1D Steady Conduction⚠ unverified
Physics / Heat Transfer · Steady one-dimensional conduction heat rate through a slab
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| k | k | W/m/K | 1.0 | Thermal conductivity |
| A | A | m^2 | 1.0 | Cross-sectional area |
| dT | ΔT | K | 10.0 | Temperature difference |
| L | L | m | 0.1 | Thickness |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| Q | Q | W | Heat rate |
The science & history
Understanding the Parameters
- $k$ — metals high; insulation low. Often temperature-dependent in real materials.
- $A$ — larger area → more heat flow.
- $\Delta T$ — driving potential; same as $T_1 - T_2$ for the two faces.
- $L$ — thicker wall → less heat flow (higher thermal resistance $R = L/(kA)$).
Derivation (Approaching a Proof)
Fourier’s law: $\mathbf{q} = -k\nabla T$. For 1-D steady state through constant $k$ and area $A$, $Q = q A = k A (T_1 - T_2)/L$. Equivalent circuit: $Q = \Delta T / R$ with $R = L/(kA)$ (Thermal Resistance Conduction).
History
Joseph Fourier’s heat theory (1822) established conduction as a continuum law; plane-wall $Q = kA\Delta T/L$ is the first engineering form.
Related Concepts: Thermal Resistance Conduction, Conduction Cylindrical, Convection Heat Transfer, Heat Flux
Notes: Registry calculator conduction-steady-1d (unverified). Constant $k$, plane wall, steady state.