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.