Transient temperature rise of conductor by ohmic losses

This is the transient temperature rise of conductor above outer surface caused by ohmic losses. The transient response of a cable circuit to a step function of load current, considered in isolation, that is with the right-hand pair of terminals of the thermal circuit short-cuircuited, is found with the following formula calculating the transient temperature rise of conductor above outer surface. The parameter $W_c$ is the power loss per unit length in a conductor or an equivalent conductor based on the maximum conductor temperature attained. The power loss is assumed to be constant during the transient.

Symbol
$\Delta \theta_{c_{t}}$
Unit
K
Formulae
$W_{c} n_{c} \left(T_{a0} \left(1 - e^{- a_{0} \tau}\right) + T_{b0} \left(1 - e^{- b_{0} \tau}\right)\right)$
$W_{c}$
Used in
$\Delta \theta_{t}$
Image
IEC standard 60853-2 Ed. 1.0 (1989) Figure 2