E,4 • ANALYSIS FOR CONSTANT FLUID PROPERTIES 



crease the effect of x/D for turbulent heat transfer. In that case, however, 

 the shape of the temperature profile within the boundary layer changes 

 and becomes considerably flatter at high Prandtl numbers. This effect 

 apparently more than offsets the effect previously mentioned, so that the 

 entrance region becomes less important at the higher Prandtl numbers. 

 Fig. E,4g gives a comparison between predicted results and experi- 

 mental results from [50] for water and for oil flowing in the entrance 

 region of a tube. The velocity profile is again fully developed and the 



2.0 

 1.5 



Nu 



Nud 



Prrr: 1 



Pr= 10 



1.0 

 2.0 



1.5 



1.0 



2.0 



1.5 



1.0 



012345678 



Pr=100 



x/D 



Fig. E,4f. Effect of Reynolds and Prandtl numbers on heat transfer in thermal 

 entrance region of tube. Uniform wall heat flux, uniform initial temperature distribu- 

 tion, and fully developed velocity distribution. 



wall heat flux uniform. In general the agreement between theory and 

 experiment is satisfactory. 



Various other cases, including that in which the initial velocity profile 

 is uniform, and in which the wall temperature, rather than the heat flux, 

 is uniform, are calculated in [47]. It was found that the heat transfer 

 coefficients in the entrance region are higher for a uniform than for a 

 fully developed initial velocity profile. Very little difference was, however, 

 obtained between the results for the cases of uniform wall heat flux and 

 uniform wall temperature. That result would not be expected to apply to 

 liquid metals. 



Liquid metal heat transfer. Liquid metals are characterized, from the 

 point of view of heat transfer, by their very low Prandtl numbers {Pr ^ 

 0.01). Eq. 2-6 indicates that, at sufficiently low Prandtl numbers, the 



(301 > 



