# Rayleigh Number

Written by Jerry Ratzlaff on . Posted in Dimensionless Numbers

Rayleigh number, abbreviated as Ra, is a dimensionless number associated with free or natural convection. It is a modified Grashof number used for natural convection calculations.  This calculator determines the Rayleigh Number where the absolute viscosity, fluid density, length, temperature differential, thermal diffusivity and thermal expansion are known values.  Some common values of non-metallic thermal diffusivity values can be found here.

### Rayleigh Number FORMULA

$$\large{ Ra = \frac{\rho \; g \; \alpha_c \; \Delta T \; l^3}{\mu \; \alpha} }$$

Where:

$$\large{ Ra }$$ = Rayleigh number

$$\large{ \mu }$$ (Greek symbol mu) = absolute viscosity

$$\large{ \rho }$$ (Greek symbol rho) = density of the fluid

$$\large{ g }$$ = gravitational acceleration

$$\large{ l }$$ = length

$$\large{ \Delta T }$$ = temperature differential

$$\large{ \alpha }$$ (Greek symbol alpha) = thermal diffusivity

$$\large{ \alpha_c }$$ (Greek symbol alpha) = thermal expansion coefficient