Heat flows in series through four resistances: the inner convective resistance (tank contents to tank wall), the conductive resistance of the tank wall, the conductive resistance of the insulation annulus, and the outer air-film resistance (natural convection at the jacket outer surface). Each conductive resistance is expressed per unit tank-diameter basis, accounting for the cylindrical geometry.

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

Note

The inner convection coefficient \(h_{inner}\) = 10 BTU/(hr·ft²·°F) is a standard assumption for natural convection of process fluid inside the tank.

Symbols

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