Radiation shape factor

Radiation shape factor from object surface to ambient tunnel or free air considering the view factor for one system and for concentric cylindrical annuli (cable to duct) such as in a riser/J-tube.

Symbol
$K_r$
Formulae
$\frac{1-F_m}{1-F_m \left(1-K_t\right)}$in tunnel or free air
$\frac{1}{1+\frac{1-\epsilon_e}{\epsilon_e}+\frac{A_{er} \left(1-\epsilon_{di}\right)}{A_{di} \epsilon_{di}}}$riser/J-tube single cable
$\frac{1}{1+\frac{\eta_e}{\epsilon_e}+\frac{\zeta_{er} A_{er} \eta_{di}}{A_{di} \epsilon_{di}}}$riser/J-tube touching cables