# Rayleigh number

## Rayleigh number

Rayleigh number is a dimensionless number that represents the ratio of buoyancy and thermal diffusivity.

It can be obtained by the following equation:

where;

Ra : Rayleigh number

g : Gravitational acceleration [m/s2]

β : Termal expansion coefficient [1/K]

L : Characteristic length [m]

ΔT : Characteristic temperature difference [K]

ν: Kinematic viscosity coefficient [m2/s]

α : Thermal diffusivity [m2/s]

Difference between solid surface temperature and free stream temperature can be used as the characteristic temperature difference.

Rayleigh number is an index that characterizes heat transfer in natural convection phenomena. Below the critical Rayleigh number, convection does not occur and heat is transferred through thermal conduction. Above the critical Rayleigh number, heat is transferred through convection. Take a flat, vertical board as an example. When Rayleigh number is approximately 109, airflow makes a transition into a turbulent flow.

Rayleigh number can also be expressed in the following equation using Grashof number Gr and Prandtl number Pr.

Rayleigh number is named after the English physicist John William Strutt, 3rd Baron Rayleigh.