The resistance to heat flow through a hollow cylinder (pipe wall or insulation annulus) depends on the ratio of its outer to inner radius and on the thermal conductivity of the material. The formula accounts for the geometry of radial heat conduction through a cylindrical shell.

\begin{equation}\label{eq:insulated-pipe-thermal-resistance} R = \frac{d_a \ln\!\left(\frac{d_b}{d_c}\right)}{2 k}\end{equation}

Symbols

\(R\)	Thermal resistance per unit length \([\unit{ \meter\kelvin\per\watt}]\)
\(d_a\)	Outer diameter of the shell \([\unit{ \meter}]\)
\(d_b\)	Outer boundary diameter of the conductive layer \([\unit{ \meter}]\)
\(d_c\)	Inner boundary diameter of the conductive layer \([\unit{ \meter}]\)
\(k\)	Thermal conductivity of the shell material \([\unit{ \watt\per\meter\per\kelvin}]\)