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Temperature of duct outer wall

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
Formulae
$\theta_{di}-T_{4ii} n_{cc} W_t+\frac{T_{4ii} W_{duct}}{2} n_{cc}$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 of the duct wall [K.m/W]
$T_{4\mu}$
Thermal resistance to ambient [K.m/W]
$T_{4pii}$
Thermal resistance of the pipe wall [K.m/W]
$T_{sa}$
Thermal resistance by convection, surface to air [K.m/W]
$T_{st}$
Radiation thermal resistance, surface to tunnel [K.m/W]
$\theta_a$
Ambient temperature [°C]
$\theta_{at}$
Air temperature under load [°C]
$\theta_{di}$
Temperature of duct inner wall [°C]
$\theta_e$
External temperature of the object [°C]
$\theta_t$
Temperature of inner tunnel wall [°C]
$v_4$
Ratio thermal resistivity dry/moist soil
$W_{duct}$
Losses in duct [W/m]
$W_{sum}$
Sum of total losses of all systems [W/m]
$W_t$
Total losses per phase [W/m]
$W_{tot}$
Total losses per object [W/m]
Used in
$\alpha_{st}$
Heat transfer coefficient for radiation [W/(K.m$^2$)]
$\Delta \theta_s$
Temperature difference surface to ambient [K]
$\mathrm{Gr}_{ext}$
Grashof number, duct in air
$h_{rad,ext}$
Radiation heat transfer coefficient, duct to air [W/(K.m$^2$)]
$I_c$
Conductor current [A]
$k_t$
Temperature rise ratio [p.u.]
$\mathrm{Ra}_{ext}$
Rayleigh number outside riser
$T_{4iii}$
Thermal resistance to ambient [K.m/W]
$T_{sa}$
Thermal resistance by convection, surface to air [K.m/W]
$T_{st}$
Radiation thermal resistance, surface to tunnel [K.m/W]
$\theta_c$
Temperature of conductor [°C]
$\theta_{di}$
Temperature of duct inner wall [°C]
$\theta_{film}$
Film temperature [°C]
$\theta_{gas}$
Gas temperature [°C]
$\theta_{tm}$
Mean temperature between surface and air in tunnel or trough [°C]
$W_{conv,ext}$
Convection heat transfer, duct to air [W/m]
$W_{rad,ext}$
Radiation heat transfer, duct to air [W/m]