F • CONVECTIVE HEAT TRANSFER IN GASES 



1.0 



Cf 



0.8 



0.6 



0.4 



0.2 



10 



Me 



Fig. F,llh. Effect of heat transfer and Mach number on local skin friction 

 coefficient according to Eq. 11-28 for a Reynolds number of 10^. 



which is different from Eq. 11-28 by the term | log {T^/Te). When the 

 plate is insulated, Eq. 11-29 reduces to the formula derived by Wilson [33]. 

 Other formulas are readily derivable. For example, Cope [34] held the 

 density constant and equal to the wall value in Eq. 11-20, so that, with 

 I = Ky, he obtained for the velocity profile 



u 



Ue 



F + — 



H^Jl 



(11-30) 



When the density is allowed to vary according to Eq. 11-24, the von 

 Kdrmdn integral (Eq. 11-27) then leads to the following expression: 



242 T 



(11-31) 



Cope originally derived this formula for the case of the insulated plate 

 only, where 



T y — I 



— = 1 + M^ 



Te ^2 " 



i.e. B = Oin Eq. 11-24. 



The most simple approach (and the first attempted) was that used by 

 von Kdrmdn [35], who allowed the density to remain constant and equal 



< 384 ) 



