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.

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: $ln(g_{u})=ln(u+\sqrt{u^2-1})=\cosh^{-1}u$

Symbol
$T_{4iii}$
Unit
K.m/W
Formulae
$\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
$\frac{1}{\frac{1}{T_{sa}+T_{at}}+T_{st}}$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
$\frac{\theta_{de}-\theta_{air}}{W_{conv,da}+W_{rad,da}-W_{sun}}$riser in air
$T_{4pi}+T_{4pii}+T_{4piii}$Air-filled pipe