = 



si.1) L 



l-/i,(0)+^^P(l) 

 <343 > 



du^ \ du^ (3-15) 



(3-16) 



