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

Abstract

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.

Modeling of the Temperature Regimes in a Layered Bimetallic Plate under Short-Term Induction Heating

“…The mathematical model of electrically conductive bodies induction heating under the conditions of the non-stationary electromagnetic field, introduced in this paper, is a generalization of the previous mathematical model studied in [10] for a homogeneous plate. Such generalization aims at the development of analytical and numerical approaches similar to those in [10] for the case of a two-layer metallic plate. The model takes into account the conditions of ideal electromagnetic and thermal contacts on the surface of the plate layers connection.…”

“…To find integral characteristics Φ s (t) of the searched functions Φ (n) (z, t), the original Equations ( 2) and ( 6) should be integrated according to the Formula (11) considering the expressions (10). As a result, the original data of the initial boundary value problem on key functions Φ (n) (z, t) have been reduced to the corresponding Cauchy problems on their integral characteristics Φ s (t).…”

“…2j are determined as a result of using expression (10) in accordance with Formula (11) and boundary conditions (1), ( 3), ( 7) and (8). Their values depend on the characteristics of the materials of the constituent layers of the plate.…”

“…In recent years, mathematical models of induction heating processes under the effect of a non-stationary electromagnetic field (NSEMF) have also been studied. Musii et al [10] proposed a mathematical model for determining the temperature field of a conductive plate element, which is affected by a uniform non-stationary electromagnetic field. The initial boundary value problems for determining the parameters of NSEMF and temperature are formulated.…”

Study on the Uniformity of Temperature Distribution of Transverse Flux Induction Heating Based on a New Magnetic Pole

“…In Ref. [13], Joule heat and temperature in conductive plate elements subjected to short-term induction heating by a nonstationary electromagnetic field are investigated. The research process of TFIH technology involves using existing or improved optimization algorithms (such as genetic algorithm, velocity-controlled particle swarm optimization algorithm, etc.)…”