Discretisation of Thermal Diffusion Equation in Multilayer Structures with Variable Material Parameters and Different Thicknesses

Abstract

The paper presents details of discretisation of a thermal diffusion equation in one-dimensional space in terms of the Finite Volume Method. In the following sections, the method of space discretisation is discussed along with the approximation of a spatial derivative, matrix notation of a system of equations, special cases, approximation of three types of boundary conditions and derivative approximation over time. Much attention is also given to the issue of averaging material properties which can generally be different in adjacent cells.The study aims to analyse various multilayer structures for their suitability as heat storage. The launch of studies described in the paper has been driven by the lack of methods for effective heat storage, which is currently one of the key problems faced by the renewable energy industry.