E • CONVECTIVE HEAT TRANSFER AND FRICTION 



molecular heat transfer term will be important in comparison with the 

 turbulent term, even in the region away from the wall. Martinelli was 

 the first to extend the analysis to low Prandtl numbers by retaining the 

 molecular term in Eq. 2-6, in the region away from the wall [9]. Also, 

 q/qy, cannot be set equal to one for low Prandtl number fluids, because 

 the important temperature changes with respect to distance from the 

 wall do not all take place near the wall, as they do at higher Prandtl 

 numbers. Martinelli approximated q/q,y by using a linear variation in 



Nu 0.9 

 NUd 1.2 



1.0 



7.0 (water) 

 63 (oil) 



■®"9— ^ 



X Oil uD/v = 37,000 



O Water uD/v = 33,600. 

 — Predicted 



1.1 



1.0 



0.9 



Pr = 1.0 



Pr = 7.3 (water) 



Pr= 61 (oil) 



.^ O 



o— o- 



X Oil uD/v = 46,600 



o Water uD/v r= 44,300. 

 — Predicted 



•o 



10 



20 



30 



40 



x/D 



50 



60 



70 



Fig. E,4g. 



Comparison between predicted and experimental Nusselt numbers 

 in thermal entrance region for liquids. Data from [50]. 



which q/q^ = at the tube center. More accurate variations of q/q^ were 

 later used in [28,51]. 



Most of the data for liquid metal heat transfer fall somewhat below 

 the original Martinelli analysis (about 30 per cent) although considerable 

 scatter exists in the data. Several attempts have been made to bring the 

 analysis into better agreement with the data by making various modifi- 

 cations of the turbulence mechanism [28,52]. However, the reason for the 

 discrepancy between analysis and experiment has not been established. 

 It is possible that the low experimental heat transfer coefficients are due 

 to a thermal resistance at the interface between the wall and the liquid 

 metal. It appears that more experimental information will be needed be- 

 fore any of the existing theories can be verified or an adequate theory 



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