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Temperature of steel pipe

The formulae to calculate the loss factor for steel pipe $\lambda_3$ use the resistance of the pipe $R_{sp}$ at its maximum operating temperature. Because the temperature of the steel pipe is a function of the current, $I_c$, an iterative method is used for the calculation.

With crossing heat sources, a temperature rise of $\Delta\theta_{0x}$ applies at the hottest point.

Symbol
$\theta_{sp}$
Unit
°C
Formulae
$\theta_c-T_1 \left(W_c+\frac{W_d}{2}\right)+n_{ph} T_2 \left(W_c \left(1+\lambda_1+\lambda_2\right)+W_d\right)$
Related
$\Delta \theta_{0x}$
Temperature rise by crossing heat sources [K]
$\lambda_1$
Loss factor of shield (screen and sheath)
$\lambda_2$
Loss factor of armour
$n_{ph}$
Number of phases in a cable
$T_1$
Thermal resistance between one conductor and sheath [K.m/W]
$T_2$
Thermal resistance of armour bedding [K.m/W]
$\theta_c$
Temperature of conductor [°C]
$W_c$
Conductor losses [W/m]
$W_d$
Dielectric losses [W/m]
Used in
$R_{sp}$
Electrical resistance of steel pipe [$\Omega$/m]
$\theta_{spf}$
Mean temperature of the medium in the steel pipe [°C]