Study of temperature regimes of a steel rod under the action of an unsteady electromagnetic field
DOI:
https://doi.org/10.15407/fmmit2025.41.082Keywords:
steel rod, unsteady electromagnetic field, axial component of the magnetic field strength vector, Joule heat, temperature.Abstract
A physical and mathematical model is proposed for determining the temperature field in a steel rod under the action of an unsteady electromagnetic field. This model is described by sequentially coupled Maxwell equations and Fourier equations of thermal conductivity. It consists of two stages: determining the axial component of the magnetic field strength vector and temperature. The initial relations of the initial-boundary problems of electrodynamics and thermal conductivity for the rod under consideration are recorded. To construct their solutions, a cubic approximation of the distribution of determining functions along the radial coordinate is used. As a result, the initial-boundary problems for determining functions are reduced to Cauchy problems with time variation for the integral characteristics of determining functions along the radial variable. General solutions of Cauchy problems are recorded using the Laplace integral transform. The coefficients of the approximation polynomials are given in the form of a linear combination of integral characteristics and determining functions on the rod surface. The expressions for Joule heat and temperature in the rod under consideration under the action of an unsteady electromagnetic field are obtained. A numerical analysis is performed to investigate the change in temperature over time and its distribution across the radius of the rod, depending on the duration of the unsteady electromagnetic field and the magnitude of the magnetic field strength.
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