Numerical Simulation of Heat Conduction in Building Materials Using Finite Difference Methods

This study uses finite difference numerical methods to simulate heat conduction processes in building materials commonly used in Nigerian construction, examining the thermal performance of laterite brick, sandcrete block, and compressed stabilised earth blocks under ambient temperature conditions typical of the semi-arid North East and the humid South South geopolitical zones. Thermal comfort and building energy efficiency are increasingly important concerns in Nigeria given the rising costs of air conditioning, the unreliability of grid electricity, and the growing urban heat island effect in rapidly expanding cities. The one-dimensional transient heat conduction equation is discretised using both explicit and implicit finite difference schemes, and temperature distributions within walls of specified thickness are computed over a 24-hour simulation period using boundary conditions derived from measured hourly ambient temperature profiles recorded in Maiduguri and Calabar. The von Neumann stability criterion is applied to determine maximum allowable time steps for the explicit scheme, and both schemes are compared against analytical solutions for validation. Results demonstrate that laterite brick provides superior thermal buffering relative to sandcrete block, maintaining interior surface temperatures within a narrower range over the diurnal cycle, a finding with practical implications for low-cost housing design. The study provides quantitative thermal performance data for material types that have been insufficiently characterised in the Nigerian building science literature. Keywords: heat conduction, finite difference method, building materials, thermal performance, numerical simulation