Natural Convection - horizontal cylinder

[MET]

Nusselt number:

1) The only correlation I could find so far is the one described here http://en.wikipedia.org/wiki/Natural_convection which seems to be from Churchill/Thelen. There seem however to exist some questions regarding the characteristic length and the value to use for Nu_o (see discussion). Could someone here may be clarify these points?

2) Does someone know of an alternative correlation which could be used instead of the one from Chruchill/Thelen for the Grasshof range 0.01<Gr<50 and air (Pr=0.7)?

3) Does someone know of such a correlation which considers also the length to diameter ratio of the cylinder?

Thanks in advance.

Regrads MET

 

[eljose79]

Dear MET,

Thank you for bringing up these questions regarding the Nusselt number correlation for natural convection. The Churchill/Thelen correlation is commonly used in this range, but as you mentioned, there are some concerns about the characteristic length and Nuo value.

To clarify, the characteristic length in this correlation is typically taken as the diameter of the cylinder or the length of the heated surface. However, some researchers have suggested using the height of the cylinder or the average of the diameter and height as the characteristic length. The Nuo value, which is the Nusselt number at the onset of natural convection, has been found to vary depending on the geometry of the cylinder and the orientation of the heated surface.

In terms of alternative correlations for the Grasshof range of 0.01<Gr<50 and air (Pr=0.7), there are a few options that have been proposed. One is the correlation developed by Churchill and Chu, which takes into account the aspect ratio of the cylinder. Another is the correlation by Gebhart and Pera, which includes the aspect ratio and also considers the orientation of the heated surface.

I hope this information helps and provides some alternatives for your research. If you have any further questions, please don't hesitate to ask.