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
$\beta_{\mathrm{t}}$
Unit
°C
Formulae
$\left(- \frac{1}{2} \operatorname{expi}{\left (- \frac{D_{\mathrm{o}}^{2}}{16 \delta _{\mathrm{soil}} \tau} \right )} + \frac{1}{2} \operatorname{expi}{\left (- \frac{L_{\mathrm{cm}}^{2}}{\delta _{\mathrm{soil}} \tau} \right )}\right) \ln{\left (\frac{4 L_{\mathrm{cm}}}{D_{\mathrm{o}}} \right )}$
Related
$D_{\mathrm{o}}$
$\delta _{\mathrm{soil}}$
$L_{\mathrm{cm}}$
Used in
$\theta_{\mathrm{R}}$