Eckert number#
Named after: Ernst Rudolph Georg Eckert (1904-2004).
$$\text{Ec} \stackrel{\text{def}}{=} \frac{U^{2}}{c_p (T_s - T_\infty)} \sim \frac{\text{kinetic energy}}{\text{sensible enthalpy}}$$
Description#
Measures kinetic energy relative to sensible enthalpy based on a temperature difference. It indicates when viscous or compressible heating affects the thermal field.
Quantities#
| Name | Symbol | SI units | Dimension |
|---|---|---|---|
| velocity | \(U\) | \(\mathrm{m}\,\mathrm{s}^{-1}\) | \(\text L\,\text T^{-1}\) |
| specific heat capacity | \(c_p\) | \(\mathrm{m}^{2}\,\mathrm{s}^{-2}\,\mathrm{K}^{-1}\) | \(\text L^{2}\,\Theta^{-1}\,\text T^{-2}\) |
| surface-ambient temperature difference | \(T_s - T_\infty\) | \(\mathrm{K}\) | \(\Theta\) |
Regimes#
High speed heat transfer
| Range | Regime | Description |
|---|---|---|
| 0 – 0.01 | thermal | Kinetic energy is small compared with the imposed thermal energy scale. |
| 0.01 – 1 | viscous heating relevant | Conversion of kinetic energy into heat can affect temperature predictions, especially near walls or shocks. |
| 1 – ∞ | kinetic energy dominated | Kinetic energy is comparable to or larger than the sensible heat scale. Compressible heating effects are central. |