Rayleigh Number Formula

Equation for calculate rayleigh number is,

$R a_{x} = \frac{g β}{ν α} (T_{s} - T_{\infty}) x^{3}$

where,

g is acceleration due to gravity
β is the thermal expansion coefficient (equals to 1/T, for ideal gases, where T is absolute temperature).
ν is the kinematic viscosity
α is the thermal diffusivity
T_s is the surface temperature
T_∞ is the quiescent temperature (fluid temperature far from the surface of the object)
x is the characteristic length
Ra_x is the Rayleigh number for characteristic length x

g is acceleration due to gravity

β is the thermal expansion coefficient (equals to 1/T, for ideal gases, where T is absolute temperature).

ν is the kinematic viscosity

α is the thermal diffusivity

T_s is the surface temperature

T_∞ is the quiescent temperature (fluid temperature far from the surface of the object)

x is the characteristic length

Ra_x is the Rayleigh number for characteristic length x