Визначення та аналіз температурного поля у тришаровій пластині із заданим початковим розподілом температури

• Date: 2023
• Author Affiliations: Роман Мусій; Уляна Жидик; Богдан Бандирський; Ольга М’яус
• Keywords: keywords
• Main Authors: Мусій, Роман, Жидик, Уляна, Бандирський, Богдан, М’яус, Ольга
• Format: Article
• Language: Ukrainian
• Published: Інститут прикладних проблем механіки і математики ім. Я. С. Підстригача НАН України 2023
• Subjects: тришарова пластина,ізотропні матеріали; температурне поле; металокераміка.
• Online Access: https://www.fmmit.lviv.ua/index.php/fmmit/article/view/336
• Journal Title: Physico-mathematical modeling and informational technologies

An approximate system of two-dimensional heat conduction equations for a multilayer isotropic plate is written down. Boundary conditions for a rectangular plate of finite dimensions are formulated. A general solution of the non-stationary heat conduction problem for this plate was found using integral Fourier transforms in spatial variables and Laplace transform in time.On the basis of the obtained general solutions, the solution of the thermal conductivity problem for a three-layer plate, which at the initial moment of time is heated by a temperature field linear in its thickness, which is uniformly distributed over the surface of the plate in a rectangular region, was analyzed. The numerical analysis of the temperature field was performed for a three-layer plate, the middle layer of which is made of metal, and the outer layers are made of ceramics.