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Temperature rise by buried object k

This is the temperature rise of cable p due to the total power $W_{tot}$ dissipated in cable k.

When both cables p and k are embedded in the same concrete (backfill), the temperature rise by buried object k is adjusted with the difference between the thermal resistivity of the backfill material $\rho_b$ and the thermal resistivity of the soil $\rho_4$: $$\Delta\theta_{kp}=\Delta\theta_b+(\Delta\theta_{kp}-\Delta\theta_b)*\rho_b/\rho_4$$ $\Delta\theta_b$ is the temperature rise by buried object k on the top border of the backfill. With this method, the difference in temperature rise inside the backfill due to the difference in thermal resistivity is taken into consideration.

Symbol
$\Delta \theta_{kp}$
Unit
K
Formulae
$\frac{W_{tot} \rho_4}{2\pi} \ln\left(\frac{d_{pk1}}{d_{pk2}}\right)$
Related
$d_{pk1}$
Distance to mirrored buried object [mm]
$d_{pk2}$
Distance between buried objects [mm]
$\Delta \theta_p$
Temperature rise by other buried objects [K]
$\pi$
Archimedes' constant $\pi$
$\rho_4$
Thermal resistivity of soil [K.m/W]
$\rho_b$
Thermal resistivity backfill [K.m/W]
$W_{tot}$
Total losses per object [W/m]