Seyer and Metzner 



Tracer Studies 



Studies using small particles or bubbles suspended in liquids, although rep- 

 resenting tedious experiments, may be of special merit owing to the restrictions 

 applicable to the use of conventional probes. A recent study by Uebler (57) has 

 shown that tracer particles closely follow the flow field for flows in which only 

 moderate accelerations are present (entry flow into a tube) and for very small 

 tracer particles (bubbles ~ 0.05 cm in diameter). However, for large bubbles 

 and high flow rates spurious effects were noted. A tentative analysis of this 

 phenomenon (37) shows these effects could also be significant in the high- 

 wavenumber region of a turbulent field; nevertheless the confidence level of 

 such data would clearly be superior to that of impact probe measurements at 

 the present time. 



Heat Transfer 



Recent heat transfer results (29), for drag reducing system, have shown 

 that in conjunction with the decrease in drag coefficient there is a corresponding 

 but much larger relative decrease in the heat transfer coefficient. The accom- 

 panying detailed analysis shows no matter what the change in the bulk velocity 

 profile might be, it alone is insufficient to explain the low heat transfer rates. 

 Therefore, one may conclude that the wall region is thicker or that the turbu- 

 lence levels near the wall (where the greatest resistance to heat transfer is) 

 are much weaker, or both. It is interesting to note that the same conclusion has 

 been drawn elsewhere (18) on the basis of velocity profile measurements which, 

 as noted earlier, could have been expected to be incorrect. 



ACKNOWLEDGMENT 



This work has been supported by the Office of Naval Research, U.S. Navy, 

 and reproduction of this work, in whole or in part, is permitted for any purpose 

 of the United States Government. 



LIST OF SYMBOLS 



A Slope of universal velocity correlation, Eq. (9) 



B Constant in universal velocity correlation, Eq. (9) 



d Rate-of-strain tensor, having components d'J 



dj Second Rivlin-Ericksen tensor (15) 

 D Tube diameter 



f Observed friction factor = ry-zi pw^ 



f 1 Laminar friction factor = 16/N^g 



32 



