Orthogonal Methods of Weighted Residuals in Thermal Conductivity Problems for Multilayer Structures

Abstract

An analytical solution of the heat conduction problem for a two-layer plate based on the Galerkin method and usage of additional boundary conditions (ABC) is obtained. The ABCs are found in such a way that their implementation is to be adequate to the implementation of the original equations at the boundary points. Execution of equations at boundary points leads to their execution over the entire range of spatial coordinates. The use of ABC allows us to obtain chain systems of algebraic equations for unknown solution coefficients. The equations of these systems have highly sparse well-conditioned square matrices. In this connection, their solutions are so simplified that with a large number of approximations, in general form, a system of only two algebraic equations should be solved. A high accuracy of finding the eigenvalues is observed that is explained by the use of a special ABC design.