# Thermal resistance to ambient

Thermal resistance to ambient of a single cable or duct depends on laying.

For touching cables or ducts, different formulae are being used.

• Metallic sheathed cables are taken to be cables where it can be assumed that there is a metallic layer that provides an isotherm at, or immediately under, the outer sheath of the cable or for metallic ducts
• Cables of the same system are assumed to be touching, when they are located at a distance smaller than 10H of their diameter. In the same way, two ducts are assumed to be touching, when they are closer than 5% of their diameter. Touching of cables from different systems is not adressed
• When the cables or ducts are embedded in concrete (backfill), the thermal resistivity of soil $\rho_4$ is replaced with the thermal resistivity of the bank material $\rho_b$ in the equations below.
• The formulas for buried cables, touching, flat formation, are valid for u >= 5 and in trefoil formation for u >= 4.
• For three buried single-core cables in touching trefoil formation, metallic sheathed or part-metallic covered, the thermal resistance of the serving over the sheath or armour, $T_3$, shall be multiplied by a factor of 1.6.
• For part-metallic covered cables (where helically laid armour or screen wires cover from 20 to 50% of the cable circumference), the thermal resistance of the insulation $T_1$, shall be multiplied by the factor 1.07 for cables up to 35 kV and by 1.16 for cables from 35 kV to 150 kV.

For cables in a channel acc. Heinhold, the thermal resistance to ambient is the total convection and radiation thermal resistance between cable and channel (Heinhold equation 18.103).

Symbol
$T_{4iii}$
Unit
K.m/W
Formulae
 $\frac{\rho_4}{2\pi} \ln\left(F_{mh} \left(u+\sqrt{u^2-1}\right)\right)$ 1 buried cable/duct non-touching, or with drying-out, or with cyclic loading $\frac{\rho_4}{\pi} \left(\ln\left(u+\sqrt{u^2-1}\right)-0.451\right)$ 2 buried cables/ducts, flat touching, metallic sheathed $\frac{\rho_4}{\pi} \left(\ln\left(u+\sqrt{u^2-1}\right)-0.295\right)$ 2 buried cables/ducts, flat touching, non-metallic sheathed $\rho_4 \left(0.475\ln\left(u+\sqrt{u^2-1}\right)-0.346\right)$ 3 buried cables/ducts, flat touching, metallic sheathed $\rho_4 \left(0.475\ln\left(u+\sqrt{u^2-1}\right)-0.142\right)$ 3 buried cables/ducts, flat touching, non-metallic sheathed $3\frac{\rho_4}{2\pi} \left(\ln\left(u+\sqrt{u^2-1}\right)-0.63\right)$ 3 buried cables/ducts, trefoil touching, (part-)metallic sheathed $\frac{\rho_4}{2\pi} \left(\ln\left(u+\sqrt{u^2-1}\right)+2\ln\left(u\right)\right)$ 3 buried cables/ducts, trefoil touching, non-metallic sheathed $\frac{1}{\pi D_o h_{bs} {\Delta \theta_s}^{\frac{1}{4}}}$ cylinders in air/trough $\frac{h_{T4}}{\pi D_o h_{bs} {\Delta \theta_s}^{\frac{1}{4}}}$ multiple groups of cylinders in air/trough $\frac{1}{\frac{1}{R_{CG,L}}+\frac{1}{R_{CG,R}}}$ cables in multi-layer backfill $\frac{1}{\frac{1}{T_{sa}+T_{at}}+T_{st}}$ Cables in channel (Heinhold) $\frac{\theta_e-\theta_a}{W_{conv,sa}+W_{rad,sa}-W_{sun}}$ PAC/GIL in air $\frac{1}{\pi D_{ext} U_{OHTC}}$ subsea $\frac{\theta_{de}-\theta_{air}}{W_{conv,da}+W_{rad,da}-W_{sun}}$ riser in air
Related
$D_{ext}$
$D_o$
$\Delta \theta_s$
$T_{at}$
$T_{sa}$
$T_{st}$
$\theta_a$
$\theta_{air}$
$\theta_{de}$
$\theta_e$
$U_{OHTC}$
$W_{conv,da}$
$W_{conv,sa}$
$W_{rad,da}$
$W_{rad,sa}$
$W_{sun}$
Used in
$\Delta \theta_c$
$\delta \theta_c$
$\Delta \theta_d$
$\Delta \theta_s$
$\Delta \theta_{sun}$
$I_c$
$T_{4ss}$
$T_C$
$\theta_e$
$\theta_{hs}$
$W_{hs}$