Cableizer
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Transient temperature rise of outer surface by object k

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

Symbol
$\Delta \theta_{kp,t}$
Unit
K
Formulae
$\frac{W_{tot} \rho_4}{4\pi} \left(-\operatorname{expi}\left(\frac{-\left(\frac{d_{pk2}}{1000}\right)^2}{4\tau \delta_{soil}}\right)+\operatorname{expi}\left(\frac{-\left(\frac{d_{pk1}}{1000}\right)^2}{4\tau \delta_{soil}}\right)\right)$
Related
$d_{pk1}$
Distance to mirrored buried object [mm]
$d_{pk2}$
Distance between buried objects [mm]
$\delta_{soil}$
Soil thermal diffusivity [m$^2$/s]
$\Delta \theta_{p,t}$
Transient temperature rise of outer surface by other buried objects [K]
$\pi$
Archimedes' constant $\pi$
$\rho_4$
Thermal resistivity of soil [K.m/W]
$\tau$
Transient load period [s]
$W_{tot}$
Total losses per object [W/m]