Analysis of the Thermal Mode of an Electrically Conductive Tubular Element with a Thin External Electrically Conductive Coating Under the Action of an Unstable Electromagnetic Field

• Дата: 2022
• Автори: Мусій, Роман, Мельник, Наталія, Свідрак, Інга, Шиндер, Валентин
• Формат: Стаття
• Мова: Ukrainian
• Опубліковано: Кам'янець-Подільський національний університет імені Івана Огієнка 2022
• Онлайн доступ: http://mcm-math.kpnu.edu.ua/article/view/274086
• Назва журналу: Mathematical and computer modelling. Series: Physical and mathematical sciences

An electrically conductive tubular element with a thin external electrically conductive coating under the action of an unsteady electromagnetic field of the radio frequency range is considered. To analyze the thermal regime, the initial-boundary problem of electrodynamics for a two-layer conductive non-ferromagnetic hollow cylinder under the action of an external non-stationary electromagnetic field is formulated. The electromagnetic field is given by the values of the axial component of the magnetic field intensity vector on the inner and outer surfaces of the cylinder. To construct the general solution of the formulated initial-boundary value problem, a quadratic approximation of the key function (the axial component of the magnetic field intensity vector) along the radial coordinate in each constituent layer (base and cover) of the hollow cylinder was used. As a result, the original initial-boundary value problem for the key function is reduced to the Cauchy problem in terms of the time variable for the characteristics of the key function integral over the radial coordinate. The coefficients of the approximation polynomials are presented through the integral characteristics of the key function and its given values on the inner and outer surfaces of the cylinder as a function of time. The solution of the Cauchy problem is obtained using the integral Laplace transform. Expressions of the key function in each component layer of the cylinder are recorded in the form of quadratic polynomials, the coefficients of which are convolutions of functions describing the given limit values of the key function on the inner and outer surfaces of the cylinder and homogeneous solutions of the Cauchy problem on integral characteristics. Expressions of the key function and Joule heat in the base and coating of the considered tubular element under the action of an unsteady electromagnetic field in the mode with a pulsed modulating signal were obtained on the basis of general solutions for homogeneous non-stationary electromagnetic action. A computer analysis of the change in time and thickness of the constituent layers of this tubular element of the axial component of the vector of magnetic field intensity and Joule heat was carried out.