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

where

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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How do you derive the rayleigh distribution?

Here is the derivation on dsplog: http://www.dsplog.com/2008/07/17/derive-pdf-rayleigh-random-variable/


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The main difference between the Rayleigh-Ritz method (RRM) and the finite element method lies in the definition of the basis functions. For FEM, these are element-related functions, whereas for RRM these are valid for the whole domain and have to fit the boundary conditions. The Rayleigh-Ritz method for homogeneous boundary conditions leads to the same discretized equations as the Galerkin method of weighted residuals.


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A real number which is not a rational number is an irrational number.

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For free convection near a vertical wall, the Rayleigh number is defined aswherex = Characteristic length (in this case, the distance from the leading edge)Rax = Rayleigh number at position xGrx = Grashof number at position xPr = Prandtl numberg = acceleration due to gravityTs = Surface temperature (temperature of the wall)T∞ = Quiescent temperature (fluid temperature far from the surface of the object)ν = Kinematic viscosityα = Thermal diffusivityβ = Thermal expansion coefficientIn the above, the fluid properties Pr, ν, α and β are evaluated at the film temperature, which is defined asFor most engineering purposes, the Rayleigh number is large, somewhere around 106 to 108.


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