Determination and Analysis of Joule’s Heat and Temperature in an Electrically Conductive Plate Element Subject to Short-Term Induction Heating by a Non-Stationary Electromagnetic Field

We propose a mathematical model that allows us to determine the temperature field of a parallel-sided electrically conductive plate element subject to uniform non-stationary electromagnetic action. We formulate initial-boundary value problems to determine the parameters of the non-stationary electromagnetic field (NEMF) and the temperature. We develop a methodology to solve these initial-boundary value problems using the approximation of determining functions by cubic polynomials over thickness of the plate element. General solutions for the related Cauchy problems at uniform non-stationary electromagnetic action are obtained. Based on these solutions, the temporal variation of Joule’s heat and temperature in the plate element, subject to short-term induction heating by an NEMF in the mode of impulse modulating signal (MIMS), is analyzed. Temperature dependencies on the different values of electromagnetic field stress and on the different time duration were obtained. The choice of the carrier frequency of electromagnetic field oscillations is explained for the frequencies mostly used in industrial devices for inductive heating.