E,5 • ANALYSIS FOR VARIABLE FLUID PROPERTIES 



for heating and cooling of the hquid. In the case of heat transfer, the 

 reference temperature does not depart greatly from that in the experi- 

 mental Colburn equation [69, p. 168], wherein the viscosity is evaluated 

 at To. 5, except at the lower Prandtl numbers. Deviations from the curves 

 in Fig. E,5e might occur for very high viscosity ratios or for cases in 

 which the viscosity variation with temperature could not be represented 

 by a simple power function. 



An analysis for liquids with variable viscosity by Rannie [11] utilized 

 somewhat different assumptions than those in the analysis given here. It 



I 



H 



^ 1 



0.5 

 



0.5 



Heat transfer 



1 



10 



Friction 



Pr 



100 



1000 



Fig. E,5e. Values of r = (Tr — Th)/(T^ — T^) against Prandtl number for evalu- 

 ating viscosity in Prandtl and Reynolds numbers in Fig. E,4c or a similar curve for 

 friction factors, m/mw = (T/T^)~^ or (^/^w)-^• Mb/ixw ^ 0.5 or 2. 



assumed that the oscillations in the wall layer are produced by the dis- 

 turbances or turbulence outside the wall layer. An attempt was then made 

 to determine the effect of a viscosity gradient on these impressed oscil- 

 lations. It appears that the available experimental data are not sufficient 

 to decide whether that theory or the one presented here is to be preferred. 

 Fluids near the critical point. The last subject to be discussed is that 

 of heat transfer to supercritical fluids. A supercritical fluid is defined as 

 one in which the pressure is above critical and the temperature is in the 

 vicinity of the critical temperature. In that region all the fluid properties 

 vary rapidly with temperature and also with pressure. The viscosity, 

 thermal conductivity, and density decrease rapidly as the temperature 

 increases above the critical point. The specific heat peaks at a temper- 

 ature near the critical point and then decreases. With such unusual 



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