This correlation is recommended for natural convection from long horizontal cylinders over the full range of Rayleigh numbers.

\begin{equation}\label{eq:insulated-pipe-nusselt-free} \mathrm{Nu}_{free} = \left[0.6 + \frac{0.387\,\mathrm{Ra}^{1/6}} {\left[1+\left(\frac{0.559}{\mathrm{Pr}}\right)^{9/16}\right]^{8/27}} \right]^2 \end{equation}

Symbols

\(\mathrm{Nu}_{free}\)	Free-convection Nusselt number \([\unit{ \unitless}]\)
\(\mathrm{Ra}\)	Rayleigh number \([\unit{ \unitless}]\)
\(\mathrm{Pr}\)	Prandtl number of air at the film temperature \([\unit{ \unitless}]\)