Mathematical model of heat and mass transfer during the vacuum drying of peanuts with combined heat supply

The paper presents a mathematical model of heat and mass transfer for the vacuum drying of peanuts with combined heat input. The model takes into account two main stages of the process: surface evaporation and internal evaporation. For each stage, drying kinetic equations and heat balance equations were formulated, linearized, and solved both analytically and numerically. The simulation results showed that the moisture content of peanuts decreases at a decreasing rate, approaching an equilibrium value. The rate of this process increases with a higher drying coefficient. The dynamics of the material temperature are significantly influenced by such parameters as the specific heat transfer surface area, the heat transfer coefficient, and the heater temperature. An increase in any of these parameters leads to a more intensive rise in product temperature. Based on the model, an optimization problem for process control was solved, with criteria including minimizing drying time under a constraint on the maximum allowable material temperature. It was shown that the optimal regime consists of heating the product to the allowable limit as quickly as possible, followed by maintaining this temperature through controlled adjustment of the heater temperature. It was established that implementing an optimal continuous or stepwise regime significantly reduces drying time compared to a constant heater temperature regime. The main conclusions of the work are: the developed model adequately describes the physical nature of the vacuum drying process with combined heat input; effective heat input control strategies were identified, ensuring a reduction in drying time without exceeding the allowable product temperature. The obtained results are of practical importance for the design and optimization of vacuum drying equipment.