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In Natural Fluid Convection becomes dependant on Rayleigh number 

LaTeX Math Inline
body\rm Ra
 and Prandtl number 
LaTeX Math Inline
body\rm Pr
LaTeX Math Inline
body--uriencoded--\mbox%7BNu%7D = f (\mbox%7BRa%7D, \mbox%7BPr%7D)
.:


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\mbox{Nu}_D= \left[ 0.825 + \frac{0.387 \, \mbox{Ra}_D^{1/6}}{ \left[ 1+ (0.492/\mbox{Pr})^{9/16} \right]^{8/27}} \right]^2



Churchill and Chu 



All convection regimes in pipelines

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body--uriencoded--\mbox%7BRa%7D_D \leq 10%5e%7B12%7D


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\mbox{Nu}_L= 0.68 + \frac{0.663 \, \mbox{Ra}^{1/4}}{ \left[ 1+ (0.492/\mbox{Pr})^{9/16} \right]^{4/9}}



Churchill and Chu



Laminar convection

LaTeX Math Inline
body--uriencoded--\mbox%7BRa%7D \leq 10%5e9


In case of natural convection in the annulus the Nusselt number becomes also dependant on the annulus geometry:


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{\rm Nu} = \frac{2 \cdot \epsilon_{app}}{\ln (r_{ci}/r_t)}



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{\rm Nu} = \frac{2 \cdot \epsilon}{\ln (r_{ci}/r_t)}


where

LaTeX Math Inline
body--uriencoded--\epsilon_%7Bann%7D

Natural Convection Heat Transfer Multiplier


Forced Convection

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In Forced Fluid Convection the 
Nusselt number becomes dependant on Reynolds number 

LaTeX Math Inline
body\rm Re
 and Prandtl number 
LaTeX Math Inline
body\rm Pr
LaTeX Math Inline
body--uriencoded--\mbox%7BNu%7D = f (\mbox%7BRe%7D, \mbox%7BPr%7D)
.

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