Investigation of the Heating Regimes of a Steel Strip by a Quasi-Steady Electromagnetic Field

A two-dimensional physical and mathematical model is proposed for studying the laws of induction heating of a steel strip by a quasi-steady electromagnetic field. A two-dimensional non-stationary problem of electrodynamics is formulated for an electrically conductive strip of rectangular section under the action of a homoheneous non-stationary electromagnetic field. The component of the magnetic field strength vector tangential to the front surfaces of the strip was chosen as the determining function. The boundary conditions for matching the values of the determining function at the corner points of the rectangle of the cross-section of the strip, that is, the boundary conditions on its edges, are recorded. To construct the solution of the formulated problem, double finite integral transformations over the thickness and transverse coordinates of the strip and the Laplace integral transformation over time were used. As a result, the expression of the determining function in the form of a double functional series is obtained. The change in Joule heat at the characteristic points of the cross-section of the steel strip was numerically analyzed depending on the characteristic dimensionless time and the parameter characterizing the penetration depth of induction heating currents relative to the half-thickness of the strip. Two limiting cases of near-surface and continuous heating of the strip by an external quasi-steady electromagnetic field are considered.