Theory of cable heating - emorell96/CableHeatingPy GitHub Wiki

This code uses a steady state method, meaning it assumes the system has reached thermal equilibrium and uses this assumption to calculate the final temperature by balancing the heat gain and the heat losses of the system.

For this we say that the power per unit length generated by the system of {Conductor Core + Insulation} is equal to that of $P_j=I^2R$ where Pj is the power per unit length generated through Joule heating, I is the current being pushed through the cable, and R is its resistance by unit length. Then, we look at how the system loses heat: radiation and convection losses.

Using Stephan Boltzmann law, we can write $P_r=\sigma\epsilon\pi D(T_c^4-T_a^4)$ which describe the radiation losses. $\sigma$ is the Stephan Boltzmann constant, $\epsilon$ is the emissivity of the material used in the insulation, $D$ is the outer diameter of the cable plus insulator, $T_c$ and $T_a$ are the conductor temperature and the ambient temperature respectively (in Kelvin). All units are SI.

Next the convection losses of the system are written as follow: $P_c=h\pi D(T_c-T_a)$ with $h=\lambda Nu K_{wd} /D$ , $Nu=0.64 Re^{0.2} 0.2Re^{0.61}$ , and Re is the Reynolds number which is dimensionless and can be calculated as $Re=Dv_w/\nu_f$ , with $v_w, \nu_f$ being the wind speed and the viscosity of the air.