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 a three-dimensional numerical analysis of natural convection during the postharvest storage of corn and wheat in a galvanized steel silo with a conical roof and floor, measuring 3 m in radius and 18.7 m in height, located in the Bajío region of Mexico. Simulations were carried out specifically for December, a period characterized by cold ambient temperatures (10–20 °C) and comparatively lower solar radiation than in warmer months, yet still sufficient to induce significant heating of the silo’s metallic surfaces. The governing conservation equations of mass, momentum, energy, and species were solved using the finite volume method under the Boussinesq approximation. The model included grain–air sorption equilibrium via sorption isotherms, as well as metabolic heat generation: for wheat, a constant respiration rate was assumed due to limited biochemical data, whereas for corn, respiration heat was modeled as a function of grain temperature and moisture, thereby more realistically representing metabolic activity. The results, obtained for December storage conditions, reveal distinct thermal and hygroscopic responses between the two grains. Corn, with higher thermal diffusivity, developed a central thermal core reaching 32 °C, whereas wheat, with lower diffusivity, retained heat in the upper region, peaking at 29 °C. Radial temperature profiles showed progressive transitions: the silo core exhibited a delayed response relative to ambient temperature fluctuations, reflecting the insulating effect of grain. In contrast, grain at 1 m from the wall displayed intermediate amplitudes. In contrast, zones adjacent to the wall reached 40–41 °C during solar exposure. In comparison, shaded regions exhibited minimum temperatures close to 15 °C, confirming that wall heating is governed primarily by solar radiation and metal conductivity. Axial gradients further emphasized critical zones, as roof-adjacent grain heated rapidly to 38–40 °C during midday before cooling sharply at night. Relative humidity levels exceeded 70% along roof and wall surfaces, leading to condensation risks, while core moisture remained stable (~14.0% for corn and ~13.9% for wheat). Despite the cold ambient temperatures typical of December, neither temperature nor relative humidity remained within recommended safe storage ranges (10–15 °C; 65–75%). These findings demonstrate that external climatic conditions and solar radiation, even at reduced levels in December, dominate the thermal and hygroscopic behavior of the silo, independent of grain type. The identification of unstable zones near the roof and walls underscores the need for passive conservation strategies, such as grain redistribution and selective ventilation, to mitigate fungal proliferation and storage losses under non-aerated conditions.

Grain storage in silos plays a fundamental role in preserving the quality and safety of agricultural products. This study presents a comparative evaluation of two-dimensional (2D) and three-dimensional (3D) mathematical models to predict the temperature and moisture distribution during unventilated corn storage in cylindrical silos with conical roofs. The models incorporate external temperature fluctuations, solar radiation, grain moisture equilibrium with air humidity via sorption isotherm (water activity), and grain respiration to simulate real-world storage conditions. The 2D model offers computational efficiency and is suitable for preliminary assessments but simplifies natural convection effects and underestimates axial temperature gradients. Conversely, the 3D model provides a detailed representation of heat and moisture transfer phenomena, capturing complex interactions such as buoyancy-driven flow and localized effects of solar radiation. The results reveal that temperature and moisture accumulation are more pronounced in the upper regions of the silo, driven by solar radiation and natural convection, with significant implications for large-scale silos where thermal inertia plays a key role. This dual modeling approach demonstrates that while the 2D model is valuable for quick evaluations, the 3D model is essential for comprehensive insights into thermal and moisture gradients. The findings support informed decision-making in silo design, optimization, and management, enhancing grain storage strategies globally.

This study presents a numerical comparison between Direct numerical simulation (DNS) and the standard κ-ε turbulence model to evaluate natural convection in a two-dimensional, differentially heated, air-filled cavity over the Rayleigh number range 10³ to 10¹⁰. The objective is to assess the predictive capabilities of both methods across laminar and turbulent regimes, with a particular emphasis on the quantitative comparison of thermal characteristics under high Rayleigh number conditions. The Navier–Stokes and energy equations were solved using the finite element method with Boussinesq approximation, employing refined meshes near the hot and cold walls to resolve thermal and velocity boundary layers. The results indicate that for Ra ≤ 10⁶, the κ-ε model significantly underestimates temperature gradients, maximum velocities, and average Nusselt numbers, with errors up to 19.39%, due to isotropic assumptions and empirical formulation. DNS, in contrast, achieves global energy balance errors of less than 0.0018% across the entire range. As Ra increases, the κ-ε model predictions converge to DNS, with Nusselt number deviations dropping below 1.2% at Ra = 10¹⁰. Streamlines, temperature profiles, and velocity distributions confirm that DNS captures flow dynamics more accurately, particularly near the wall vortices. These findings validate DNS as a reference solution for high-Ra natural convection and establish benchmark data for assessing turbulence models in confined geometries

This paper presents analytical approximations for the inverse error function, its complementary inverse, and the cumulative distribution function using the Power Series Extender Method (PSEM). The proposed expressions exhibit high accuracy over a wide portion of the domain, particularly in the central region, while maintaining a compact structure based on elementary functions. This formulation ensures practical implementation and computational efficiency without the need for specialized numerical algorithms. The use of strategically selected cancellation points further enhances the accuracy of the approximations, especially in regions of interest. As expected for this class of elementary approximations, a gradual loss of accuracy is observed near the boundaries of the domain due to the asymptotic behavior of the inverse functions. To demonstrate the effectiveness and practical relevance of the proposed expressions, two case studies are presented, involving applications in statistical analysis and engineering contexts.

Refractory geopolymers derived from aluminosilicate sources and alkaline activation are a promising alternative to traditional fired bricks, particularly when low-cost, waste-derived raw materials are used. This study improves the workability of a refractory brick formulated with clays (Kaolin and Tepozan–Bauwer), seashell waste, sodium silicate, potassium hydroxide, and water by incorporating sodium lignosulfonate (LS) and polycarboxylate (PC) plasticizers. Clays from Comonfort, Guanajuato, Mexico, and seashells were ground and sieved to pass a 100 Tyler mesh. A base mixture was prepared and evaluated using the Mini Slump Test, varying plasticizer content from 0 to 2% relative to the solid fraction. Based on workability, 0.5% LS and 1% PC (by solids) increased the slump, and a blended plasticizer formulation (1.5% by solids, 80%PC+20%LS) produced the highest workability. These additives act through different mechanisms, with LS primarily promoting electrostatic repulsion and PC steric repulsion. Bricks with and without plasticizers exhibited thermal resistance up to 1200 °C. After four calcination cycles, compressive strength values were 354.74 kg_f/cm² for the brick without plasticizer, 597.25 kg_f/cm² for 1% PC, 433.63 kg_f/cm² for 0.5% LS, and 519.05 kg_f/cm² for 1.5% of the 80%PC+20%LS blend. Strength was consistent with changes in porosity and apparent density, and 1% PC provided a favorable combination of high workability and high compressive strength after cycling. Because the cost of clays and seashells is negligible, formulation selection was based on plasticizer cost per brick. Although 1% PC and the 1.5% of 80%PC+20%LS blend showed statistically comparable strength after cycling, 1% PC was selected as the preferred option due to its lower additive cost ($0.0449 per brick) compared with the blend ($0.0633 per brick). Stereoscopic microscopy indicated pore closure after calcination with no visible cracking, and SEM–EDS identified O, Si, and Al as the significant elements, with traces of S and K. Overall, the study provides an integrated assessment of workability, multi-cycle calcination, microstructure, and performance for refractory bricks produced from readily available clays and seashell waste.