Rayleigh Number - Definition

Definition

For free convection near a vertical wall, the Rayleigh number is defined as

where

  • x = Characteristic length (in this case, the distance from the leading edge)
  • Rax = Rayleigh number at position x
  • Grx = Grashof number at position x
  • Pr = Prandtl number
  • g = acceleration due to gravity
  • Ts = Surface temperature (temperature of the wall)
  • T = Quiescent temperature (fluid temperature far from the surface of the object)
  • ν = Kinematic viscosity
  • α = Thermal diffusivity
  • β = Thermal expansion coefficient

In the above, the fluid properties Pr, ν, α and β are evaluated at the film temperature, which is defined as

For most engineering purposes, the Rayleigh number is large, somewhere around 106 to 108.

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