E,5 • ANALYSIS FOR VARIABLE FLUID PROPERTIES 



formulated. A review of the present status of research on Hquid metal 

 heat transfer is given in [53]. 



Noncircular passages. Although most of the preceding calculations 

 were for turbulent flow in circular tubes, it is shown in [46] that, except 

 for liquid metals, the Nusselt numbers and friction factors for round tubes 

 apply with small error to flow between parallel plates. It is only neces- 

 sary to use the hydraulic diameter in the definitions of Nusselt number, 

 Reynolds number, and friction factor. The hydraulic diameter is defined 

 as 4 times the cross-sectional area divided by the wetted perimeter. 



In an analysis in [54] it is found that the results for a tube can be used 

 with small error for a concentric annulus with a diameter ratio of S^. As 

 the annulus became eccentric, however, the Nusselt numbers and friction 

 factors decreased appreciably. 



Flow and heat transfer in the vicinity of corners have been analyzed 

 in [55,56]. It was found that, for uniform heat generation in the passage 

 wall, the temperature at the corner may be considerably higher than the 

 average, because the convective heat transfer is zero at the corner. Al- 

 though average Nusselt numbers and friction factors for passage cross 

 sections were not predicted in [55,56], experimental results [57] indicated 

 that the results for tubes apply reasonably well to rectangular and tri- 

 angular passages when the equivalent diameter is used. That result, again, 

 would not be expected to apply to liquid metals. Further discussion of 

 flow and heat transfer in noncircular passages is given in [58,59].^ 



E,5. Analysis for Variable Fluid Properties. The analysis for 

 constant fluid properties in the preceding section applies, strictly speak- 

 ing, only to the limiting case of heat transfer, with infinitesimal tem- 

 perature difference, inasmuch as the fluid properties of a real fluid are 

 temperature-dependent. This does not imply that the results of a con- 

 stant-property analysis are not useful. In many instances, substantial 

 temperature differences are required before the effect of variable proper- 

 ties becomes important. Also, in the case of variable properties, it is often 

 possible to use the results of a constant-property analysis by evaluating 

 the fluid properties in the various dimensionless groups at a suitable refer- 

 ence temperature. In order to calculate the required reference temper- 

 ature, however, an analysis for variable properties is necessary, 



Eq. 2-5, 2-6, 3-1', and 3-2' are already in a form suitable for a variable- 

 property analysis. For a given wall temperature and pressure, the various 

 property ratios in those equations are functions of T/T^. From the 

 definitions of /3 and T* 



Y^^-^T* (5-1) 



See also [86,87]. 



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