For free convection near a vertical wall, the Rayleigh number is defined as:
where:
*x is the characteristic length
*Ra is the Rayleigh number for characteristic length x
*g is acceleration due to gravity
*β is the thermal expansion coefficient (equals to 1/T, for ideal gases, where T is absolute temperature).
* is the kinematic viscosity
*α is the thermal diffusivity
*T is the surface temperature
*T is the quiescent temperature (fluid temperature far from the surface of the object)
*Gr is the Grashof number for characteristic length x
*Pr is the Prandtl number
In the above, the fluid properties Pr, ν, α and β are evaluated at the film temperature, which is defined as:
For a uniform wall heating flux, the modified Rayleigh number is defined as:
where:
*q&Prime; is the uniform surface heat flux
*k is the thermal conductivity.