# 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.

Symbol
$T_{4i}$
Unit
K.m/W
Formulae
 $\frac{U_d}{1+0.1\left(V_d+Y_d \theta_{dm}\right) D_{eq}}$ 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
Related
$D_{eq}$
$Di_d$
$\rho_{d,fill}$
$\theta_{di}$
$\theta_{dm}$
$\theta_e$
$U_d$
$V_d$
$W_{conv,gd}$
$W_{conv,od}$
$W_{conv,og}$
$W_{rad,od}$
$Y_d$
Used in
$\Delta \theta_c$
$\Delta \theta_d$
$I_c$
$Q_{B,ab}$
$Q_{B,d}$
$Q_{B,f}$
$Q_{B,j}$
$T_{4ss}$
$T_B$
$T_{eq}$
$\theta_{di}$
$\theta_e$
$U_{wall}$
OHTC of pipe wall [W/(K.m$^2$)]
Image
Heat Transfer - A Practical Approach by Yunus A. Cengel (2014) Table 3-5