E,4 • ANALYSIS FOR CONSTANT FLUID PROPERTIES 



various curves are approximately equal on a log-log plot. This result 

 justifies the usual practice in heat transfer investigations of writing 

 Nu = /{Re, Pr) as f{Re) X f{Pr) (usually as Re'^Pr^). The same result 

 does not hold for very low Prandtl numbers where the slopes change 

 considerably. 



A comparison between predicted and experimental results is given in 

 Fig. E,4d. Fully developed mass transfer as well as heat transfer data are 

 included, inasmuch as an analogy exists between heat and mass transfer 

 when the concentration of the diffusing substance is small. The Stanton 

 number is plotted against the Prandtl or Schmidt number for a Reynolds 

 number of 10,000. Similar results were obtained for Reynolds num- 

 ber, of 25,000 and 50,000 [15]. The predicted Stanton numbers were 



0.01 



13 



111 



oo 0.001 



o.ooo: 



LO 



0.00001 



0. 



Pr 



10 



Cp|j[/k 



or 



100 



Sc = [Ji/pX 



000 



10,000 



Fig. E,4d. Comparison of analytical and experimental results 

 for fuUy developed heat and mass transfer. 



obtained from Fig. E,4c and the relation St — Nu/{RePr). The symbols 

 represent mean lines through data for heat transfer in gases [IJi] and in 

 liquids [29,30,31 ,32,33,34] and mass transfer by evaporation from wetted 

 walls [35,36,37] by solution of the wall material in a hquid [38,39] and by 

 diffusion-controlled electrodes [4-0]. The predicted and measured values 

 are in good agreement over the entire range of Prandtl and Schmidt 

 numbers shown (0.5 to 3000). 



A simplified equation can be obtained for the case of very high 

 Prandtl numbers. For that case the essential temperature changes take 

 place in the region very close to the wall where w* is very nearly equal to 

 y*. Converting Eq. 3-2 to dimensionless form, setting u* = y*, expand- 

 ing the exponential function in a series, and retaining only the first two 



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