Nusselt number#
Named after: Wilhelm Nusselt (1882-1957).
$$\text{Nu} \stackrel{\text{def}}{=} \frac{h L}{k} \sim \frac{\text{convective heat transfer}}{\text{conductive heat transfer}}$$
Description#
Measures convective heat transfer relative to pure conduction across the same length scale. It indicates how much motion enhances heat transfer above the conductive reference.
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#
Forced convection
| Range | Regime | Description |
|---|---|---|
| 1 – 2 | conduction dominated | Heat transfer is close to the purely conductive reference limit. Occurs in stagnant fluids or weakly convective boundary layers. |
| 2 – ∞ | convection dominated | Convection enhances heat transfer above the purely conductive reference rate. Occurs in moving or well mixed fluids and thin thermal boundary layers. |