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Radiation shape factor for touching cables

Symbol
$\zeta_{er}$
Formulae
$\left(2-\frac{2\pi-4}{4\pi}\right) \epsilon_e$two cables touching
$\frac{3}{1-\frac{6\pi A_e \epsilon_e \eta_{di}}{\epsilon_{di} A_{di}}}$three cables touching trefoil acc. to Anders 1997
$\frac{3}{1-6\pi \eta_e}$three cables touching trefoil acc. to Anders 1995
$\frac{N_c D_o}{D_{di}} \frac{1}{1-\frac{\pi N_c D_o}{D_{di}} \frac{\epsilon_e}{\epsilon_{di}} \left(N_c-1\right) \left(1-\epsilon_{di}\right)}$n cables touching acc. to Weely 1988
Related
$A_{di}$
Surface of duct inner wall [m$^2$]
$A_e$
Surface of object [m$^2$]
$D_{di}$
Inner diameter of duct [m]
$D_o$
Outer diameter [m]
$\epsilon_{di}$
Emissivity of duct inner surface
$\epsilon_e$
Emissivity of cable surface
$\eta_{di}$
Reflectivity of (opaque) duct inner surface
$\eta_e$
Reflectivity of (opaque) cable surface
$N_c$
Number of sources in system
$\pi$
Archimedes' constant $\pi$
Used in
$K_r$
Radiation shape factor