Solving the problem of heating (cooling) a fixed porous layer of material by the method of elementary balances

The article considers the issue of informal derivation of a system of finite-difference equations for heating (cooling) a fixed layer of material with ideal thermal conductivity based on the analysis of equations made by the method of elementary heat balances. The physical essence of various calculation schemes is shown and an improved method for calculating the heating (cooling) of a fixed layer of material is proposed. A comparative analysis of the results of calculating the heating (cooling) of a fixed layer of material according to an analytical solution, according to an implicit scheme with a formal approximation of differential equations and according to the proposed method was carried out.