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Cylindrical thermal resistance

For an insulated pipe, the thermal resistance is not linear in the thickness as for a plane wall, because the area the heat passes through grows with the radius outward. The resistance therefore depends logarithmically on the ratio of the outer to the inner radius.

R = \dfrac{\ln(r_2/r_1)}{2\pi kL}

thermal resistance, cylindrical layer

Symbols

$r_1,\ r_2$	inner/outer radius	m
$L$	pipe length	m

Example

Insulation from $r_1 = 40$ mm to $r_2 = 70$ mm, $k = 0.045$ W/(m·K), $L = 8$ m. $R = \ln(70/40)/(2\pi\cdot 0.045\cdot 8) \approx 0.247$ K/W.

Never use the plane-wall formula

R = L/(kA)

for a pipe – use the

\ln(r_2/r_1)

formula instead.

Practise conduction for free →

← Thermal resistance in series · U-value →

Part of Heat Transfer: Conduction.