Conduction Heat Transfer Through Composite Walls Using the Finite Volume Method (FVM)

Abstract

This paper presents a systematic numerical investigation of steady-state heat conduction through homogeneous and composite walls using the Finite Volume Method (FVM). The governing diffusion equations are discretized in one-, two-, and three-dimensional Cartesian domains, with and without internal heat generation. The finite volume formulation is derived from integral conservation principles, ensuring strict energy conservation at the discrete level. Numerical solutions are obtained using matrix-based solvers implemented in MATLAB, and the results are validated through comparison with analytical solutions where available. Several case studies are presented, including a single-layer wall, a multilayer composite wall consisting of cement plaster, brick, and EPS insulation, and a two-dimensional wall with prescribed boundary temperatures. The results demonstrate the robustness, accuracy, and flexibility of the FVM in modeling conduction heat transfer problems relevant to building and thermal engineering applications.