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Transient temperature rise outer surface

The transient response of the cable environment is calculated by an exponential integral formula.

Note: The parameters $D_o$ and $L_{cm}$ are in meters.

Symbol
$\delta \theta_{e,t}$
Unit
K
Formulas
$\frac{\rho_{4} W_{I}}{4\pi} \left(-\operatorname{expi}\left(\frac{-{D_{o}}^2}{16\tau \delta_{soil}}\right)--\operatorname{expi}\left(\frac{-{L_{cm}}^2}{\tau \delta_{soil}}\right)\right)$normal case
$\frac{n_{cc} \rho_{4} W_{I}}{4\pi} \left(-\operatorname{expi}\left(\frac{-{D_{o}}^2}{16\tau \delta_{soil}}\right)--\operatorname{expi}\left(\frac{-{L_{cm}}^2}{\tau \delta_{soil}}\right)\right)$multi-core cables
Related
$D_{o}$
Outer diameter [m]
$\delta_{soil}$
Thermal diffusivity soil [m$^2$/s]
$L_{cm}$
Depth of laying [m]
$n_{cc}$
Number of conductors combined
$\pi$
Archimedes' constant $\pi$
$\rho_{4}$
Thermal resistivity soil [K.m/W]
$\tau$
Transient load period [s]
$W_{I}$
Ohmic losses (phase) [W/m]
Used in
$\delta \theta_{c,t}$
Transient temperature rise conductor [K]