Software Implementation of the Matrix Method for Solving the Heat Conduction Problem in a Multilayer Medium

Abstract

we developed an algorithm to solve stationary and non-stationary heat conduction problems involving ideal and non-ideal contact between layers. This algorithm integrates the Bers generalized power method, matrix method, and the method of separation of variables (Fourier method). Our approach provides a unified framework for deriving approximate analytical solutions for media with an arbitrary number of layers in flat, cylindrical, or spherical configurations.
We also implemented this approach in the Maple environment, which can address four types of problems: stationary heat conduction with ideal or non-ideal contact and non-stationary heat conduction with ideal or non-ideal contact between layers. The algorithm can solve boundary value problems of the first or third type. The results are temperature distribution curves, either 2D for stationary problems, or 3D for non-stationary ones, enabling clear visualization of the results.