Number of Rayleigh

In Mechanical of the fluids, the number of Rayleigh characterizes the transfer of heat within a fluid: lower than a breaking value, the transfer takes place primarily by conduction, while beyond of this value it is the Convection which becomes important. It is a Nombre without dimension, which draws its name from Lord Rayleigh.

One can define it as the product of the Nombre of Grashof, connecting the force of Archimedes to the Viscosité of the fluid, and the Nombre of Prandtl.

For a vertical wall, one can write

$\ mathit {Ra} _ {X, C} = \ mathit {gr.} _ {X, C} \ mathit {Pr} = \ frac {G \ naked beta} {\ \ alpha} (T_s - T_ \ infin) x^3$

where

Ra = number of Rayleigh
gr. = Number of Grashof
Pr = Number of Prandtl
G = acceleration of gravity
X = dimension characteristic of the phenomenon
T_s = temperature of the wall
T_∞ = temperature of the fluid far from the wall
ν = kinematic Viscosity
α = thermal Diffusivity
β = volumetric thermal dilation coefficient

In the majority of the cases, the number of Rayleigh is large, of 10⁶ with 10⁸.

In Geophysical the number of Rayleigh to an major importance: on geological time scales, the terrestrial coat is a fluid whose breaking value is relatively low, the quite lower estimate of the number of Rayleigh, which indicates that this coat is traversed movements of convection: the mantellic Convection.

See too

Category: Fluid mechanics Category: Convection -->

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