Thermal resistance of medium in the duct

Thermal resistance between cable and duct.

The equation for ducts with bentonite filling is based on the conduction shape factor of a cylinder surrounded by an eccentric cylinder of larger radius, refer to Table 5.4 in the book 'A Heat Transfer Textbook' by John H. Lienhard IV and V (Phlogiston Press 2008) or to table 3.5 in the book 'Heat Transfer - A Practical Approach' by Yunus A. Cengel (2014). It is assumed that the cables are in the duct so that it comes to contact.

$\frac{U_d}{1+0.1\left(V_d+Y_d \theta_{dm}\right) D_{eq}}$Default
$\frac{\rho_{d,fill}}{2\pi} \cosh^{-1}\left(\frac{{Di_d}^2+{D_{eq}}^2-\left(\frac{Di_d}{2}-\frac{D_{eq}}{2}\right)^2}{2Di_d D_{eq}}\right)$Bentonite filling, steady-state
$\frac{\theta_e-\theta_{di}}{W_{conv,og}-W_{conv,gd}+W_{rad,od}}$Cables in riser
$\frac{\theta_e-\theta_{di}}{W_{conv,od}+W_{rad,od}}$Cables in riser acc. Chippendale
Heat Transfer - A Practical Approach by Yunus A. Cengel (2014) Table 3-5