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 hamb (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, Dext. The coefficients Uground and Uburied depend explicitly on the heat transfer coefficients hin and Uwall.
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 hin and and heat transfer coefficient Uwall are removed from the definition of Uburied. The pipe and ground Biot numbers are more rigorously based on the reference diameter Dref instead of Dext. The heat transfer coefficient Uground is derived from the limit of Uburied when H approaches Dext/2, bearing in mind that α0 = 0 at H = Dext/2; sinh(x) = x+O(x³); and cosh(x) = 1+x²/2+O(x⁴).