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

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

Symbol
$T_{\mathrm{4iii}}$
Unit
K.m/W
Formulae
$\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)
Related
$D_{\mathrm{o}}$
$\Delta \theta_{\mathrm{s}}$
$F_{\mathrm{eq}}$
$h_{\mathrm{T4}}$
$N_{\mathrm{c}}$
$\rho_{\mathrm{4}}$
$\rho_{\mathrm{b}}$
$T_{\mathrm{tr}}$
Used in
$\delta \theta_{\mathrm{c}}$
$\Delta \theta_{\mathrm{c}}$
$\Delta \theta_{\mathrm{d}}$
$\Delta \theta_{\mathrm{d_{\mathrm{t}}}}$
$\Delta \theta_{\mathrm{s}}$
$\Delta \theta_{\mathrm{sun}}$
$I_{\mathrm{c}}$
$k_{\mathrm{l}}$
$T_{\mathrm{4ss}}$
$\theta_{\mathrm{hs}}$
$W_{\mathrm{hs}}$