Investigation of Processes of Heating a Non-Ferromagnetic Rod under the Action of an Unsteady Electromagnetic Field

A physical and mathematical model is formulated for determining the axial component of the magnetic field intensity vector and specific Joule heat density in a non-ferromagnetic conductive rod under the conditions of its induction heating through an unsteady electromagnetic field. The initial relations for the initial-boundary value problem of electrodynamics were written for the considered rod. We chose the axial component of the magnetic field intensity vector as a determining function. To obtain the solution, the cubic approximation along the radial coordinate of distribution of the determining function along the radius of the rod was used. In consequence of this, the original initial-boundary value problem is reduced to Cauchy problem in time for the integral characteristics of the determining function in the radial variable. Applying the integral Laplace transform, the expression for the integral characteristics and the axial component of the magnetic field intensity vector is written down. Expressions of Joule heat and the determining function in the considered rod under the action of an unsteady electromagnetic field were obtained. A numerical analysis of change in time and distribution along radius of the rod of the axial component of the magnetic field intensity vector and Joule heat was performed depending on frequency of the carrier electromagnetic oscillations and duration of the unstable electromagnetic field.