The ratio of convective to conductive heat transfer across (normal to) the boundary:
{\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 and laminar flows the Nusselt number is a constant number (OEIS sequence A282581):
(1) | {\rm Nu}=3.66 |
For transient and turbulent flow in pipelines Nusselt number can be estimated through empirical correlation (Gnielinski):
(2) | {\rm Nu}=\frac{ (f/8) \, ({\rm Re} - 1000) {\rm Pr} }{ 1 + 12.7 \, (f/8)^{1/2} \, ({\rm Pr}^{2/3} -1) } |
where \rm Pr is Parndtl number.
See also
Physics / Thermodynamics / Heat Transfer