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Transient temperature rise of 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
Formulae
$\frac{\rho_4 W_I}{4\pi} \left(-\operatorname{expi}\left(\frac{-{D_o}^2}{16\tau \delta_{soil}}\right)--\operatorname{expi}\left(\frac{-{L_{cm}}^2}{\tau \delta_{soil}}\right)\right)$
Related
$D_o$
Outer diameter [m]
$\delta_{soil}$
Soil thermal diffusivity [m$^2$/s]
$L_{cm}$
Depth of laying [m]
$\pi$
Archimedes' constant $\pi$
$\rho_4$
Thermal resistivity of soil [K.m/W]
$\tau$
Transient load period [s]
$W_I$
Ohmic losses per phase [W/m]
Used in
$\Delta \theta_{c,t}$
Transient temperature rise of conductor [K]