Nusselt Eqn. for a Sphere

[trojanknight]

I have an equation relating the Prandtl and Rayleigh numbers of a vertical cylinder to its Nusselt number. Unfortunately, I do not have the same type of relationship equation for a shpere and am in desperate need of it. Any help would be greatly appreciated.

Thanks in advance.

 

[prex]

McAdams in 'Heat Transmission' Ch.7 references some studies where the equation Y=CXⁿ (Y=Nu, X=Gr x Pr) used for short vertical planes, where L is the height, may be used unchanged for horizontal cylinders (L=diameter), for spheres (L=radius) and for blocks (1/L=1/L_vert+1/L_horiz).
In the equation C=0.13 and n=1/3 for X between 3.5E7 and 1E12, C=0.55 and n=1/4 for X between 3.5E7 and 1E4.

prex

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