Cableizer ®

Temperature duct outer surface

This is the temperature of the outer surface of a duct or a riser/J-tube.

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

Symbol
$\theta_{de}$
Unit
°C
Formulas
$\theta_{di}-T_{4ii} n_{cc} W_{t}+\frac{T_{4ii} n_{cc} W_{duct}}{2}$cables in duct
$\frac{W_{tot} T_{st} T_{sa}+\theta_{t} T_{sa}+\theta_{at} T_{st}}{T_{sa}+T_{st}}$cables,heat sources or PAC/GIL in ventilated tunnel
$\theta_{di}-T_{4ii} n_{cc} W_{t}$cables in trough, in channel
$\theta_{e}$heat sources in trough, in channel
$\theta_{a}+v_{4} \Delta \theta_{p}+\left(1-v_{4}\right) \Delta \theta_{x}+n_{cc} W_{tot} v_{4} T_{4\mu}$PAC/GIL buried in duct
$\theta_{di}-T_{4pii} W_{sum}$air-filled pipe with objects
Related
$\Delta \theta_{0x}$
Temperature rise by crossing heat sources [K]
$\Delta \theta_{p}$
Temperature rise by other buried objects [K]
$\Delta \theta_{x}$
Critical soil temperature rise [K]
$n_{cc}$
Number of conductors combined
$T_{4ii}$
Thermal resistance duct wall [K.m/W]
$T_{4\mu}$
Thermal resistance ambient [K.m/W]
$T_{4pii}$
Thermal resistance pipe wall [K.m/W]
$T_{sa}$
Thermal resistance convection object—air [K.m/W]
$T_{st}$
Thermal resistance radiation object—tunnel [K.m/W]
$\theta_{a}$
Ambient temperature [°C]
$\theta_{at}$
Air temperature with load [°C]
$\theta_{di}$
Temperature duct inner surface [°C]
$\theta_{e}$
External temperature object [°C]
$\theta_{t}$
Temperature wall (inner) [°C]
$v_{4}$
Ratio thermal resistivity dry/moist soil
$W_{duct}$
Duct losses [W/m]
$W_{sum}$
Sum of total losses of all systems [W/m]
$W_{t}$
Total losses (phase) [W/m]
$W_{tot}$
Total losses (object) [W/m]
Used in
$\alpha_{st}$
Heat transfer coefficient radiation [W/(K.m$^2$)]
$\Delta \theta_{s}$
Temperature difference surface—ambient [K]
$\mathrm{Gr}_{ext}$
Grashof number riser—air
$h_{rad,ext}$
Heat transfer coefficient radiation riser—air [W/(K.m$^2$)]
$I_{c}$
Conductor current [A]
$k_{t}$
Temperature rise ratio [p.u.]
$\mathrm{Ra}_{ext}$
Rayleigh number riser—air
$T_{4iii}$
Thermal resistance ambient [K.m/W]
$T_{sa}$
Thermal resistance convection object—air [K.m/W]
$T_{st}$
Thermal resistance radiation object—tunnel [K.m/W]
$\theta_{c}$
Temperature conductor [°C]
$\theta_{di}$
Temperature duct inner surface [°C]
$\theta_{film}$
Film temperature [°C]
$\theta_{gas}$
Gas temperature [°C]
$\theta_{tm}$
Mean temperature between surface and air in tunnel or trough [°C]
$W_{conv,ext}$
Convective heat transfer riser—air [W/m]
$W_{rad,ext}$
Radiation heat transfer riser—air [W/m]