Transient thermal resistance for yearly load

Effective transient thermal resistance in the earth for yearly load (transient period $\tau$ of 1 year):

For deeply buried cables and for tunnels, the yearly load variations play a significant role because of the very long constants at great depths.

Symbol
$T_{4y}$
Unit
K.m/W
Formulae
$\frac{\rho_4}{2\pi} \ln\left(\frac{D_{x,y}}{Do_d}\right)$buried
$\frac{\rho_4}{2\pi} \ln\left(\frac{D_{x,y}}{Do_d}\right)+\frac{\rho_d}{2\pi} \ln\left(\frac{Do_d}{Di_d}\right)+\frac{\rho_{d,fill}}{2\pi} \ln\left(\frac{Do_d}{D_{eq}}\right)$buried in bentonite-filled ducts
Used in