The Rayleigh number reference article from the English Wikipedia on 24-Jul-2004 (provided by Fixed Reference: snapshots of Wikipedia from wikipedia.org)

Rayleigh number

The Rayleigh number is a dimensionless number of fundamental importance in geophysics, where it is an indicator of the presence and strength of convection within a fluid body such as the Earth's liquid mantle. The Rayleigh number results from a comparison of buoyancy and viscosity, and its low value for the Earth's mantle indicates that convection occurs throughout the mantle as a whole, and not just within mantle layers. It is defined as the product of the Grashof number, which describes the relationship between buoyancy and inertia within a fluid, and the Prandtl number, which describes the relationship between the viscosity of a fluid and its temperature.

For free convection near a vertical wall, this number is

where

• Ra = Rayleigh number
• Gr = Grashof number
• Pr = Prandtl number
• g = gravity
• T_s = Temperature of surface
• T_∞ = Quiescent temperature
• ν = kinematic viscosity
• α = thermal diffusivity
• β = thermal expansion coefficient

The Rayleigh number is named after Lord Rayleigh.

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