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Thermal resistance to ambient of a single cable or duct depends on laying.
For touching cables or ducts, different formulae are being used:
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).
Note: $ln(g_{u})=ln(u+\sqrt{u^2-1})=\cosh^{-1}u$
| $\frac{\rho_{4}}{2\pi} \ln\left(g_{u}\right)$ | buried cables/ducts non-touching (or drying-out of soil cyclic load variation finite element method multi-layer backfill) |
| $\frac{\rho_{4}}{\pi} \left(\ln\left(g_{u}\right)-0.451\right)$ | 2 buried cables/ducts, flat touching, metallic sheathed |
| $\frac{\rho_{4}}{\pi} \left(\ln\left(g_{u}\right)-0.295\right)$ | 2 buried cables/ducts, flat touching, non-metallic sheathed |
| $\rho_{4} \left(0.475\ln\left(g_{u}\right)-0.346\right)$ | 3 buried cables/ducts, flat touching, metallic sheathed |
| $\rho_{4} \left(0.475\ln\left(g_{u}\right)-0.142\right)$ | 3 buried cables/ducts, flat touching, non-metallic sheathed |
| $3\frac{\rho_{4}}{2\pi} \left(\ln\left(g_{u}\right)-0.63\right)$ | 3 buried cables/ducts, trefoil touching, (part-)metallic sheathed |
| $\frac{\rho_{4}}{2\pi} \left(\ln\left(g_{u}\right)+2\ln\left(u\right)\right)$ | 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 |
| $\frac{1}{\frac{1}{T_{sa}+T_{at}}+\frac{1}{T_{st}}}$ | 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 |
| $\frac{\theta_{de}-\theta_{air}}{W_{conv,ext}+W_{rad,ext}-W_{sun}}$ | riser in air |
| $\frac{1}{\pi D_{do} \left(h_{conv,ext}+h_{rad,ext}\right)}$ | riser in air IEC 60287 |
| $\frac{\rho_{4}}{2\pi} \left(\ln\left(g_{u}\right)+\ln\left(F_{mh}\right)\right)$ | buried cables/ducts non-touching (apply Fₘₕ) |