DETERMINATION AND ANALYSIS OF THE TEMPERATURE FIELD IN A THREE-LAYER ISOTROPIC PLATE WITH A GIVEN INITIAL TEMPERATURE DISTRIBUTION

Abstract

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.