Temperature rise of conductor

This is the conductor temperature rise above the ambient temperature respectively above the surface temperature of cable or duct in tunnel and in trough (method by Anders 2010) and the surface temperature of the cable in riser.

For DC, the dielectric losses $W_d$ are zero and the corresponding terms disappear.

$\Delta \theta_c$
$n_c \left(W_c T_{int}+W_d T_d\right)+n_{cc} \left(W_I+W_d\right) \left(T_{4i}+T_{4ii}+T_{4iii}\right)+n_{cc} W_{duct} \left(\frac{T_{4ii}}{2}+T_{4iii}\right)$Cables in air
$n_c \left(W_c T_{int}+W_d T_d\right)+n_{cc} W_I \left(T_{4i}+T_{4ii}+v_4 T_{4mu}\right)+n_{cc} W_d \left(T_{4i}+T_{4ii}+v_4 T_{4ss}\right)+n_{cc} W_{duct} \left(\frac{T_{4ii}}{2}+v_4 T_{4mu}\right)$Cables buried
$n_c \left(W_c T_{int}+W_d T_d\right)+n_{cc} \left(W_I+W_d\right) \left(T_{4i}+T_{4ii}\right)$Cables in tunnel
$n_c \left(W_c T_{int}+W_d T_d+\left(W_I+W_d\right) T_{4t}\right)$Cables in tunnel (IEC 60287-2-3)
$n_c \left(W_c T_{int}+W_d T_d\right)+n_{cc} \left(W_I+W_d\right) \left(T_{4i}+T_{4ii}+T_{4iii}\right)$Cables in trough or in channel (Heinhold)
$n_c \left(W_c T_{int}+W_d T_d\right)+n_{cc} \left(W_I+W_d\right) T_{4iii}$Cables subsea
$n_c \left(W_c T_{int}+W_d T_d\right)$Cables in riser
$n_c \left(W_c T_{int}+W_d T_d\right)+n_{cc} W_I v_4 T_{4mu}+n_{cc} W_d v_4 T_{4ss}+n_{cc} W_{duct} \left(\frac{T_{4ii}}{2}+v_4 T_{4mu}\right)$Cables buried in ducts with bentonite filling and transient loading
Used in