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In Natural Fluid Convection becomes dependant on Rayleigh number
and Prandtl number : | LaTeX Math Inline |
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| body | --uriencoded--\mbox%7BNu%7D = f (\mbox%7BRa%7D, \mbox%7BPr%7D) |
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:
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| \mbox{Nu}_D= \left[ 0.825 + \frac{0.387 \, \mbox{Ra}_D^{1/6}}{ \left[ 1+ (0. |
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492/\mbox{Pr})^{9/16} \right]^{8/27}} \right]^2 |
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All convection regimes in pipelines
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| body | --uriencoded--\mbox%7BRa%7D_D \leq |
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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}} |
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Laminar convection
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| body | --uriencoded--\mbox%7BRa%7D \leq 10%5e9 |
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In case of natural convection in the annulus the Nusselt number becomes also dependant on the annulus geometry:
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| {\rm Nu}_{ann} = \frac{2 \cdot \epsilon({\rm Ra})}{\ln (r_{out}/r_{in})} |
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where
Forced Convection
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In Forced Fluid Convection the Nusselt number becomes dependant on Reynolds number
and Prandtl number :
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| body | --uriencoded--\mbox%7BNu%7D = f (\mbox%7BRe%7D, \mbox%7BPr%7D) |
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.For laminar flows in pipeline the Nusselt number can be estimated through empirical correlation:
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| {\rm Nu}=3.66 + \frac{ 0.065 \cdot {\rm Re} \cdot {\rm Pr} \cdot {D/L} }{ 1 + 0.04 \cdot ({\rm Re} \cdot {\rm Pr} \cdot {D/L})^{2/3} } |
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Laminar flow in pipeline with diameter and length . |
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| {\rm Nu}=0.023 \cdot \mbox{Re}_D^{3/4} \cdot \mbox{Pr}^{0.4} |
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| --uriencoded--\mbox%7BRe%7D \geq 10,000 |
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| {\rm Nu}=\frac{ (f/8) \, ({\rm Re} - 1000) {\rm Pr} }{ 1 + 12.7 \, (f/8)^{1/2} \, ({\rm Pr}^{2/3} -1) } |
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| body | --uriencoded--%7B\displaystyle 3000\leq \mathrm %7BRe%7D\leq 5\cdot 10%5e%7B6%7D%7D |
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| LaTeX Math Inline |
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| body | --uriencoded--0.5\leq \mathrm %7BPr%7D \leq 2000 |
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| is Darcy friction factor |
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| {\rm Nu}=0.3 + \frac{0.62 \, \mbox{Re}^{1/2} \, \mbox{Pr}^{1/3} }
{\left[ 1+ (0.4/\mbox{Pr})^{2/3} \right]^{1/4}}
\left[ 1 + \left( \frac{\mbox{Re}}{282000} \right)^{5/8}\right]^{4/5} |
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| \mbox %7BRe%7D \cdot \mbox %7BPr%7D \geq 0.2 |
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Accuracy | LaTeX Math Inline |
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| body | --uriencoded--\sim 20 \%25 |
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Both numbers naturally arise in modelling the heat exchange between solid body and fluid.
Both numbers have similar definition except that Nusselt number is based on thermal conductivity of the fluid while Biot Number is based on thermal conductivity of the solid body.
Normally Nusselt number indicates whether conductive or convective heat transfer dominates across the interface between solid body and fluid.
While Biot Number indicates whether significant thermal gradient will develop inside a solid body based on the ratio of heat transfer away from the surface of a solid body to heat transfer within the solid body.
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Churchill–Bernstein correlation
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See also
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Physics / Thermodynamics / Heat Transfer
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[ Dimensionless Heat Transfer Numbers ]
References
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[ Prandtl number ] [ Rayleigh number ] [ Reynolds number ] [ Biot Number ]
References
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