@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 : .



\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



Churchill and Chu 

Churchill, S.W. and Chu, H.H.S. (1975) Correlating Equations for Laminar and Turbulent Free Convection from a Vertical Plate. International Journal of Heat and Mass Transfer, 18, 1323-1329.
http://dx.doi.org/10.1016/0017-9310(75)90243-4



All flow regimes


\mbox{Nu}= 0.68 + \frac{0.663 \, \mbox{Ra}^{1/4}}{ \left[ 1+ (0.492/\mbox{Pr})^{9/16} \right]^{4/9}}



Churchill and Chu

Churchill, S.W. and Chu, H.H.S. (1975) Correlating Equations for Laminar and Turbulent Free Convection from a Vertical Plate. International Journal of Heat and Mass Transfer, 18, 1323-1329.
http://dx.doi.org/10.1016/0017-9310(75)90243-4



Laminar flows


Forced Convection


In Forced Fluid Convection the Nusselt number becomes dependant on Reynolds number  and Prandtl number : .



{\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} }




Laminar flow in pipeline



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

 is Darcy friction factor

Gnielinski

Gnielinski, Volker (1975). "Neue Gleichungen für den Wärme- und den Stoffübergang in turbulent durchströmten Rohren und Kanälen". Forsch. Ing.-Wes. 41 (1): 8–16.



Laminar-turbulent transition and turbulent flow in pipeline

 


{\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}


Churchill–Bernstein 

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



Accuracy 


See also

Physics / Thermodynamics / Heat Transfer

[ Heat Transfer Coefficient (HTC) ] [ Heat Transfer Coefficient @model ]

[ Dimensionless Heat Transfer Numbers ]


References