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Dimensionless quantity characterising the development of Natural Thermal Convection:
| (1) | \mbox{Ra}_L = \mbox{Gr} \cdot \mbox{Pr} = \frac{g \, \beta \, \Delta T \, L^3}{\nu \cdot a} |
where
\Delta T | Temperature gradient across Natural Thermal Convection | \nu | Kinematic viscosity of the fluid |
|---|---|---|---|
\beta | Thermal expansion coefficient of the fluid | a | Thermal Diffusivity of the fluid |
L | Characteristic length of Natural Thermal Convection | g | Standard gravity constant |
\displaystyle {\rm Pr} = \frac{\nu}{a} | Prandtl number | \displaystyle {\rm Gr} = \frac{g \, \beta \, \Delta T \, L^3}{\nu^2} | Grashof number \displaystyle {\rm Pr} \frac{\nu}{a} |
For the Natural Thermal Convection in the annulus between two concentric pipes:
| (2) | \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
D_o | outer pipe |
D_i | inner pipe |
L = 0.5 \cdot ( D_o - D_i) | annulus gap |
See also
Physics / Thermodynamics / Heat Transfer
[ Dimensionless Heat Transfer Numbers ]