Thermal resistance for daily load cycle

Effective transient thermal resistance in the earth for a transient period of $\tau$. The used equations ensure that the transient thermal resistance cannot become negative for very short transient periods.

The transient component of the heat flow will penetrate the earth only to a limited distance from the cable, thus the corresponding thermal resistance will be smaller than its steady-state counterpart $T_{4ss}$. It is assumed that the temperature rise over the internal thermal cable resistance is complete by the end of the transient cycle.

$\frac{\rho_4}{2\pi} \ln\left(\frac{\operatorname{Max}\left(D_x, Do_d\right)}{Do_d}\right)$buried
$\frac{\rho_b}{2\pi} \ln\left(\frac{\operatorname{Max}\left(D_x, Do_d\right)}{Do_d}\right)$buried in backfill or filled troughs
$\frac{\rho_4}{2\pi} \ln\left(\frac{\operatorname{Max}\left(D_x, Do_d\right)}{Do_d}\right)+\frac{\rho_d}{2\pi} \ln\left(\frac{Do_d}{Di_d}\right)+\frac{\rho_{d,fill}}{2\pi} \ln\left(\frac{Di_d}{D_{eq}}\right)$buried in bentonite-filled ducts
Used in