Stanton number#
Named after: Thomas Ernest Stanton (1865-1931).
$$\text{St}_h \stackrel{\text{def}}{=} \frac{h}{\rho c_p U} \sim \frac{\text{surface heat transfer}}{\text{convective heat capacity flow}}$$
Description#
Measures surface heat-transfer rate relative to the thermal capacity advected by a flow. It indicates what fraction of the moving fluid thermal capacity is exchanged.
Quantities#
| Name | Symbol | SI units | Dimension |
|---|---|---|---|
| convective heat transfer coefficient | \(h\) | \(\mathrm{W}\,\mathrm{m}^{-2}\,\mathrm{K}^{-1}\) | \(\text M\,\Theta^{-1}\,\text T^{-3}\) |
| mass density | \(\rho\) | \(\mathrm{kg}\,\mathrm{m}^{-3}\) | \(\text L^{-3}\,\text M\) |
| specific heat capacity | \(c_p\) | \(\mathrm{m}^{2}\,\mathrm{s}^{-2}\,\mathrm{K}^{-1}\) | \(\text L^{2}\,\Theta^{-1}\,\text T^{-2}\) |
| velocity | \(U\) | \(\mathrm{m}\,\mathrm{s}^{-1}\) | \(\text L\,\text T^{-1}\) |
Regimes#
Convective heat transfer
| Range | Regime | Description |
|---|---|---|
| 0 – 0.001 | weak exchange | Only a small fraction of the bulk thermal capacity is exchanged with the surface over the reference length. |
| 0.001 – 0.01 | moderate exchange | Surface heat transfer has a measurable effect on the moving fluid temperature. |
| 0.01 – ∞ | strong exchange | Surface exchange is strong relative to the advected thermal capacity of the flow. |