Dimensionless quantity characterising the ratio of thermal convection to thermal conduction in fluids across (normal to) the boundary with solids:
(1) | {\rm Nu} = \frac{\rm Convective \ heat \ transfer}{\rm Conductive \ heat \ transfer} = \frac{U}{\lambda / L} =\frac{U \cdot L}{\lambda } |
where U is the convective heat transfer coefficient of the flow, L is the characteristic length, \lambda is the thermal conductivity of the fluid.
Stagnant Fluid
For Stagnant Fluid the Nusselt number is a constant number (OEIS sequence A282581):
(2) | {\rm Nu}=3.6568 |
Natural Convection
In Natural Fluid Convection becomes dependant on Rayleigh number \rm Ra and Prandtl number \rm Pr: \mbox{Nu} = f (\mbox{Ra}, \mbox{Pr}).
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\mbox{Ra}_D \leq 10^{12} | ||
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\mbox{Ra} \leq 10^9 | ||
| Churchill and Chu |
Forced Convection
In Forced Fluid Convection the Nusselt number becomes dependant on Reynolds number
\rm Re and Prandtl number
\rm Pr:
\mbox{Nu} = f (\mbox{Re}, \mbox{Pr}).
| Laminar flow in pipeline with diameter D and length L. | |||
| Dittus-Boelter | |||
| Gnielinski |
{\displaystyle 3000\leq \mathrm {Re}\leq 5\cdot 10^{6}} 0.5\leq \mathrm {Pr} \leq 2000 | ||
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Accuracy \sim 20 \% |
See also
Physics / Thermodynamics / Heat Transfer
[ Heat Transfer Coefficient (HTC) ] [ Heat Transfer Coefficient @model ]
[ Dimensionless Heat Transfer Numbers ]
[ Prandtl number ] [ Rayleigh number ] [ Reynolds number ]