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}).
Churchill and Chu correlation which works with \mbox{Ra} \leq 10^8:
| (3) | \mbox{Nu}= 0.68 + \frac{0.663 \, \mbox{Ra}^{1/4}}{ \left[ 1+ (0.492/\mbox{Pr})^{9/16} \right]^{4/9}} |
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}).
For laminar flows in pipeline the Nusselt number can be estimated through empirical correlation:
| (4) | {\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} } |
For laminar-turbulent transition and turbulent flow in pipeline the Nusselt number (Nu) becomes also dependant on friction with wall, quantifiable by Darcy friction factor f, and can be estimated through empirical correlation (Gnielinski ):
| (5) | {\rm Nu}=\frac{ (f/8) \, ({\rm Re} - 1000) {\rm Pr} }{ 1 + 12.7 \, (f/8)^{1/2} \, ({\rm Pr}^{2/3} -1) } |
for 0.5\leq \mathrm {Pr} \leq 2000 and {\displaystyle 3000\leq \mathrm {Re}\leq 5\cdot 10^{6}}.
Churchill–Bernstein correlation:
See also
Physics / Thermodynamics / Heat Transfer
[ Heat Transfer Coefficient (HTC) ] [ Heat Transfer Coefficient @model ]
[ Dimensionless Heat Transfer Numbers ]
References
Gnielinski, Volker (1975). "Neue Gleichungen für den Wärme- und den Stoffübergang in turbulent durchströmten Rohren und Kanälen". Forsch. Ing.-Wes. 41 (1): 8–16.
Churchill, S. W.; Bernstein, M. (1977), "A Correlating Equation for Forced Convection From Gases and Liquids to a Circular Cylinder in Crossflow", Journal of Heat Transfer, 99 (2): 300–306, Bibcode:1977ATJHT..99..300C, doi:10.1115/1.3450685