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).

Symbol
$T_{4iii}$
Unit
K.m/W
Formulae
$\frac{\rho_{4} \ln{\left(F_{eq} \left(u + \sqrt{u^{2} - 1}\right) \right)}}{2 \pi}$1 buried cable/duct, non-touching or with partial drying-out of the soil
$\frac{\rho_{4} \left(\ln{\left(2 u \right)} - 0.451\right)}{\pi}$2 buried cables/ducts, flat touching, metallic sheathed
$\frac{\rho_{4} \left(\ln{\left(2 u \right)} - 0.295\right)}{\pi}$2 buried cables/ducts, flat touching, non-metallic sheathed
$\rho_{4} \left(0.475 \ln{\left(2 u \right)} - 0.346\right)$3 buried cables/ducts, flat touching, metallic sheathed
$\rho_{4} \left(0.475 \ln{\left(2 u \right)} - 0.142\right)$3 buried cables/ducts, flat touching, non-metallic sheathed
$\frac{3 \rho_{4} \left(\ln{\left(2 u \right)} - 0.63\right)}{2 \pi}$3 buried cables/ducts, trefoil touching, (part-)metallic sheathed
$\frac{\rho_{4} \left(2 \ln{\left(u \right)} + \ln{\left(2 u \right)}\right)}{2 \pi}$3 buried cables/ducts, trefoil touching, non-metallic sheathed
$\frac{h_{T4}}{D_{o} \Delta \theta_{s}^{0.25} h_{bs} \pi}$cables/ducts in air
$\frac{1}{D_{o} \Delta \theta_{s}^{0.25} h_{bs} \pi}$cables in trough
$\frac{2}{\frac{1}{R_{CG shorter}} + \frac{1}{R_{CG longer}}}$cables in multi-layer backfill
$\frac{1}{T_{st} + \frac{1}{T_{at} + T_{sa}}}$cables in channels acc. Heinhold
$\frac{- \theta_{a} + \theta_{e}}{W_{conv_{sa}} + W_{rad_{sa}} - W_{sun}}$GIL in air
$\frac{1}{D_{ext} U_{OHTC} \pi}$subsea
Related
$D_{ext}$
$D_{o}$
$\rho_{4}$
$\theta_{a}$
Ambient temperature [$^{\circ}$C]
$\theta_{e}$
$U_{OHTC}$
Used in
$\Delta \theta_{c}$
$\Delta \theta_{sun}$
$\theta_{hs}$