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Temperature rise by crossing heat sources at z

Temperature rise by crossing heat sources, at the point z along the cable.

Symbol
$\Delta \theta_{uh}$
Unit
K
Formulae
$\frac{\rho W_h}{4\pi} \ln\left(\frac{\left(L_r+L_h\right)^2+\left(\nu \Delta z\right)^2 \mathrm{sin}^{2}\beta}{\left(L_r-L_h\right)^2+\left(\nu \Delta z\right)^2 \mathrm{sin}^{2}\beta}\right)$single source crossing
$\frac{\rho W_h}{4\pi} \ln\left(\frac{\left(L_r+L_h\right)^2+\left(|z_r-z_h|+\nu \Delta z \mathrm{sin}\beta\right)^2}{\left(L_r-L_h\right)^2+\left(|z_r-z_h|+\nu \Delta z \mathrm{sin}^{2}\beta\right)^2}\right)$several crossings
Related
$\Delta z$
Length of the interval [m]
$L_h$
Depth of laying of crossing element [mm]
$L_r$
Depth of laying of the rated object [mm]
$\nu$
Summation step 1 - $N_X$
$\pi$
Archimedes' constant $\pi$
$W_h$
Heat generated by external object [W/m]
$z_h$
Location of the heat source [m]
$z_r$
Location of the hottest point [m]