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External temperature of the object

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

Symbol
$\theta_e$
Unit
°C
Formulae
$\theta_c-T_1 \left(W_c+\frac{W_d}{2}\right)+n_c T_2 \left(W_c \left(1+\lambda_1\right)+W_d\right)+n_c T_3 \left(W_I+W_d\right)$Cables
$\theta_{hs}-W_{hs} T_{hs}$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
$\theta_a+T_{4iii} W_{tot}$PAC/GIL in channel (Heinhold)
$\sum_{i=0}^{n-1} \theta_{e,i}$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]
$\Delta \theta_s$
Temperature difference surface to ambient [K]
$\Delta \theta_x$
Critical soil temperature rise [K]
$\lambda_1$
Loss factor of shield (screen and sheath)
$n_c$
Number of conductors in object
$n_{cc}$
Number of conductors combined
$T_1$
Thermal resistance between one conductor and sheath [K.m/W]
$T_2$
Thermal resistance of armour bedding [K.m/W]
$T_3$
Thermal resistance of jacket [K.m/W]
$T_{4i}$
Thermal resistance of medium in the duct [K.m/W]
$T_{4iii}$
Thermal resistance to ambient [K.m/W]
$T_{4\mu}$
Thermal resistance to ambient [K.m/W]
$T_{hs}$
Thermal resistance of heat source [K.m/W]
$\theta_a$
Ambient temperature [°C]
$\theta_{at}$
Air temperature under load [°C]
$\theta_c$
Temperature of conductor [°C]
$\theta_{di}$
Temperature of duct inner wall [°C]
$\theta_{hs}$
Temperature of heat source [°C]
$v_4$
Ratio thermal resistivity dry/moist soil
$W_c$
Conductor losses [W/m]
$W_d$
Dielectric losses [W/m]
$W_{hs}$
Heat dissipation of heat source [W/m]
$W_I$
Ohmic losses per phase [W/m]
$W_{tot}$
Total losses per object [W/m]
Used in
$\Delta \theta_{ce}$
Temperature difference, conductor to surface [K]
$\Delta \theta_{gas}$
Temperature difference, conductor to enclosure [°C]
$\Delta \theta_s$
Temperature difference surface to ambient [K]
$\mathrm{Gr}_{gd}$
Grashof number, gas to duct
$\mathrm{Gr}_{od}$
Grashof number, object to duct
$\mathrm{Gr}_{og}$
Grashof number, object to gas
$\mathrm{Gr}_{prot}$
Grashof number, surface to air
$h_{rad,od}$
Radiation heat transfer coefficient, object to duct [W/(K.m$^2$)]
$h_{rad,sa}$
Radiation heat transfer coefficient, surface to air [W/(K.m$^2$)]
$I_c$
Conductor current [A]
$T_{4i}$
Thermal resistance of medium in the duct [K.m/W]
$T_{4iii}$
Thermal resistance to ambient [K.m/W]
$T_{conv,od}$
Thermal resistance by convection, object to duct [K.m/W]
$T_{conv,sa}$
Thermal resistance by convection, surface to air [K.m/W]
$T_{rad,od}$
Radiation thermal resistance, object to duct [K.m/W]
$T_{rad,sa}$
Radiation thermal resistance, surface to air [K.m/W]
$T_{rad,sun}$
Solar radiation thermal resistance [K.m/W]
$\theta_c$
Temperature of conductor [°C]
$\theta_{de}$
Temperature of duct outer wall [°C]
$\theta_{di}$
Temperature of duct inner wall [°C]
$\theta_{dm}$
Mean temperature of the medium in the duct [°C]
$\theta_{encl}$
Temperature of enclosure [°C]
$\theta_{film}$
Film temperature [°C]
$\theta_{gas}$
Gas temperature [°C]
$\theta_{hs}$
Temperature of heat source [°C]
$W_{conv,od}$
Convection heat transfer, object to duct [W/m]
$W_{conv,og}$
Convection heat transfer, object to gas [W/m]
$W_{conv,sa}$
Convection heat transfer, surface to air [W/m]
$W_{hs}$
Heat dissipation of heat source [W/m]
$W_{rad,od}$
Radiation heat transfer, object to duct [W/m]
$W_{rad,sa}$
Radiation heat transfer, surface to air [W/m]