F • CONVECTIVE HEAT TRANSFER IN GASES 



skin. Such a procedure becomes quite laborious because it usually involves 

 the numerical method of finite differences [62]. Fortunately, it is still suf- 

 ficiently accurate to consider only the heat transfer normal to the plate. 

 In the steady state (cruise), the left-hand side of Eq. 16-1 is zero. 

 The results of typical temperature calculations in the steady state are 

 shown in Fig. F,20d for a flat plate at zero angle of attack for both laminar 

 and turbulent boundary layers. The plate was assumed to be moving at 

 Mach number 3 at elevation 50,000 ft. in the NACA Standard Atmos- 

 phere. The emissivity was taken at 0.5 and the incident radiation was 

 assumed to be 200 BTU/ft^ hr. The heat transfer coefficients were ob- 

 tained from Fig. F,5i for laminar flow and from Eq. 11-2, 11-19, and 11-29 



2500 



2000 



an 



o 



^ 1500 



E 

 CD 



1000 



500 



4 6 8 10 12 



Velocity, (ft/sec) X 10"^ 



14 



16 



Fig. F,20g. Flat plate flight temperature at point 5 ft from 

 leading edge. Altitude constant at 40,000 ft. Steady state. 



for turbulent flow. To facilitate calculations with turbulent flow, Eq. 

 11-29 can be put in nomographic form \6S\. It is seen that the temper- 

 atures decrease with distance from the leading edge and that they are 

 considerably higher for a fully turbulent boundary layer than for a 

 laminar boundary layer. 



Fig. F,20e and F,20f may be useful in hypersonic cruising-missile 

 design, because they show at what altitude a missile must cruise in order 

 to maintain a given temperature at a distance 5 ft aft of the leading edge, 

 assuming the missile can be represented by a flat plate. The plate is at 

 zero angle of attack, the radiation emissivity was again taken at 0.5, and 

 the NACA Standard Atmosphere was used. Fig. F,20e is for laminar flow 

 and Fig. F,20f for turbulent flow. Lines of constant Reynolds number 

 per foot of length are also indicated in the figures. The temperature con- 



(410) 



