Mathematical Modeling of Heat Transfer in Building Envelopes

This paper investigates the mathematical modeling of heat conduction problems within multilayered composite building envelopes (walls) to minimize structural heat loss. A non-steady-state, one-dimensional partial differential equation (PDE) of the parabolic type, supplemented with a system of Robin (Type III) boundary conditions, is formulated to simulate thermal dynamics. To solve the differential model, an implicit finite difference method (FDM) scheme and the tridiagonal matrix algorithm (Thomas algorithm) are implemented. Based on local climatic datasets, the temperature distribution across the wall layers is simulated under extreme winter conditions (severe ambient temperature drop). The thermal insulation efficiency of modern materials, specifically basalt wool and expanded polystyrene, is quantitatively evaluated and analyzed.