Abstract

Every year, up to 3-5% of stored raw cotton is lost worldwide due to spontaneous heating, causing significant economic damage and creating fire hazards at cotton processing plants. The development of a three-dimensional mathematical model of heat and mass transfer in a raw cotton bale, taking into account microbiological heat generation, moisture evaporation, air filtration, and external meteorological influences, is a pressing area of research. A system of nonlinear partial differential equations is solved in this study using a finite difference method using a longitudinal-transverse scheme. Cross effects are described within the framework of Onsager thermodynamics. Spatiotemporal distributions of temperature, humidity, and pressure in a bale measuring 20x12x8 m over a period of 20-40 days are obtained. Critical zones with temperatures above 35°C and humidity above 10% are identified. It was found that the maximum risk of spontaneous heating occurs between days 15 and 30 of storage, with the upper-central region of the bin being most at risk. Adding a ventilation opening reduces peak temperatures by 4-6°C. The principal novelty of this work lies in three key aspects: (i) the generalization of the classical Lykov–Mikhailov two-equation model to a three-equation coupled system (temperature–moisture–vapor pressure) that captures barodiffusive and barothermal cross-effects within the Onsager thermodynamic framework; (ii) the integration of microbiological heat generation with a substrate depletion mechanism that realistically limits self-heating; and (iii) the development of a second-order accurate, stable longitudinal-transverse finite-difference scheme for solving the resulting nonlinear system. The proposed model provides a practical tool for designing early-warning monitoring systems, optimizing ventilation strategies, and guiding sensor placement in industrial cotton storage facilities.