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Thermal resistance by convection, surface to air

Convection thermal resistance between surface of cable and air inside the tunnel and in free air.

Symbol
$T_{sa}$
Unit
K.m/W
Formulae
$\frac{1}{\pi k_{air} K_{cv} {\mathrm{Re}_{air}}^{0.65}}$in tunnel (turbulent flow), $Re_{air}$ > 2000
$\frac{1}{\left(\pi D_o h_{bs}-\frac{1}{{30}^{0.25}T_{st}}\right) {|\theta_{de}-\theta_{at}|}^{0.25}}$in tunnel (laminar flow), $Re_{air}$ ≤ 2000
$\frac{1}{\left(\pi D_o h_{bs}-\frac{1}{{30}^{0.25}T_{st}}\right) {|\theta_{o,L}-\theta_{at,L}|}^{0.25}}$in tunnel (laminar flow), $Re_{air}$ ≤ 2000, IEC 60287-2-3
$\frac{1}{\pi D_o k_{sa} \alpha_{sa} {f_{atm}}^{0.5}}$in channel (Heinhold)
Related
$\alpha_{sa}$
Heat transfer coefficient for convection [W/(K.m$^2$)]
$D_o$
Outer diameter [m]
$f_{atm}$
Relation atmospheric pressure to standard atmosphere
$h_{bs}$
Heat dissipation coefficient for black surfaces in free air [W/m$^2$/K$^{5/4}$]
$k_{air}$
Thermal conductivity of air [W/(m.K)]
$K_{cv}$
Convection factor
$k_{sa}$
Convection factor (Heinhold)
$\pi$
Archimedes' constant $\pi$
$\mathrm{Re}_{air}$
Reynolds number for air
$T_{st}$
Radiation thermal resistance, surface to tunnel [K.m/W]
$\theta_{at}$
Air temperature under load [°C]
$\theta_{at,L}$
Air temperature in tunnel at outlet [°C]
$\theta_{de}$
Temperature of duct outer wall [°C]
$\theta_{o,L}$
Temperature of the surface of object at outlet [°C]
Used in
$\Delta \theta_s$
Temperature difference surface to ambient [K]
$T_{4iii}$
Thermal resistance to ambient [K.m/W]
$T_a$
Star thermal resistance of air [K.m/W]
$T_s$
Star thermal resistance of object [K.m/W]
$T_t$
Star thermal resistance of tunnel [K.m/W]
$\theta_{de}$
Temperature of duct outer wall [°C]
$\theta_{hsj}$
Temperature of outer jacket [°C]
$W_{hs}$
Heat dissipation of heat source [W/m]
Choices
IdMethodInfo
0CableizerThe method developed by Cableizer is applicable to any type of cable or heat source installed in ventilated tunnels and up to six different systems, unequally loaded, can be calculated. The method applies to natural as well as forced ventilation. and the longitudinal heat transfer in the tunnel air is calculated every meter of tunnel length. The method is described in the paper 'Ampacity Calculation of Multiple Independent Cable Systems in Ventilated Tunnels' from 2019.
1IEC 60287-2-3The method acc. IEC 60287-2-3 is applicable to any type of cable installed in ventilated tunnels. The method applies to natural as well as forced ventilation. Longitudinal heat transfer within the cables and the surroundings of the tunnel is assumed to be negligible. All cables are assumed to be identical and equally loaded within the tunnel.
2HeinholdThe method acc. Heinhold is applicable to any type of cable installed in channels near the surface and does not consider ventilation. The method is described in the book 'Kabel und Leitungen für Starkstrom' by L. Heinhold from 1999 (in English only earlier edition available of 'Power Cables and their Applications' from 1990).