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LaTeX Math Inline
body\Delta T

Temperature gradient across Natural Thermal Convection

LaTeX Math Inline
body\nu

Kinematic viscosity of the fluid

LaTeX Math Inline
body\beta

Thermal expansion coefficient of the fluid

LaTeX Math Inline
bodya

Thermal Diffusivity of the fluid

LaTeX Math Inline
bodyL

Characteristic length of Natural Thermal Convection

LaTeX Math Inline
bodyg

Standard gravity constant

LaTeX Math Inline
body--uriencoded--\displaystyle %7B\rm Pr%7D = \frac%7B\nu%7D%7Ba%7D

Prandtl number

LaTeX Math Inline
body--uriencoded--\displaystyle %7B\rm Gr%7D = \frac%7Bg \, \beta \, \Delta T \, L%5e3%7D%7B\nu%5e2%7D

Grashof number

LaTeX Math Inline
body--uriencoded--\displaystyle %7B\rm Pr%7D \frac%7B\nu%7D%7Ba%7D



See also

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Physics / Thermodynamics / Heat Transfer

[ Dimensionless Heat Transfer Numbers ]


Show If
grouparax


Panel
bgColorpapayawhip
titleARAX

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

LaTeX Math Block
anchor4LI0Z
alignmentleft
\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

LaTeX Math Inline
bodyD_o

outer pipe

LaTeX Math Inline
bodyD_i

inner pipe

LaTeX Math Inline
bodyL = 0.5 \cdot ( D_o - D_i)

annulus gap

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See also

Physics / Thermodynamics / Heat Transfer

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