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Temperature rise by crossing heat sources z

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

Symbol
$\Delta \theta_{uh}$
Unit
K
Formulas
$\frac{\rho W_{h}}{4\pi} \ln\left(\frac{\left(L_{r}+L_{h}\right)^2+\left(\nu \Delta z\right)^2 \mathrm{sin}^{2}\beta}{\left(L_{r}-L_{h}\right)^2+\left(\nu \Delta z\right)^2 \mathrm{sin}^{2}\beta}\right)$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]