Biot number#
Named after: Jean-Baptiste Biot (1774-1862).
$$\text{Bi} \stackrel{\text{def}}{=} \frac{h L}{k} \sim \frac{\text{internal conduction resistance}}{\text{surface convection resistance}}$$
Description#
Measures internal conduction resistance relative to surface convection resistance. It indicates whether a solid can be treated as nearly uniform in temperature.
Quantities#
| Name | Symbol | SI units | Dimension |
|---|---|---|---|
| convective heat transfer coefficient | \(h\) | \(\mathrm{W}\,\mathrm{m}^{-2}\,\mathrm{K}^{-1}\) | \(\text M\,\Theta^{-1}\,\text T^{-3}\) |
| characteristic length | \(L\) | \(\mathrm{m}\) | \(\text L\) |
| thermal conductivity | \(k\) | \(\mathrm{W}\,\mathrm{m}^{-1}\,\mathrm{K}^{-1}\) | \(\text L\,\text M\,\Theta^{-1}\,\text T^{-3}\) |
Regimes#
Heat conduction in solids
| Range | Regime | Description |
|---|---|---|
| 0 – 0.1 | lumped/uniform temperature | Internal conduction resistance is small compared with surface convection resistance. Temperature gradients inside the solid are negligible and the lumped capacitance model applies. |
| 0.1 – 40 | internal temperature gradients | Internal conduction resistance is significant. Temperature gradients develop inside the solid and the heat equation must usually be solved. |
| 40 – ∞ | conduction limited | Internal conduction resistance dominates over surface convection resistance. The surface equilibrates rapidly relative to the interior, and strong internal gradients can persist. |