Abstract
<jats:p>This research presents a multidimensional mathematical model and a robust secondorder numerical algorithm for coupled heat and moisture transfer with pressure-driven gas flow. Utilizing fractional Caputo derivatives (0 < ???? ⩽ 1), the model accounts for system memory and anomalous diffusion in heterogeneous porous media, integrating convection, phase transitions, and pressure dynamics. It incorporates environmental interactions, internal heat/moisture sources, solar radiation, and spatially varying transfer coefficients. A high-order stable difference scheme ensures computational efficiency and numerical stability. The algorithm effectively predicts the spatiotemporal evolution of temperature, moisture, and pressure fields. Results highlight how material heterogeneity and diurnal solar radiation create localized zones of high temperature and moisture accumulation, significantly impacting the overall dynamics of storage and drying processes.</jats:p>