Determination and Analysis of the Thermal and Temperature Regimes of a Hollow Aluminum Cylinder During Induction Treatment

Source abstract

A physical-mathematical model is proposed for studying Joule heat and temperature in an electrically conductive, non-ferromagnetic hollow cylinder under induction treatment. The model comprises two stages. The first stage involves formulating an electrodynamic problem for the long hollow cylinder to determine the induced electromagnetic field and the Joule heat density. The second stage addresses the resulting heat conduction problem, from which the temperature distribution caused by Joule heating is obtained. The solutions to both the electrodynamic and heat conduction problems are constructed using a cubic approximation of the axial component of the magnetic field intensity vector and the temperature with respect to the radial coordinate. The coefficients of these approximating polynomials are expressed as linear combinations of the radial integral characteristics of the governing functions together with their values at the inner and outer surfaces of the cylinder. This approach reduces the original boundary-value problems to systems of equations for the integral characteristics, for which general solutions under transient electromagnetic excitation are derived. Explicit expressions are then presented for the axial component of the magnetic field intensity, the Joule heat, and the temperature arising from the transient electromagnetic action. A numerical analysis of these quantities is carried out for a long hollow aluminum cylinder, examining their dependence on the amplitude-frequency characteristics of the applied field and on the duration of its action.