Comparison of analytical and numerical simulations of cowpea (Vigna unguiculata) grain drying using Fick's law and the finite element method

This article presents a comprehensive analysis of the drying process of a single cowpea bean (Vigna unguiculata) using both analytical and numerical approaches. The process, governed by coupled heat and mass transfer (Bird et al., 2002) mechanisms, was simulated by modeling the bean as an ellipsoidal body under isotropic conditions. The analytical solution was based on a truncated series representation of Fick’s second law, while the numerical solution employed the Finite Element Method (FEM) with convective boundary conditions. Simulations were implemented in Python, incorporating thermophysical properties of air and grain derived from empirical models in the literature. Drying behavior at different temperatures was evaluated, and the results from both methods were compared using relative error and standard error of the estimates. The two solutions exhibited strong agreement, particularly during the active drying phase, confirming the accuracy and robustness of both modeling strategies. This comparative study contributes to the development of accurate thin-layer drying models (Madamba, 1996) and supports the optimization of post-harvest processing techniques.