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: $ln(g_{u})=ln(u+\sqrt{u^2-1})=\cosh^{-1}u$
| $\frac{\rho_4}{2\pi} \left(\ln\left(g_u\right)+\ln\left(F_{mh}\right)\right)$ | 1 buried cable/duct non-touching, or with drying-out, or with cyclic loading |
| $\frac{\rho_4}{\pi} \left(\ln\left(g_u\right)-0.451\right)$ | 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 |
