# 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 10% 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
 $\frac{\rho_{4} \ln{\left(F_{eq} \left(u + \sqrt{u^{2} - 1}\right) \right)}}{2 \pi}$ 1 buried cable/duct, non-touching or with partial drying-out of the soil $\frac{\rho_{4} \left(\ln{\left(2 u \right)} - 0.451\right)}{\pi}$ 2 buried cables/ducts, flat touching, metallic sheathed $\frac{\rho_{4} \left(\ln{\left(2 u \right)} - 0.295\right)}{\pi}$ 2 buried cables/ducts, flat touching, non-metallic sheathed $\rho_{4} \left(0.475 \ln{\left(2 u \right)} - 0.346\right)$ 3 buried cables/ducts, flat touching, metallic sheathed $\rho_{4} \left(0.475 \ln{\left(2 u \right)} - 0.142\right)$ 3 buried cables/ducts, flat touching, non-metallic sheathed $\frac{3 \rho_{4} \left(\ln{\left(2 u \right)} - 0.63\right)}{2 \pi}$ 3 buried cables/ducts, trefoil touching, (part-)metallic sheathed $\frac{\rho_{4} \left(2 \ln{\left(u \right)} + \ln{\left(2 u \right)}\right)}{2 \pi}$ 3 buried cables/ducts, trefoil touching, non-metallic sheathed $\frac{h_{T4}}{D_{o} \Delta \theta_{s}^{0.25} h_{bs} \pi}$ cables/ducts in air $\frac{1}{D_{o} \Delta \theta_{s}^{0.25} h_{bs} \pi}$ cables in trough $\frac{2}{\frac{1}{R_{CG shorter}} + \frac{1}{R_{CG longer}}}$ cables in multi-layer backfill $\frac{1}{T_{st} + \frac{1}{T_{at} + T_{sa}}}$ cables in channels acc. Heinhold $\frac{- \theta_{a} + \theta_{e}}{W_{conv_{sa}} + W_{rad_{sa}} - W_{sun}}$ GIL in air $\frac{1}{D_{ext} U_{OHTC} \pi}$ subsea
Related
$D_{ext}$
$D_{o}$
$\Delta \theta_{s}$
$\rho_{4}$
$T_{at}$
$T_{sa}$
$T_{st}$
$\theta_{a}$
Ambient temperature [$^{\circ}$C]
$\theta_{e}$
$U_{OHTC}$
$W_{conv_{sa}}$
$W_{rad_{sa}}$
$W_{sun}$
Used in
$\Delta \theta_{c}$
$\delta \theta_{c}$
$\Delta \theta_{d}$
$\Delta \theta_{s}$
$\Delta \theta_{sun}$
$I_{c}$
$T_{4ss}$
$T_{C}$
$\theta_{hs}$
$W_{hs}$