Transient temperature rise 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

$\delta \theta_{c,t,o}$

Unit

Formulas

$W_c \left(T_{a0} \left(1-e^{-a_0 \tau}\right)+T_{b0} \left(1-e^{-b_0 \tau}\right)\right)$	normal case
$N_c W_c \left(T_{a0} \left(1-e^{-a_0 \tau}\right)+T_{b0} \left(1-e^{-b_0 \tau}\right)\right)$	cables in common duct

Related

$a_0$

Coefficient a partial transient temperature rise [1/s]

$b_0$

Coefficient b partial transient temperature rise [1/s]

$N_c$

Number of sources in system

$T_{a0}$

Apparent thermal resistance a [K.m/W]

$T_{b0}$

Apparent thermal resistance b [K.m/W]

$\tau$