Orthogonal Methods for Multilayer Structures in Heat Conduction Problems

Theoretical properties of a method for construction of analytical solutions pertaining to heat conduction boundary value problem for multilayer structures have been given on the basis of the Kantarovich orthogonal method.Methodology for construction of coordinate function systems has been developed that satisfy boundary conditions in any approximation and satisfy matching conditions at any number of contacting bodies. Analytical solution of the heat conduction problem has been obtained on the basis of temperature perturbation front introduction and additional boundary conditions with regard to the last layer of the multilayer system. The solution makes it possible to evaluate temperature state of a structure for small and very small time values.