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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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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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