Rayleigh number#
Named after: John William Strutt, 3rd Baron Rayleigh (1842-1919).
$$\text{Ra} \stackrel{\text{def}}{=} \frac{g \beta (T_s - T_\infty) L^{3}}{\nu \alpha} \sim \frac{\text{buoyancy}}{\text{momentum and heat diffusion}}$$
Description#
Measures buoyancy forcing relative to combined momentum and thermal diffusion. It indicates the onset and strength of natural convection.
Quantities#
| Name | Symbol | SI units | Dimension |
|---|---|---|---|
| gravitational acceleration | \(g\) | \(\mathrm{m}\,\mathrm{s}^{-2}\) | \(\text L\,\text T^{-2}\) |
| thermal expansion coefficient | \(\beta\) | \(\mathrm{K}^{-1}\) | \(\Theta^{-1}\) |
| surface-ambient temperature difference | \(T_s - T_\infty\) | \(\mathrm{K}\) | \(\Theta\) |
| characteristic length | \(L\) | \(\mathrm{m}\) | \(\text L\) |
| kinematic viscosity | \(\nu\) | \(\mathrm{m}^{2}\,\mathrm{s}^{-1}\) | \(\text L^{2}\,\text T^{-1}\) |
| thermal diffusivity | \(\alpha\) | \(\mathrm{m}^{2}\,\mathrm{s}^{-1}\) | \(\text L^{2}\,\text T^{-1}\) |
Regimes#
Buoyancy driven heat transfer
| Range | Regime | Description |
|---|---|---|
| 0 – 1708 | conductive | Thermal diffusion suppresses buoyant motion. Heat transfer is mainly conductive in the classic horizontal-layer reference case. |
| 1708 – 1e+09 | convective | Buoyant motion is sustained and enhances heat transport above conduction. |
| 1e+09 – ∞ | turbulent convection | Buoyancy-driven flow becomes strongly unsteady and turbulent, producing vigorous mixing and enhanced heat transfer. |