E • CONVECTIVE HEAT TRANSFER AND FRICTION 



°F. This differs from the case for gases where the temperatures were 

 measured in °R. From the definitions of T* and /S, 



-^ = (1 - ^T*y 



The analysis proceeds similarly to that for air, with the exception that 

 p/p^ = k/K = 1 in Eq. 2-5, 2-6, and 3-2' [15]. 



Generalized temperature distributions for a Prandtl number at the 

 wall of 10 and a d of —4 are shown for various values of the heat flux 

 parameter in Fig. E,5d. Corresponding curves can be obtained for the 

 variation of u* with y*. From these curves, Nusselt numbers and Reyn- 

 olds numbers with properties evaluated at the wall temperature can be 



TOO 



T* 



60 



40 



20 



10 



100 



1000 



10,000 



Fig. E,5d. Generalized temperature distribution for liquid with 

 variable viscosity, m/mw = {T IT^y^. Prandtl number = 10. 



calculated by using Eq. 3-4, 3-5, 3-6, and 3-7. Reference temperatures for 

 evaluating the viscosity in the Reynolds and Prandtl numbers in order to 

 eliminate the effects of heat flux, or variable viscosity, can then be 

 calculated. 



Fig. E,5e summarizes the results of the calculations. Curves are shown 

 for both Nusselt numbers and friction factors. If we define the reference 

 temperature Tr by 



Tr ^ r{T^ - T,) + T, (5-5) 



then r is given by Fig. E,5e. Nusselt numbers can be obtained from Fig. 

 E,4c if the viscosity in the Reynolds and Prandtl numbers is evaluated 

 at Tr. The values of r in Fig. E,5e were computed for values of d (m/mw = 

 {T/T^Y) of —1 and -4 and for values of Mb/Mw of about 0.5 and 2. The 

 value of d had little effect on the curves, but different curves are obtained 



< 308 ) 



