Prediction of temperature profiles and ampacity for a monometallic conductor considering the skin effect and temperature-dependent resistivity

In the present work, we have developed a theoretical model to examine the combined effects of heat conduction produced by Joule's effect and an alternating current signal that flows in a circular electric conductor, taking into account variations of electric resistivity with temperature. The above hypothesis leads to a coupled thermo-electric formulation. Under this approach and considering an electric current composed by high frequencies, we have considered the presence of the skin effect that yields important radial differences of temperature controlled by the heat conduction equation for the conductor. On the other hand, a wave equation is required to analyze the electromagnetic propagation of the current. It is well-known that high-voltage transmission lines are constructed with conductive materials that are composed by strands, for this reason, trapped-air between these strands complicates the analysis of the electromagnetic conduction phenomena. To circumvent this problem, the air-aluminum system is represented by a porous medium with effective properties used in the mathematical model for the heat conduction equation. Finally, the imposed thermal boundary conditions reveal that the environmental conditions are a fundamental factor to control the above effects.