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.
Hewitt, G. F., Shires, G. L. and Bott, T. R. (1994) Process Heat Transfer, CRC Press.