Electrothermal behavior of a finite cylindrical conductor

Electric current can be used to assist the forming of metallic materials and actuate/excite electromechanical structures. In the heart of current-assisted forming and actuation/excitation is the electrothermal interaction from electric-Joule heating. In this work, we analyze the electrothermal problem of a finite cylindrical conductor with the passing of an alternating current under a weak skin effect at steady state. Closed-form solution is derived for the spatiotemporal evolution of the temperature in the finite cylindrical conductor, which consists of time-independent temperature and time-dependent temperature. Both the time-independent temperature and time-dependent temperature are proportional to the power input to the cylindrical conductor and decrease slightly with increasing the distance to the axisymmetric axis of the cylindrical conductor. The time-independent temperature reaches maximum at the center of the finite cylindrical conductor. The time-dependent temperature exhibits cyclic change with time, which depends on the angular frequency of alternating current and geometrical dimensions of the finite cylindrical conductor. The largest cyclic variation of the time-dependent temperature appears near the ends of the finite cylindrical conductor. The analytical solutions derived in this work can be used to analyze the temperature evolution in a finite cylindrical conductor under the action of a periodic current in different forms, such as a square or triangular form.