Transient temperature rise outer surface by object k

This is the temperature rise of cable p due to the total ohmic power $W_{I}$ dissipated in cable k. The increase in temperature caused by the dielectic losses is considered with $\delta\theta_{d_{t}}$.

Symbol

$\Delta \theta_{kp,t}$

Unit

Formulas

$\frac{W_I \rho_4}{4\pi} \left(-\operatorname{expi}\left(\frac{-\left(\frac{d_{pk2}}{1000}\right)^2}{4\tau \delta_{soil}}\right)+\operatorname{expi}\left(\frac{-\left(\frac{d_{pk1}}{1000}\right)^2}{4\tau \delta_{soil}}\right)\right)$	buried cables, PAC/GIL, heat sources
$\frac{W_{sum} \rho_4}{4\pi} \left(-\operatorname{expi}\left(\frac{-\left(\frac{d_{pk2}}{1000}\right)^2}{4\tau \delta_{soil}}\right)+\operatorname{expi}\left(\frac{-\left(\frac{d_{pk1}}{1000}\right)^2}{4\tau \delta_{soil}}\right)\right)$	air-filled pipe with objects, air-filled trough

Related

$d_{pk1}$

Distance to mirrored object [mm]

$d_{pk2}$

Distance to buried objects [mm]

$\delta_{soil}$

Thermal diffusivity soil [m$^2$/s]

$\Delta \theta_{p,t}$

Transient temperature rise outer surface by other buried objects [K]

$\pi$

Archimedes' constant $\pi$

$\rho_4$