Attainment factor cable surface—ambient

This is the surface to ambient temperature rise attainment factor for the cable or duct external surface, i.e. the ratio of the temperature rise at time i to the rise in the steady state.

Note: Dimension for $L_{cm}$ and $D_o$ is in meters.

Symbol

$\beta_{t}$

Formulas

$\frac{-\operatorname{expi}\left(\frac{-{D_{o}}^2}{16\tau \delta_{soil}}\right)+\operatorname{expi}\left(\frac{-{L_{cm}}^2}{\tau \delta_{soil}}\right)}{2\ln\left(\frac{4L_{cm}}{D_{o}}\right)}$

Related

$\beta_{6}$

Factor $|1-\beta(6)|$

$D_{o}$

Outer diameter [m]

$\delta_{soil}$

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

$L_{cm}$

Depth of laying [m]

$\tau$

Transient load period [s]

Used in