Without insulation, heat conducts through the pipe wall only before being dissipated from the bare outer surface. The formula is identical to the insulated case except that the insulation resistance is absent and the air-film resistance acts directly on the pipe outer surface.

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

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

\begin{equation}\label{eq:insulated-pipe-bare-heat-length} q_L = q \cdot \pi \cdot d_{pipe}\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 \([\unit{ \meter\kelvin\per\watt}]\)
\(h_{air}\)	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 \([\unit{ \watt\per\meter}]\)
\(d_{pipe}\)	Pipe outer diameter \([\unit{ \meter}]\)
\(\pi\)	Mathematical constant pi \([\unit{ \unitless}]\)