Conduction Cylindrical⚠ unverified
Physics / Heat Transfer · Compute radial conduction heat rate through a cylindrical shell
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| k | k | — | 1.0 | Thermal conductivity of the wall, in watts per metre-kelvin (W/(m*K)) |
| L | L | m | 1.0 | Axial length of the cylinder |
| T1 | T1 | K | 1.0 | Temperature at the inner radius |
| T2 | T2 | K | 1.0 | Temperature at the outer radius |
| r1 | r1 | m | 1.0 | Inner radius |
| r2 | r2 | m | 1.0 | Outer radius |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | Q | W | Radial conduction heat rate, in watts (W). Returns 0.0 unless ``r2 > r1 > 0`` |
The science & history
Understanding the Parameters
- $k$, $L$ — material and length scale the heat rate.
- $T_1 - T_2$ — radial driving difference.
-
$\ln(r_2/r_1)$ — geometric factor; thermal resistance $R = \ln(r_2/r_1)/(2\pi k L)$.
-
$k$ may be mislabelled dimensionless in the registry.
Derivation (Approaching a Proof)
In cylindrical coordinates, steady radial conduction $Q_r = -k(2\pi r L)\,dT/dr$ is constant. Separate and integrate from $r_1$ to $r_2$ to obtain the log form.
History
Cylindrical conduction is standard pipe-insulation analysis and the basis of critical-radius design.
Related Concepts: 1D Steady Conduction, Critical Radius Insulation, Thermal Resistance Conduction
Notes: Registry calculator conduction-cylindrical (unverified). Steady, constant $k$, pure radial.