F • CONVECTIVE HEAT TRANSFER IN GASES 



in Fig. F,9b, where the 0°F and 200°F supply-temperature curves are 

 taken from Fig. F,6d. The local Reynolds number varied from 2 X 10^ to 

 1.5 X 10^ Now in the case of fiat plates in wind tunnels, the theory pre- 

 dicts hardly any effect of Mach number as compared to free flight con- 

 ditions. Thus, according to Fig. F,9b, the theory seems to be corroborated. 

 The fact of the matter is that, in the wind tunnel, the density effect is 

 offset by the nearly Hnear viscosity variation at the lower wind tunnel 

 temperatures. Indeed, for linear viscosity-temperature variation, there is 

 no effect of Mach number or heat transfer. It should be pointed out that 

 according to Fig. F,6a, free flight data with moderate heating or coohng 

 (nearly insulated cone) would show more clearly the compressibility 

 effect, although the effect compared to the drag of the entire test vehicle 



0) 



u^ 



1.0 

 0.8 

 0.6 

 0.4 

 0.2 



Supply 

 temperature, °F 



200 



NOLdata,(67°F) 

 O 1 0° cone 

 n 20° 

 A 60° 



O Heat flow into cone 

 • Heat flow out of cone 



1 2 3 4 5 



Local Mach number Me 



Fig. F,9b. Comparison of theory and experiment on local heat transfer 

 coefficient for laminar boundary layers on cones in a wind tunnel. 



would be difficult to detect, owing to the small proportion of the laminar 

 flow drag compared to the drag of the whole vehicle. The Reynolds num- 

 ber effect is certainly verified in Fig. F,9b, since the error in the data is 

 small compared to the range of the square root of the Reynolds number. 



TURBULENT FLOW 



F,10. Flat Plate Solution. When the boundary layer is turbulent, the 

 energy equation can be solved in the same way as for laminar flow. How- 

 ever, the momentum equation is not amenable to solution, even after 

 certain assumptions are made concerning the turbulent mechanism. The 

 integral method will therefore be used in the following paragraphs to 

 obtain surface friction, based on a velocity profile derived from mixing- 

 length theory. 



It can be shown [21] that the continuity, momentum, and energy 

 equations for a thin turbulent boundary layer in the mean steady state 



< 370 > 



