Dimensionless quantity characterizing the ratio of convective to conductive heat transfer across (normal to) the boundary:
| (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.
For stagnant fluid the Nusselt number is a constant number (OEIS sequence A282581):
| (2) | {\rm Nu}=3.6568 |
In moving fluids the convection component becomes contributing and the Nusselt number becomes dependant on Reynolds number \rm Re and Prandtl number \rm Pr.
For laminar flows in pipeline the Nusselt number can be estimated through empirical correlation:
| (3) | {\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 becomes also depdedant on friction with wall, quantifiable by Darcy friction factor f, and can be estimated through empirical correlation (Gnielinski ):
| (4) | {\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}}.
See also
Physics / Thermodynamics / Heat Transfer
[ Heat Transfer Coefficient (HTC) ] [ Heat Transfer Coefficient @model ]
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.