Nusselt number, surface to water

External surfaces of a subsea pipeline, cable (or duct) and internal sufaces of a subsea pipeline or duct come in contact with fluids (water), so convection heat transfer will occur when there is a temperature difference between the surface and the fluid. The convection coefficient is also called a film heat transfer coefficient in the flow assurance field because convection occurs at a film layer adjacent to the surface.

Convection heat transfer occurs between the fluid flowing and the surface. It depends on the fluid properties, the flow velocity, and the pipe diameter.

All of the properties used in the correlations are evaluated at the temperature of film between the external surface and the surrounding fluid or internal surface and internal fluid. Many of the parameters used in the correlation are themselves dependent on temperature. Because the temperature drop along most pipelines and cables is relatively small, average values for physical properties may be used.

$C_{Nu,w} {\mathrm{Re}_w}^{m_{Nu,w}} {\mathrm{Pr}_w}^{0.333}$external
$0.0255{\mathrm{Re}_w}^{0.8} {\mathrm{Pr}_w}^{0.4}$internal
$3.66+\frac{0.0668\frac{D_{in}}{L_{leg}} \mathrm{Re}_w \mathrm{Pr}_w}{1+0.4\left(\frac{D_{in}}{L_{leg}} \mathrm{Re}_w \mathrm{Pr}_w\right)^{0.666}}$internal, laminar flow
$3.66$internal, laminar flow ($D_{in}$ ≪ $L_{leg}$)