The full Stefan–Boltzmann radiation term is divided by the temperature difference to produce a linearized coefficient that can be added directly to the convective coefficient. This linearization is valid when the temperature difference is small relative to the absolute temperatures involved.

\begin{equation}\label{eq:insulated-pipe-radiation} h_{rad} = \frac{\sigma \varepsilon \left(T_s^4 - T_\infty^4\right)}{T_s - T_\infty} \end{equation}

Symbols

\(h_{rad}\)	Radiative heat transfer coefficient \([\unit{ \watt\per\meter\squared\per\kelvin}]\)
\(\sigma\)	Stefan–Boltzmann constant (5.670373 × 10⁻⁸) \([\unit{ \watt\per\meter\squared\per\kelvin\tothe{4}}]\)
\(\varepsilon\)	Surface emissivity (0–1) \([\unit{ \unitless}]\)
\(T_s\)	Outer surface temperature \([\unit{ \kelvin}]\)
\(T_\infty\)	Ambient air temperature \([\unit{ \kelvin}]\)