TY  - JOUR
AU  - Ali, Ishtiaq
PY  - 2026
TI  - Two-dimensional numerical modeling and simulation of heat and moisture transfer during drying
JO  - AIMS Mathematics
SP  - 8762
EP  - 8791
VL  - 11
IS  - 3
AB  - This study explores a two-dimensional model for transient heat and moisture transfer in a rectangular domain subject to convective boundary conditions. The governing equations consist of parabolic partial differential equations, which are derived from Fourier's law of heat conduction and Fick's law of mass diffusion. The model equations are discretized using central finite-difference approximations in space and a Crank–Nicolson (CN) scheme in time. To efficiently handle the multidimensional diffusion operators, an operator splitting strategy based on the Peaceman–Rachford alternating direction implicit (ADI) method is employed. This approach decomposes the two-dimensional diffusion operator into a sequence of one-dimensional subproblems, each associated with a single spatial direction, which significantly reduces the computational complexity of the fully implicit scheme while retaining second-order accuracy in time and space and unconditional stability for linear diffusion operators. The numerical scheme is shown to be unconditionally stable for the diffusion operators and computationally efficient for long-time simulations. The numerical results for the temperature and moisture fields are validated through comparison with available analytical solutions and experimental data from the literature, demonstrating very good agreement in all cases. In addition, a structure-preserving iteration method (SPIM) applied to the unsplit CN formulation is used as a benchmark reference, confirming that the proposed ADI–CN splitting achieves accuracy comparable to the unsplit CN scheme while maintaining competitive computational efficiency.
UR  - https://doi.org/10.3934/math.2026360
DO  - 10.3934/math.2026360