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Radiation thermal resistance, surface to tunnel

Radiation thermal resistance between cable surface and inner wall of the tunnel.

Symbol
$T_{st}$
Unit
K.m/W
Formulae
$\frac{1}{\pi D_o K_r K_t \sigma \left(\left(\theta_{de}+\theta_{abs}\right)^2+\left(\theta_t+\theta_{abs}\right)^2\right) \left(\theta_{de}+\theta_t+2\theta_{abs}\right)}$ventilated tunnel (multi-system)
$\frac{1}{\pi D_o K_r K_t \sigma \left(\left(\theta_{o,L}+\theta_{abs}\right)^2+\left(\theta_{t,L}+\theta_{abs}\right)^2\right) \left(\theta_{o,L}+\theta_{t,L}+2\theta_{abs}\right)}$ventilated tunnel (IEC 60287-2-3)
$\frac{1}{\pi D_o K_r \alpha_{st}}$in channel (Heinhold)
Related
$\alpha_{st}$
Heat transfer coefficient for radiation [W/(K.m$^2$)]
$D_o$
Outer diameter [m]
$K_r$
Radiation shape factor
$K_t$
Effective emissivity of surface
$\pi$
Archimedes' constant $\pi$
$\sigma$
Stefan Boltzmann constant [W/m$^2$K$^4$]
$\theta_{abs}$
Absolute temperature [K]
$\theta_{de}$
Temperature of duct outer wall [°C]
$\theta_{o,L}$
Temperature of the surface of object at outlet [°C]
$\theta_t$
Temperature of inner tunnel wall [°C]
$\theta_{t,L}$
Temperature of tunnel wall 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]
$T_{sa}$
Thermal resistance by convection, surface to air [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]