In fluid mechanics, the Rayleigh number (, after Lord Rayleigh) for a fluid is a dimensionless number associated with buoyancy-driven flow, also known as free (or natural) convection. It characterises the fluid's flow regime: a value in a certain lower range denotes laminar flow; a value in a higher range, turbulent flow. Below a certain critical value, there is no fluid motion and heat transfer is by conduction rather than convection. For most engineering purposes, the Rayleigh number is large, somewhere around 10 to 10.
The Rayleigh number is defined as the product of the Grashof number (), which describes the relationship between buoyancy and viscosity within a fluid, and the Prandtl number (), which describes the relationship between momentum diffusivity and thermal diffusivity: . Hence it may also be viewed as the ratio of buoyancy and viscosity forces multiplied by the ratio of momentum and thermal diffusivities: . It is closely related to the Nusselt number ().