Cylindrical Insulation Heat Loss

Estimate radial heat flow from a known pipe surface through insulation and an outside convection film.

How this calculation works

This calculation starts at a known pipe outer-surface temperature and follows heat radially through insulation into surrounding air. Enter the pipe's outside diameter, insulation thickness and conductivity, the external convection coefficient, and the straight length being considered. The model combines a logarithmic cylindrical conduction resistance with an outside convection resistance. Their sum gives heat flow per metre; multiplying by length gives total heat flow. The reported insulation surface temperature is found from the outside film temperature drop. Positive heat flow means the pipe is losing heat, while a colder pipe produces a negative value. Zero insulation thickness leaves only the convection film. Radiation, internal fluid films, pipe-wall resistance, fittings and gaps are absent, and the surface estimate is not a personnel-protection assessment.

Inputs and units

Pipe outside diameter (mm)
Insulation thickness (mm)
Insulation conductivity (W/(m·K))
Outside convection coefficient (W/(m²·K))
Straight length (m)
Pipe outer-surface temperature (°C): Must be above absolute zero
Ambient air temperature (°C): Must be above absolute zero

Method and formula

r1 = diameter/2000; r2 = r1 + thickness/1000; R′ = ln(r2/r1)/(2πk) + 1/(2πr2h); q′ = (Tpipe − Tair)/R′; Q = q′L.

Worked example

Example inputs

Pipe outside diameter: 100 mm
Insulation thickness: 50 mm
Insulation conductivity: 0.04 W/(m·K)
Outside convection coefficient: 10 W/(m²·K)
Straight length: 10 m
Pipe outer-surface temperature: 100 °C
Ambient air temperature: 20 °C

Calculation steps

Find the radii: r1 = 100/2000 = 0.05 m; r2 = 0.05 + 50/1000 = 0.10 m.
Calculate resistance per unit length: R′conduction = ln(0.10/0.05)/(2π × 0.04) = 2.757945 m·K/W; R′convection = 1/(2π × 0.10 × 10) = 0.159155 m·K/W.
Divide the temperature difference by the combined resistance: q′ = (100 − 20)/(2.757945 + 0.159155) = 27.424497 W/m.
For 10 m of pipe, Q = 27.424497 × 10 = 274.244974 W.
Use the outside-film rise above ambient: Tsurface = 20 + 27.424497 × 0.159155 = 24.364744 °C, using unrounded intermediate values.

Example results

Signed heat flow per length: 27.42449745 W/m
Signed total heat flow: 274.2449745 W
Insulation outer-surface temperature: 24.36474433 °C

Assumptions

Uniform pipe-surface temperature; constant conductivity and convection coefficient
Positive heat flow means heat leaves the pipe

Limitations

Excludes radiation, pipe-wall resistance, internal film, fittings and insulation gaps
A surface-temperature estimate is not a personnel-protection assessment

Sources

U.S. DOE Fundamentals Handbook: Heat Transfer, Volume 2: HT-02 pp. 11–17, radial conduction; pp. 18–21, convection resistance