E,5 • ANALYSIS FOR VARIABLE FLUID PROPERTIES 



data follow the predicted line very closely for Reynolds numbers above 

 15,000. For low Reynolds numbers the separation of the data from the 

 predicted Une is probably caused by a partial transition from turbulent 

 to laminar heat transfer, which was not considered in the analysis. It 

 should perhaps be mentioned that, in using the foregoing correlation for 

 calculating heat transfer coefficients, the same assumptions for the vari- 

 ation of physical properties with temperature must be made as were made 

 in the analysis : constant specific heat and both thermal conductivity and 

 viscosity proportional to T"-^^. 



800 



Q 



100 



10 

 1000 



10,000 



Reo.4 = 



100,000 

 p0.4UbD 

 [JlO.4 



600,000 



Fig. E,5c. Variation of Nusselt number with Reynolds number for flow of air with 

 heat addition and properties evaluated at ^0.4 = 0.4(!rw — Th) + ^b. Prandtl num- 

 ber = 0.73. 



Similar trends with ^, or heat flux, were obtained for friction factors 

 \lJj\. The effects of heat flux were again eliminated by evaluating the 

 properties at a temperature close to the average of the wall and fluid bulk 

 temperatures. 



Analysis for liquids. In the case of heat transfer to fiquids, the vari- 

 ation of the viscosity with temperature is considerably greater than the 

 variation of the other properties. A good approximation to the actual 

 heat transfer in liquids can therefore be obtained by considering only the 

 viscosity to vary with temperature. For some liquids, including water, oil, 

 ethylene glycol, and sodium hydroxide, m/mw can be represented approxi- 

 mately by {T/T^y if the liquid is not too near the freezing point. The 

 exponent d varies from —1 to —4 and the temperatures are measured in 



< 307 > 



