@wikipedia

Dimensionless quantity characterising the ratio of thermal convection to thermal conduction in fluids across (normal to) the boundary with solids:

{\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):

{\rm Nu}=3.6568

Natural Convection

In Natural Fluid Convection becomes dependant on Rayleigh number  and Prandtl number : .

 Churchill and Chu correlation which works with :

\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  and Prandtl number : .

For laminar flows in pipeline the Nusselt number can be estimated through empirical correlation:

{\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 , and can be estimated through empirical correlation (Gnielinski

):

{\rm Nu}=\frac{ (f/8) \, ({\rm Re} - 1000) {\rm Pr}  }{ 1 + 12.7 \, (f/8)^{1/2} \, ({\rm Pr}^{2/3} -1) }

for  and .

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