The pipe inner surface (fluid) temperature drives heat through three resistances in series: the pipe wall, the insulation annulus, and the combined air-film resistance at the jacket outer surface. The air-film resistance is the reciprocal of the sum of convective and radiative heat transfer coefficients. All resistances are per unit length.

\begin{equation}\label{eq:insulated-pipe-insulated-resistance} R_{total} = R_{pipe} + R_{ins} + \frac{1}{h_{air}}\end{equation}

\begin{equation}\label{eq:insulated-pipe-insulated-heat-flow} q = \frac{T_{pipe} - T_\infty}{R_{total}}\end{equation}

\begin{equation}\label{eq:insulated-pipe-insulated-heat-length} q_L = q \cdot \pi \cdot d_{ins,outer}\end{equation}

Symbols

\(R_{total}\)	Total thermal resistance per unit length \([\unit{ \meter\kelvin\per\watt}]\)
\(R_{pipe}\)	Pipe wall thermal resistance per unit length \([\unit{ \meter\kelvin\per\watt}]\)
\(R_{ins}\)	Insulation thermal resistance per unit length \([\unit{ \meter\kelvin\per\watt}]\)
\(h_{air}\)	Combined air-film heat transfer coefficient ( \(h_{conv}\) + \(h_{rad}\)) \([\unit{ \watt\per\meter\squared\per\kelvin}]\)
\(q\)	Heat flow per unit area \([\unit{ \watt\per\meter\squared}]\)
\(T_{pipe}\)	Pipe inner surface (fluid) temperature \([\unit{ \kelvin}]\)
\(T_\infty\)	Ambient air temperature \([\unit{ \kelvin}]\)
\(q_L\)	Heat loss per unit length \([\unit{ \watt\per\meter}]\)
\(d_{ins,outer}\)	Insulation jacket outer diameter \([\unit{ \meter}]\)
\(\pi\)	Mathematical constant pi \([\unit{ \unitless}]\)