Cableizer ®

External temperature object

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

Symbol
$\theta_{e}$
Unit
°C
Formulas
$\theta_{c}-T_{1} \left(W_{c}+\frac{W_{d}}{2}\right)-n_{ph} T_{2} \left(W_{c} \left(1+\lambda_{1}\right)+W_{d}\right)-n_{ph} T_{3} \left(W_{I}+W_{d}\right)$cables
$\theta_{hsf}-W_{hs} T_{hs}$heat sources
$\theta_{a}+\Delta \theta_{s}$PAC/GIL in air
$\theta_{a}+v_{4} \Delta \theta_{p}+\left(1-v_{4}\right) \Delta \theta_{x}+W_{tot} v_{4} T_{4\mu}$PAC/GIL buried without duct
$\theta_{di}+T_{4i} n_{cc} W_{tot}$PAC/GIL with duct
$\theta_{at}+\Delta \theta_{s}$PAC/GIL in trough in air
$\theta_{t}+T_{4iii} W_{tot}$PAC/GIL in channel (Heinhold)
$\delta \theta_{c,t}-T_{1} W_{c}-n_{ph} T_{2} W_{c} \left(1+\lambda_{1}\right)-n_{ph} T_{3} W_{I}$transient (approximation) CIGRE WG B1.72
Related
$\Delta \theta_{0x}$
Temperature rise by crossing heat sources [K]
$\delta \theta_{c,t}$
Transient temperature rise conductor [K]
$\Delta \theta_{p}$
Temperature rise by other buried objects [K]
$\Delta \theta_{s}$
Temperature difference surface—ambient [K]
$\Delta \theta_{x}$
Critical soil temperature rise [K]
$\lambda_{1}$
Loss factor shield (screen/sheath)
$n_{cc}$
Number of conductors combined
$n_{ph}$
Number of phases in a cable
$T_{1}$
Thermal resistance conductor—sheath [K.m/W]
$T_{2}$
Thermal resistance armour bedding [K.m/W]
$T_{3}$
Thermal resistance jacket [K.m/W]
$T_{4i}$
Thermal resistance medium in the duct [K.m/W]
$T_{4iii}$
Thermal resistance ambient [K.m/W]
$T_{4\mu}$
Thermal resistance ambient [K.m/W]
$T_{hs}$
Thermal resistance heat source [K.m/W]
$\theta_{a}$
Ambient temperature [°C]
$\theta_{at}$
Air temperature with load [°C]
$\theta_{c}$
Temperature conductor [°C]
$\theta_{di}$
Temperature duct inner surface [°C]
$\theta_{hsf}$
Temperature fluid [°C]
$\theta_{t}$
Temperature wall (inner) [°C]
$v_{4}$
Ratio thermal resistivity dry/moist soil
$W_{c}$
Conductor losses (phase) [W/m]
$W_{d}$
Dielectric losses (phase) [W/m]
$W_{hs}$
Heat dissipation heat source [W/m]
$W_{I}$
Ohmic losses (phase) [W/m]
$W_{tot}$
Total losses (object) [W/m]
Used in
$\Delta \theta_{ce}$
Temperature difference conductor—surface [K]
$\Delta \theta_{gas}$
Temperature difference conductor—enclosure [°C]
$\Delta \theta_{s}$
Temperature difference surface—ambient [K]
$\mathrm{Gr}_{gd}$
Grashof number gas—duct
$\mathrm{Gr}_{og}$
Grashof number cable—gas
$\mathrm{Gr}_{prot}$
Grashof number surface→air
$h_{rad,int}$
Heat transfer coefficient radiation cable—riser [W/(K.m$^2$)]
$h_{rad,sa}$
Heat transfer coefficient radiation surface—air [W/(K.m$^2$)]
$I_{c}$
Conductor current [A]
$\mathrm{Ra}_{int}$
Rayleigh number gas→riser
$T_{4i}$
Thermal resistance medium in the duct [K.m/W]
$T_{4iii}$
Thermal resistance ambient [K.m/W]
$T_{conv,int}$
Thermal resistance convection cable—riser [K.m/W]
$T_{conv,sa}$
Thermal resistance convection surface—air [K.m/W]
$T_{rad,int}$
Thermal resistance radiation cable—riser [K.m/W]
$T_{rad,sa}$
Thermal resistance radiation surface—air [K.m/W]
$T_{rad,sun}$
Thermal resistance solar radiation air—surface [K.m/W]
$\theta_{de}$
Temperature duct outer surface [°C]
$\theta_{di}$
Temperature duct inner surface [°C]
$\theta_{dm}$
Mean temperature medium in the duct [°C]
$\theta_{encl}$
Temperature enclosure [°C]
$\theta_{film}$
Film temperature [°C]
$\theta_{gas}$
Gas temperature [°C]
$\theta_{hsf}$
Temperature fluid [°C]
$W_{conv,int}$
Convective heat transfer cable→riser [W/m]
$W_{conv,og}$
Convective heat transfer cable→gas [W/m]
$W_{conv,sa}$
Convective heat transfer, surface→air [W/m]
$W_{fo}$
Heat fiber optic cable [W/m]
$W_{hs}$
Heat dissipation heat source [W/m]
$W_{rad,int}$
Radiation heat transfer cable—riser [W/m]
$W_{rad,sa}$
Radiation heat transfer surface—air [W/m]