This empirical correlation applies to turbulent natural convection along a vertical surface. It uses the cube-root dependence on Rayleigh number that is characteristic of the turbulent regime.

\begin{equation}\label{eq:insulated-tank-natural-convection} h_{nat} = 0.125 \,\mathrm{Ra}^{1/3} \frac{k}{d} \end{equation}

Symbols

\(h_{nat}\)	Natural convection heat transfer coefficient \([\unit{ \btu\per\hour\foot\squared\degreeRankine}]\)
\(\mathrm{Ra}\)	Rayleigh number \([\unit{ \unitless}]\)
\(k\)	Thermal conductivity of air at ambient temperature \([\unit{ \btu\per\hour\foot\degreeFahrenheit}]\)
\(d\)	Tank outer diameter \([\unit{ \foot}]\)