F • CONVECTIVE HEAT TRANSFER IN GASES 



The ratio i/g^ is plotted versus ^i in Fig. F,3. For algebraic calcu- 

 lations, Crocco found that the combination {X/\g*\)[{g/i) — 1] can be 

 represented by the linear expression 0.7828 + 0.0178 |^*| over the practi- 

 cal range of g'^, between —2.2 and —4 (see Fig. F,3). Thus, to within a 

 slight error, viz. 



bg^ =g^{\ -i) -g^a - i) (3-27) 



the laminar boundary layer on a fiat plate can be solved by successive 

 approximation. 



Crocco gives a method of computing the error 8g^ in Eq. 3-27 (see [1]) ; 

 however, according to the experience of the writer [2], 8g^ was found to be 

 neghgible for all practical purposes, being of the order of 10~^ for i = 0.02. 



Now that the momentum and energy equations can be integrated 

 separately, it is necessary to iterate between the two integrals in order 

 to obtain accurate enthalpy and shear distributions. Crocco found it suf- 

 ficiently accurate for his purposes to calculate the enthalpy distribution 

 only once using the Blasius shear distribution, whereupon that enthalpy 

 distribution was introduced in the momentum equation to compute a 

 new and final distribution. 



F,4. Heat Transfer. The rate of heat transfer to the boundary layer 

 per unit area is 



gw = 



= --^-/iUO)tw 



= — n K(0)t„ 



where subscript w refers to the wall. 



Substitution of Eq. 3-16 into Eq. 4-2 gives 



(4-1) 



(4-2) 



since 



1 h 



l+|_e/2(l)_/,^(0) 



S{1) We 

 1 Tw 



S{1) Ui 



8(1) 2 VRe I 2 



K + 2i2(l) ^ -h. 



eWe i 



(4-3) 



(4-4) 



^*(0) 



\PeM 



— ^Tw and Re = 



K Me 



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