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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.
| $\frac{W_{tot} \rho_4}{2\pi} \ln\left(\frac{d_{pk1}}{d_{pk2}}\right)$ | buried cables, PAC/GIL, heat sources |
| $\frac{W_{sum} \rho_4}{2\pi} \ln\left(\frac{d_{pk1}}{d_{pk2}}\right)$ | air-filled pipe with objects, air-filled trough |