F • CONVECTIVE HEAT TRANSFER IN GASES 



Crocco has shown that s = Pr^, approximately, and r = Pr^, closely, 

 where Pr is constant. Since the variation of the Prandtl number with 

 temperature is ordinarily not great for common gases such as air [4], the 

 approximate formulas s = Pr^^ and r = Pr^ can be used for practical pur- 

 poses for moderate flight conditions when an average Pr is assumed. At 

 very high speeds where skin temperatures become great, and for accurate 

 experimentation, the more exact solutions are necessary. 



F,5. Numerical Results for Zero Pressure and Temperature 

 Gradients along the Flow. Results of calculations of friction and heat 

 transfer coefficients, as well as of recovery and Reynolds analogy factors 



0.76 



0.74 

 o 



I 0.72 



C 

 "+^ 

 "2 0.70 



o 



CL 



0.68 



0.66 



3000 



1000 2000 



Temperature, °R 



Fig. F,5a. Prandtl number of dry air as a function of temperature. 



for laminar flow of air on flat plates in free flight and in heated wind 

 tunnels are presented in \S\ and reproduced to a large extent here. These 

 represent exact calculations with variable specific heat, viscosity, and 

 Prandtl number, based on the NBS-NACA Tables of Thermal Properties 

 of Gases \S\. 



The variation of Prandtl number with temperature for dry air, upon 

 which the calculations of [5] were based, is shown in Fig. F,5a. The 

 NBS-NACA Table 2.44 on Prandtl number could not be used below 

 about 400°R, because the table was based on 1-atmosphere pressure, 

 whereas the pressures in the test sections of supersonic wind tunnels are 

 usually very low under ordinary atmospheric supply conditions. There- 

 fore, in order to carry out boundary layer calculations for low pressure, 

 low temperature conditions in supersonic wind tunnels, new Prandtl 

 numbers were calculated below 400°R using the following information: 



< 350 > 



