Attainment factor for groups of cables

This is the attainment factor for groups of cables the cable or duct external surface, i.e. the ratio of the temperature rise at time i to the rise in the steady state.This function is used in calculating cyclic rating factor for groups of cables.

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

Symbol

$\gamma_t$

Formulae

$\frac{-\operatorname{expi}\left(\frac{-{D_o}^2}{16\tau \delta_{soil}}\right)+\operatorname{expi}\left(\frac{-{L_{cm}}^2}{\tau \delta_{soil}}\right)+\left(N_c-1\right) \left(-\operatorname{expi}\left(\frac{-{d_f}^2}{16\tau \delta_{soil}}\right)+\operatorname{expi}\left(\frac{-{L_{cm}}^2}{\tau \delta_{soil}}\right)\right)}{2\ln\left(\frac{4L_{cm} F_{mh}}{D_o}\right)}$

Related

$d_f$

Spacing from hottest object in group [m]

$D_o$

Outer diameter [m]

$\delta_{soil}$

Soil thermal diffusivity [m$^2$/s]

$F_{mh}$

Mutual heating coefficient

$L_{cm}$

Depth of laying [m]

$N_c$

Number of sources in system

$\tau$

Transient load period [s]

Used in

$\theta_R$

Rated current transient to steady-state ratio