Without insulation, heat flows through two resistances: the inner convective resistance and the tank wall conductive resistance. The outer air-film resistance acts directly on the tank wall outer surface.

\begin{equation}\label{eq:insulated-tank-bare-coeff} U_{bare} = \frac{1} {\dfrac{r_i}{r_{o,tank}}\cdot\dfrac{1}{h_{nat}} + \dfrac{r_i}{k_{tank}}\ln\!\left(\dfrac{r_{o,tank}}{r_i}\right) + \dfrac{1}{h_{inner}}} \end{equation}

Symbols

\(U_{bare}\)	Overall heat transfer coefficient (bare) \([\unit{ \btu\per\hour\foot\squared\degreeFahrenheit}]\)
\(r_i\)	Tank inner radius ( \(d/2\)) \([\unit{ \foot}]\)
\(r_{o,tank}\)	Tank outer radius ( \(r_i + t_{tank}\)) \([\unit{ \foot}]\)
\(h_{nat}\)	Natural convection coefficient at tank outer surface \([\unit{ \btu\per\hour\foot\squared\degreeFahrenheit}]\)
\(k_{tank}\)	Thermal conductivity of tank wall \([\unit{ \btu\per\hour\foot\degreeFahrenheit}]\)
\(h_{inner}\)	Inner surface convection coefficient (10 BTU/(hr·ft²·°F)) \([\unit{ \btu\per\hour\foot\squared\degreeFahrenheit}]\)