F • CONVECTIVE HEAT TRANSFER IN GASES 



the maximum heat transfer rate occurs at the stagnation point. This 

 follows immediately from the fact that the terms p°/poo and ii^/ix^ in Eq. 

 7-2b and 7-3b decrease as the ambient temperature decreases with expan- 

 sion of the gas about the body. The way in which 8t^ varies over the face 

 of the body was worked out by Stine and Wanlass [12]. The theoretical 

 variation as well as experimental data for Pr = 0.7 are shown in Fig. 

 F,7b, when the properties of the flow are put in terms of local conditions, 

 i.e. St^ = —q^/Cp^p^uXTe — T^) and Re^^ = p^u^x/ix^. 



All of the above formulas are for laminar flow. It is expected that the 

 flow will be laminar in the immediate vicinity of the stagnation point 

 owing to the low Reynolds numbers of the local flow. 



F,8. Effect of Variable Free Stream Pressure and Variable Wall 

 Temperature. Thus far, only the basic problem of the heat transfer to 

 a compressible boundary layer with constant wall temperature and con- 

 stant free stream velocity, but variable properties, has been discussed. 

 It is now desirable to make a few remarks about the effects of wall tem- 

 perature gradient and free stream velocity gradient. 



The effect of variation in the free stream pressure (velocity) has been 

 studied by many authors (e.g. Goland [13], Levy [14], Morris and Smith 

 [15], to mention only a few), working mainly with integral equations. 

 The results indicate that falling pressure (accelerated flow) increases the 

 local heat transfer, whereas increasing pressure (retarded flow) decreases 

 local heat transfer. 



A solution of the momentum and energy equations, including an arbi- 

 trary analytic distribution of surface temperature but with zero pressure 

 gradient, has been obtained by Chapman and Rubesin [16] (see also 

 Lighthill [17]), assuming constant specific heat and constant Prandtl 

 number. The results show, for example, that for a surface temperature 

 which is falling in the direction of flow, and which is always less than the 

 recovery temperature on an insulated wall, the local heat transfer rate 

 to a plate at a certain point is greater than that for a surface temperature 

 which is constant and equal to the temperature at the point. This result 

 is of considerable importance near points of ogives and leading edges of 

 airfoils. 



Other effects. The rate of heat transfer from a laminar boundary layer 

 to a surface can also be influenced strongly by the insulating action of 

 fluid injection (cf. Sec. G). The diffusion of a foreign gas into the bound- 

 ary layer from the wall is discussed by Smith [18], who finds that helium 

 produces considerable decrease in the rate of heat transfer to a plate. 



F,9. Status of Experimental Knowledge. At the outset, it is very 

 difficult to obtain accurate laminar flow data, because the magnitudes 

 to be measured are small. Although a number of experimental investiga- 



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