Petukhov equation

The Nusselt number relations above are fairly simple, but they may give errors as large as 25 percent. This error can be reduced considerably to less than 10 percent by using more complex but accurate relations such as the second Petukhov equation expressed as... 

Results from a mixed convection experiment with uniform wall heat flux are shown in Figure 4(b). The Reynolds number was about 10,000. Under such conditions heat transfer was found to be strongly impaired due to the influence of buoyancy. It can be seen that the local values of Nusselt number lie well below the curve for forced convection calculated using the Petukhov equation. The observed behaviour is very similar to that found in an earlier study by Li [6] using a uniformly heated test section of similar dimensions (see Jackson and Li [7]). 

The above equations offer simplicity in computation, but errors on the order of 25 percent are not uncommon. Petukhov [42] has developed a more accurate, although more complicated, expression for fully developed turbulent flow in smooth tubes ... 

For smooth pipes, the agreement between the Petukhov and Colebrook equations is very good. The friction factor is minimum for a smooth pipe (but still not zero because of the no-slip condition), and increase,s with roughness (Fig. 8-25). 

An equation that is also valid for large Reynolds numbers, was developed by Petukhov and Kirilov [3.37]. ft has been modified by Gnielinski [3.38] so that in addition the region below Re = 104 is correctly described. It reads... 

Prediction of the heat-transfer coefficient in the transition flow regime is uncertain due to the strong effects of entrance conditions and instability of the flow pattern. Gnielinski [18] modified the Petukhov-Popov equation to accommodate the transition region and extend it into the turbulent flow range ... 

Local values of Nusselt number were determined at various locations along the tube from experiments performed under conditions of forced convection with uniform heating. In Figure 4(a) the results are compared with the distribution of Nusselt number calculated using the established empirical correlation equation of Petukhov et al [5], As can be seen, the agreement is very satisfactory. 

Figures 6(a) to 6(f) show the axial distributions of Nusselt number obtained in these experiments. The flow rates induced through the test section were used to determine the Reynolds numbers shown on the figures. In each case a curve is presented for forced convection with uniform heat flux evaluated at the Reynolds number for that case using the equation of Petukhov et al [5]. The main points to note are ...

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