Overall heat transfer coefficient

Combining the previous definitions the overall heat transfer coefficient, $U_{OHTC}$, is defined as a function of burial depth.

$U_{buried}$fully buried
$U_{partially}$partially buried
$U_{exposed}$completely in water
Used in
0IEC 60287-2-1The first method is the standard calculation method for buried cables according to the international standard IEC 60287-2-1. It is only possible for completely buried cables and only accurate for sufficiently deep buried cables.
1Carslaw & JaegerThe second method is named after Carslaw & Jaeger's reference book on conduction (Carslaw, 1959). It is assuming isothermal (Dirichlet) boundary conditions at the sea/soil interface and outside surface of the pipe.
2Morud & SimonsenThe third method is the result of Morud & Simonsen's work (Morud, 2007) and is an extended version to partially buried pipes of the Bau & Sadhal formula (Bau, 1982). Unlike Carslaw & Jaeger, Morud & Simonsen is based on a convective (mixed) boundary condition at the outside surface of the pipe. An isothermal (Dirichlet) boundary is assumed at the sea/soil interface.Few differences to the original paper have been introduced: Modified definition of the pipe Biot number to include internal convection; And the external convection at the sea/soil interface when the pipe is fully buried is accounted for by means of an additional ambient film coefficient $h_{amb}$ (necessary for low values of ambient film coefficient).
3OvuworieThe fourth method is based on Ovuworie's work (Ovuworie, 2010) and is based on convective (mixed) boundary conditions at both sea/soil interface and outside surface of the pipe. Few differences to the original paper have been introduced: Unlike other formulae the Biot numbers in the Ovuworie formula are based on the overall external diameter of the pipe, $D_{ext}$. The coefficients $U_{ground}$ and $U_{buried}$ depend explicitly on the heat transfer coefficients $h_{in}$ and $U_{wall}$.
4OTC 23033The fifth method is a modified version of Ovuworie and named after the Offshore Technology Conference, OTC, where it was published 2012. The inside film coefficient $h_{in}$ and and heat transfer coefficient $U_{wall}$ are removed from the definition of $U_{buried}$. The pipe and ground Biot numbers are more rigorously based on the reference diameter $D_{ref}$ instead of $D_{ext}$. The heat transfer coefficient $U_{ground}$ is derived from the limit of $U_{buried}$ when $H$ approaches $D_{ext}/2$, bearing in mind that $\alpha_{0}$ = 0 at $H=D_{ext}/2$; $sinh(x)=x+O(x³)$; and $cosh(x)=1+x²/2+O(x⁴)$.