Heat loss per length q′
W/m
Heat-transfer rate per unit pipe length.
Thermal engineering · Heat transfer · conduction
Cylindrical conduction calculator — pipe heat loss
Calculate steady conduction through one homogeneous cylindrical layer from its inner diameter, thickness, conductivity and the temperature difference between its surfaces.
Created v1.0
By Thibaut Grzelak, Mechanical Analysis Engineer
02
q′Results
Heat-transfer rate Q̇
Calculated steady heat-transfer rate through the wall.
Resistance per length R′
K·m/W
Cylindrical conductive resistance normalized by pipe length.
Thermal resistance R
K/W
Total conductive thermal resistance over the entered length.
Outer diameter D₂
Calculated outer diameter from D₂ = D₁ + 2e.
Steady-state, one-dimensional radial conduction. One homogeneous cylindrical layer with constant thermal conductivity k.
01Formulas and symbols
Formulas used
R′
ln(r₂ / r₁) / (2πk)Resistance per length R′q′
ΔT / R′Heat loss per length q′Q̇
q′ · LHeat-transfer rate Q̇R
R′ / LThermal resistance RD₂
D₁ + 2eOuter diameter D₂02Assumptions and limits
Scope of validity
- Steady-state, one-dimensional radial conduction.
- One homogeneous cylindrical layer with constant thermal conductivity k.
- D₁ is the diameter of the conducting layer’s inner surface; for insulation, use the pipe outside diameter beneath the insulation.
- Tₕ and T𝒸 are layer surface temperatures, not fluid and ambient-air temperatures.
- Convection, radiation, contact resistance, supports and axial conduction are not included.
- This is a conduction-only physical estimate, not a regulatory or code-compliance check.
03Validation example
Reference numerical case
- Reference case: D₁ = 0.10 m, e = 0.05 m, k = 0.04 W/(m·K), L = 10 m and ΔT = 20 K.
- D₂ = 0.20 m and R′ = ln(0.20/0.10)/(2π×0.04) = 2.757945 K·m/W.
- q′ = 20/2.757945 = 7.251776 W/m.
- Q̇ = q′L = 72.517762 W and R = 0.2757945 K/W.
04References
Technical references
- Incropera et al. — Fundamentals of Heat and Mass Transfer: steady radial conduction through cylinders.
- NIST Special Publication 811 — SI units and temperature intervals.