Fourier Number⚠ unverified
Physics / Heat Transfer · Compute the Fourier number
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| alpha | α | m**2/s | 1.0 | Thermal diffusivity of the material |
| t | t | s | 1.0 | Elapsed time |
| L | L | m | 1.0 | Characteristic length |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | Fo | — | Fourier number (dimensionless). Returns 0.0 when L is not positive |
The science & history
Understanding the Parameters
- $\alpha$ — how fast heat diffuses (metals high, plastics low).
- $t$, $L$ — Fo $\propto t/L^{2}$; double thickness → four times longer for the same Fo.
- Fo — pairs with Bi in Heisler/one-term transient solutions.
Derivation (Approaching a Proof)
Nondimensionalise the heat equation $\partial T/\partial t = \alpha \nabla^{2}T$ with $x^* = x/L$, $t^* = \alpha t/L^{2}$. The dimensionless time is Fo.
History
Named after Fourier; Fo and Bi organise all classical transient conduction charts.
Related Concepts: Biot Number, 1D Steady Conduction, Prandtl Number
Notes: Registry calculator fourier-number (unverified).