Fourier number#
Named after: Jean-Baptiste Joseph Fourier (1768-1830).
$$\text{Fo} \stackrel{\text{def}}{=} \frac{\alpha t}{L^{2}} \sim \frac{\text{thermal diffusion spread}}{\text{length squared}}$$
Description#
Measures elapsed time relative to the thermal diffusion time across a length scale. It indicates how far a transient temperature disturbance has penetrated.
Quantities#
| Name | Symbol | SI units | Dimension |
|---|---|---|---|
| thermal diffusivity | \(\alpha\) | \(\mathrm{m}^{2}\,\mathrm{s}^{-1}\) | \(\text L^{2}\,\text T^{-1}\) |
| time | \(t\) | \(\mathrm{s}\) | \(\text T\) |
| characteristic length | \(L\) | \(\mathrm{m}\) | \(\text L\) |
Regimes#
Transient heat conduction
| Range | Regime | Description |
|---|---|---|
| 0 – 0.2 | early transient | Significant temperature gradients persist throughout the domain. The thermal front has not yet penetrated the full depth. |
| 0.2 – ∞ | late transient | Temperature gradients are diminishing. The body approaches thermal equilibrium with its surroundings. |