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.
- No formula for 4 cables exist which occurs when you have a two-phase system with phase-splitting. In that case, the arrangement is normally flat horizontal or vertical and the distance between the two groups (half-systems) can be set as well as the distance between the phases of the same group. For two separate groups with touching cables, the same formulas as for two cables flat are used plus 10%. If the two groups touch, we have a square arrangement and the same formulas as for trefoil cables are used plus 20% to consider for the additional mutual heating. For non-touching cables, the general case with $F_{eq}$ is used.

$T_{\mathrm{4iii}}$

K.m/W

$\frac{\rho_{\mathrm{4}}}{2 \pi} \ln{\left (F_{\mathrm{eq}} \left(u + \sqrt{u^{2} - 1}\right) \right )}$ | 1 buried cable/duct, non-touching or with partial drying-out of the soil |

$\frac{\rho_{\mathrm{4}}}{\pi} \left(\ln{\left (2 u \right )} - 0.451\right)$ | 2 buried cables/ducts, flat touching, metallic sheathed |

$\frac{\rho_{\mathrm{4}}}{\pi} \left(\ln{\left (2 u \right )} - 0.295\right)$ | 2 buried cables/ducts, flat touching, non-metallic sheathed |

$\rho_{\mathrm{4}} \left(0.475 \ln{\left (2 u \right )} - 0.346\right)$ | 3 buried cables/ducts, flat touching, metallic sheathed |

$\rho_{\mathrm{4}} \left(0.475 \ln{\left (2 u \right )} - 0.142\right)$ | 3 buried cables/ducts, flat touching, non-metallic sheathed |

$\frac{3 \rho_{\mathrm{4}}}{2 \pi} \left(\ln{\left (2 u \right )} - 0.63\right)$ | 3 buried cables/ducts, trefoil touching, (part-)metallic sheathed |

$\frac{\rho_{\mathrm{4}}}{2 \pi} \left(2 \ln{\left (u \right )} + \ln{\left (2 u \right )}\right)$ | 3 buried cables/ducts, trefoil touching, non-metallic sheathed |

$\frac{h_{\mathrm{T4}}}{D_{\mathrm{o}} \Delta \theta_{\mathrm{s}}^{0.25} h_{\mathrm{bs}} \pi}$ | cables/ducts in air |

$1.1 T_{\mathrm{4iii}}$ | 2 buried cables/ducts with phase splitting, 2 separate groups |

$1.2 T_{\mathrm{4iii}}$ | 2 buried cables/ducts with phase splitting, square arrangement |

$\frac{1}{D_{\mathrm{o}} \Delta \theta_{\mathrm{s}}^{0.25} h_{\mathrm{bs}} \pi}$ | cables in trough |

$N_{\mathrm{c}} T_{\mathrm{tr}} + T_{\mathrm{4iii}}$ | cables in trough (Anders et al 2010) |

$\Delta \theta_{\mathrm{s}}$

$F_{\mathrm{eq}}$

$h_{\mathrm{bs}}$

Heat dissipation coefficient for black surfaces in free air [W/m²/K^{5/4}]

$h_{\mathrm{T4}}$

$N_{\mathrm{c}}$

$\pi$

$\rho_{\mathrm{4}}$

Thermal resistivity of soil [K.m/W]

$\rho_{\mathrm{b}}$

Thermal resistivity backfill [K.m/W]

$T_{\mathrm{tr}}$

$u$

$\Delta \theta_{\mathrm{c}}$

$\Delta \theta_{\mathrm{d}}$

$\Delta \theta_{\mathrm{d_{\mathrm{t}}}}$

$\Delta \theta_{\mathrm{s}}$

$\Delta \theta_{\mathrm{sun}}$

$I_{\mathrm{c}}$

$k_{\mathrm{l}}$

$T_{\mathrm{4ss}}$

Steady-state thermal resistance [K.m/W]

$T_{\mathrm{C}}$

$\theta_{\mathrm{hs}}$

$W_{\mathrm{hs}}$