Point source correction

The IEC method to calculate the temperature at any point in the soil uses the exact analytical solution for a line source in an infinte environment in conjunction with Kennelly's hypthesis to account for the fact that a cable environment is semi-infinite in nature.

However, in reality the entire cable core acts as the heat source which deforms the isotherms around the cable, especially with proximity to the earth surface. And since the conductor is made of high thermal conductivity material, the entire circular region with radius $r_c$ is isothermal.

To consider this physical reality, the point source must be relocated by the point source correction distance $L_{psc}$ to a position closer to the earth surface. This yields to a tiny improvement in the ‰ range.

$- L_{cm} + \sqrt{- D_{o}^{2} + L_{cm}^{2}}$