@wikipedia
Dimensionless quantity characterizing characterising the ratio of convective to conductive heat transfer thermal convection to thermal conduction in fluids across (normal to) the boundary with solids:
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{\rm Nu} = \frac{\rm Convective \ heat \ transfer}{\rm Conductive \ heat \
transfer} = \frac{U}{\lambda / L} =\frac{U \cdot L}{\lambda } |
where
is the convective heat transfer coefficient of the flow, is the characteristic length, is the thermal conductivity of the fluid.
Stagnant Fluid
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For Stagnant FluidFor stagnant fluid the Nusselt number is a constant number (OEIS sequence A282581):
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{\rm Nu}=3.6568 |
Natural Convection
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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+ (0.492/\mbox{Pr})^{9/16} \right]^{8/27}} \right]^2 |
| | 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}} |
| | 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 In moving fluids the convection component becomes contributing and the Nusselt number becomes dependant on Reynolds number
and Prandtl number : .For laminar flows in pipeline the Nusselt number can be estimated through empirical correlation:
--uriencoded--\mbox%7BNu%7D = f (\mbox%7BRe%7D, \mbox%7BPr%7D) |
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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} |
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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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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} |
| | All flow regimes in pipelines LaTeX Math Inline |
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body | --uriencoded--\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.
See also
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Physics / Thermodynamics / Heat Transfer
[ Heat Transfer Coefficient (HTC) ] [ Heat Transfer Coefficient @model ]
[ Dimensionless Heat Transfer Numbers ]
[ Prandtl number ] [ Rayleigh number ] [ Reynolds number ] [ Biot Number ]
References
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