Attainment factor cable surface to 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
$\beta_{t}$
Formulae
$\frac{- \frac{\operatorname{expi}{\left(- \frac{D_{o}^{2}}{16 \delta _{soil} \tau} \right)}}{2} + \frac{\operatorname{expi}{\left(- \frac{L_{cm}^{2}}{\delta _{soil} \tau} \right)}}{2}}{\ln{\left(\frac{4 L_{cm}}{D_{o}} \right)}}$
Related
$D_{o}$
$\delta _{soil}$
$L_{cm}$