Imaginary layer of soil

The imaginary layer of soil is used to model a non-isothermal earth surface.

Samson Semenovich Kutateladze introduced the fictitious layer method in his book 'Osnovy Teorii Teploobmena', Mashgiz, Moscow-Leningrad, 1962 (translated by Scripta Technica Inc. as 'Fundamentals of Heat Transfer', Edward Arnold (Publishers) Inc., London, 1963. It is also called the additional wall method, used to model a non-isothermal earth surface with the help of a fictitious earth layer with thickness $d_{im}$. The cable image line source is then placed at distance $L_{cm}+d_{im}$ above the fictitious layer.

Unlike others, we do not just use a constant but actually calculate in an iterative process the thickness of this imaginary layer of soil depending on the losses and ambient conditions. The heat generated from all sources within a certain range near the center $(-3≤x≤3)$ is used to calculate the surface temperature $T_{surf}$ above the center axis $(x=0)$. This temperature is used to calculate the Nusselt number $Nu_{L}$ and the thermal conductivity of the air above ground $k_{gas}$ both used to determine the heat transfer coefficient $h_{tr}$ which is needed to calculate the imaginary layer of soil $d_{im}$. The basics of the method we used was presented in the paper 'Calculation of cable thermal rating considering non-isothermal earth surface' from 2014 by S. Purushothaman, F. de León, and M. Terracciano.

$\frac{1}{\rho_4 h_{tr}}$