E,4 • ANALYSIS FOR CONSTANT FLUID PROPERTIES 



equal, because the curves are plotted on log-log coordinates (c?(log T*)/ 

 d{log y*) = 1 at the wall). 



Included for comparison is the temperature distribution for a Prandtl 

 number of 300, calculated by assuming e„ = n'^uy (n = 0.109) close to 

 the wall rather than Eq. 3-2. This expression is a good approximation 

 for velocity profile but, as indicated in the figure, is not accurate at high 

 Prandtl numbers. Somewhat better results were obtained in [11], where it 

 was assumed that e„ = const u'^/{du/dy), but the analysis is again in- 

 accurate at very high Prandtl numbers. The sensitivity of the temper- 

 ature profile at high Prandtl numbers to various assumptions for the 



10,000 



5 



a 

 U 



I- 



1000 



100 



I- 



1 



10 100 1000 10,000 



Fig. E,4b. Generalized temperature distributions for various Prandtl numbers. ~|; 



turbulent transfer in the region close to the wall, compared with that of 

 the velocity distribution, indicates that the region very close to the wall 

 could be studied advantageously by measuring temperatures ':at high 

 Prandtl numbers, rather than by measuring velocities in that region. 

 Some work along these lines has been reported in \12\. In that case, con- 

 centration profiles, rather than temperature profiles, were measured for 

 mass transfer at high Schmidt numbers. No evidence of a purely laminar 

 layer (linear concentration profile) was found for values of y* as low as 

 one. This result is in agreement with Eq. 3-2, which indicates that e^ = 

 only at the wall. 



Relations among Nusselt, Reynolds, and Prandtl numbers. It can 

 readily be shown from the definitions of the various quantities involved 



< 295 ) 



