Temperature rise by buried object k

This is the temperature rise at the surface of the cable produced by the total power $W_{tot}$ dissipated in cable k.

When the cables or ducts are embedded in concrete (backfill), the thermal resistivity of soil $\rho_4$ is replaced with the thermal resistivity of the backfill material $\rho_b$ or with the mean value of the thermal resistivities around cable p and k.

For transient calculations, this is the transient temperature rise at the surface of the cable produced by the total power $W_{tot}$ dissipated in cable k.

Symbol
$\Delta \theta_{kp}$
Unit
K
Formulae
$\frac{W_{tot} \rho_{4} \ln{\left(\frac{d_{pk1}}{d_{pk2}} \right)}}{2 \pi}$steady-state
$\frac{W_{tot} \rho_{4} \left(\operatorname{expi}{\left(- \frac{d_{pk1}^{2}}{4000000 \delta _{soil} \tau} \right)} - \operatorname{expi}{\left(- \frac{d_{pk2}^{2}}{4000000 \delta _{soil} \tau} \right)}\right)}{4 \pi}$transient
$\delta _{soil}$
$\rho_{4}$