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Dimensionless quantity characterising the development of Natural Thermal Convection:

\mbox{Ra} = \mbox{Gr} \cdot \mbox{Pr} = \frac{g \, \beta \, \Delta T \, L^3}{\nu \cdot a}

where

	Temperature gradient across Natural Thermal Convection		Kinematic viscosity of the fluid
	Thermal expansion coefficient of the fluid		Thermal Diffusivity of the fluid
	Characteristic length of Natural Thermal Convection		Standard gravity constant
	Prandtl number		Grashof number

[ Dimensionless Heat Transfer Numbers ] [ Prandtl number ] [ Grashof number ]

For the Natural Thermal Convection in the annulus between two concentric pipes:

\mbox{Ra}_D = \frac{8}{(D_o - D_i)^3} \cdot \frac{ \left[ \ln D_o/D_i \right]^4 }{D_i^{-3/5}+D_o^{-3/5}}  \cdot \mbox{Ra}_L =
 \frac{ \left[ \ln D_o/D_i \right]^4 }{D_i^{-3/5}+D_o^{-3/5}} \cdot \frac{g \, \beta \, \Delta T }{\nu \cdot a}

where

	outer pipe
	inner pipe
	annulus gap