Cableizer ®

Temperature difference surface—ambient

It is the difference between the surface temperature of a cable or duct in air and the ambient temperature. This equation is solved by iteration with an initial value for $\Delta\theta_s$ of 16°C.

Symbol
$\Delta \theta_{s}$
Unit
K
Formulas
$\frac{\Delta \theta_{s}+T_{4iii} n_{cc} W_{t}+\Delta \theta_{sun}}{2}$cables in air
$\frac{\Delta \theta_{c}+\Delta \theta_{d}}{1+K_{A} {\Delta \theta_{s}}^{0.25}}$cables in air-filled trough, in air-filled pipe with objects
$\theta_{at}-\theta_{de}$cables in channel (Heinhold)
$\theta_{de}-\theta_{air}$cables in riser/J-tube
$\theta_{e}-\theta_{at}$heat source in air-filled trough, in air-filled pipe with objects
$\theta_{e}-\frac{T_{sa} \left(T_{sa}+T_{at}\right)}{T_{sa}+T_{at}+T_{st}} W_{hs}$heat source in channel
$\frac{\Delta \theta_{s}+T_{4iii} W_{tot}+\Delta \theta_{sun}}{2}$PAC/GIL in air
$\frac{\Delta \theta_{c}}{1+K_{A} {\Delta \theta_{s}}^{0.25}}$PAC/GIL in air-filled trough
$\theta_{de}-\frac{T_{sa} \left(T_{sa}+T_{at}\right)}{T_{sa}+T_{at}+T_{st}} n_{cc} W_{tot}$PAC/GIL in channel (Heinhold)
Related
$\Delta \theta_{c}$
Temperature rise conductor [K]
$\Delta \theta_{d}$
Temperature rise dielectric losses [K]
$\Delta \theta_{sun}$
Temperature difference solar radiation [K]
$K_{A}$
Coefficient K in air
$n_{cc}$
Number of conductors combined
$T_{4iii}$
Thermal resistance ambient [K.m/W]
$T_{at}$
Thermal resistance convection air—tunnel [K.m/W]
$T_{sa}$
Thermal resistance convection object—air [K.m/W]
$T_{st}$
Thermal resistance radiation object—tunnel [K.m/W]
$\theta_{air}$
Ambient air temperature [°C]
$\theta_{at}$
Air temperature with load [°C]
$\theta_{de}$
Temperature duct outer surface [°C]
$\theta_{e}$
External temperature object [°C]
$W_{hs}$
Heat dissipation heat source [W/m]
$W_{t}$
Total losses (phase) [W/m]
$W_{tot}$
Total losses (object) [W/m]
Used in
$\alpha_{sa}$
Heat transfer coefficient convection [W/(K.m$^2$)]
$\alpha_{st}$
Heat transfer coefficient radiation [W/(K.m$^2$)]
$T_{4iii}$
Thermal resistance ambient [K.m/W]
$\theta_{e}$
External temperature object [°C]
$W_{de}$
Losses outside of riser [W/m]