@wikipedia
Dimensionless quantity characterising the ratio of 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
For Stagnant Fluid the Nusselt number is a constant number (OEIS sequence A282581):
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{\rm Nu}=3.6568 |
Natural Convection
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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| \mbox{Nu}= \left[ 0.825 + \frac{0.387 \, \mbox{Ra}^{1/6}}{ \left[ 1+ (0.492/\mbox{Pr})^{9/16} \right]^{8/27}} \right]^2 |
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| \mbox{Nu}= 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 flows
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| body | --uriencoded--\mbox%7BRa%7D \leq 10%5e9 |
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Forced Convection
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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| {\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 |
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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) } |
| | laminar-turbulent transition and turbulent flow in pipeline the Nusselt number (Nu) becomes also dependant on friction with wall, quantifiable by Darcy friction factor , and can be estimated through empirical correlation (Gnielinski
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| body | --uriencoded--0.5\leq \mathrm %7BPr%7D \leq 2000 |
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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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| {\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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| 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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See also
Physics / Thermodynamics / Heat Transfer
[ Heat Transfer Coefficient (HTC) ] [ Heat Transfer Coefficient @model ]
[ Dimensionless Heat Transfer Numbers ]
References
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