Rayleigh number

Rayleigh number, Ra, is a dimensionless term used in the calculation of natural convection.

where g is acceleration due to gravity, β' is coefficient of thermal expansion of the fluid, ΔT is temperature difference, x is length, ν is kinematic viscosity and κ is thermal diffusivity of the fluid. Gr is the Grashof Number and Pr is the Prandtl Number.

The magnitude of the Rayleigh number is a good indication as to whether the natural convection boundary layer is laminar or turbulent. For a vertical surface, for example, the transition takes place when Ra ≈ 10⁹. Various examples of the relationship between the magnitude of natural convective heat transfer and Rayleigh number are given in the following reference.