This study analyzes the dynamics of temperature and moisture in a cylindrical silo with a conical roof and floor used for storing corn in the Bajío region of Mexico, considering conditions both with and without aeration. The model incorporates external temperature fluctuations, solar radiation, grain moisture equilibrium with air humidity through the sorption isotherm (water activity), and grain respiration to simulate real storage conditions. The model is based on continuity, momentum, energy, and moisture conservation equations in porous media. This model was solved using the finite element method (FEM) to evaluate temperature and interstitial humidity variations during January and May, representing cold and warm environmental conditions, respectively. The simulations show that, without aeration, grain temperature progressively accumulates in the center and bottom region of the silo, reaching critical values for safe storage. In January, the low ambient temperature favors the natural dissipation of heat. In contrast, in May, the combination of high ambient temperatures and solar radiation intensifies thermal accumulation, increasing the risk of grain deterioration. However, implementing aeration periods allowed for a reduction in the silo’s internal temperature, achieving more homogeneous cooling and reducing the threats of mold and insect proliferation. For January, an airflow rate of 0.15 m³/(min·ton) was optimal for maintaining the temperature within the safe storage range (≤17 °C). In contrast, in May, neither this airflow rate nor the accumulation of 120 h of aeration was sufficient to achieve optimal storage temperatures. This indicates that, under warm conditions, the aeration strategy needs to be reconsidered, assessing whether a higher airflow rate, longer periods, or a combination of both could improve heat dissipation. The results also show that interstitial relative humidity remains stable with nocturnal aeration, minimizing moisture absorption in January and preventing excessive drying in May. However, it was identified that aeration period management must be adaptive, taking environmental conditions into account to avoid issues such as re-wetting or excessive grain drying.

This study presents an integrated approach that combines the Levenberg–Marquardt (LM) and Luus–Jaakola (LJ) algorithms to enhance parameter estimation for various applications. The LM algorithm, known for its precision in solving non-linear least squares problems, is effectively paired with the LJ algorithm, a robust stochastic optimization method, to improve accuracy and computational efficiency. This hybrid LM-LJ methodology is demonstrated through several case studies, including the optimization of MESH equations in distillation processes, modeling controlled diffusion in biopolymer films, and analyzing heat and mass transfer during the drying of cylindrical quince slices. By overcoming the convergence issues typical of gradient-based methods and performing global searches without initial parameter bounds, this approach effectively handles complex models and closely aligns simulation results with experimental data. These capabilities highlight the versatility of this approach in engineering and environmental modeling, significantly enhancing parameter estimation in systems governed by differential equations.