Rayleigh number

Input(s)

g: Acceleration due to Earth's gravity $\left(\mathrm{m} / \mathrm{s}^{2}\right)$

$\beta$: Volumetric thermal expansion coefficient $(\mathrm{K})$

Ts: Surface temperature $(\mathrm{K})$

Ti: Bulk temperature $(\mathrm{K})$

$\mathrm{x}$: Characteristic Length $(\mathrm{m})$

v: Kinematic viscosity $\left(\mathrm{m}^{2} / \mathrm{s}\right)$

$\alpha$: Thermal Conductivity of fluid (K)

Output(s)

$\mathrm{Ra}$: Rayleigh number (dimensionless)

Formula(s)

$$ \mathrm{Ra}=\frac{\mathrm{g} * \beta *(\mathrm{Ts}-\mathrm{Ti}) * \mathrm{x}^{3}}{\mathrm{v} * \alpha} $$

Reference(s)

Wikipedia.org.