Mathematical modeling of heat and mass transfer in the process of drying seeds of agricultural crops in vacuum conditions

Abstract

Purpose. To analyze the effect of vacuum on the process of drying seeds of agricultural crops using mathematical modeling. Methods. Methods of differential calculus were used, in particular first-order differential equations, as well as differential geometry. The analysis of the mathematical model was carried out using graphs that were built by computer programs for solving differential equations. Results. On the basis of balance equations of heat and humidity flows of the seed drying process in the drying chamber, a system of differential equations was compiled and solved. Analytical dependencies describing the kinetics of drying and heating crop seeds when using vacuum in the drying chamber are obtained. On the example of soybean seeds, graphic dependencies of the kinetics of drying and heating at different pressures and the initial absolute humidity of the air in the drying chamber are constructed. These graphic dependences show that an increase in the vacuum in the drying chamber leads to an increase in the rate of seed drying, and a decrease in the initial absolute air humidity also increases the drying rate and decreases the equilibrium humidity. Analysis of the graphical dependencies of seed heating kinetics shows that drying in a vacuum reduces some of the thermal energy used directly to heat the seeds and reduces their heating temperature. Conclusions. To describe the process of heat and mass transfer in the process of drying seeds of agricultural crops under vacuum conditions, a mathematical model has been developed using a system of differential equations. The solution of which, on the example of soybean seeds, shows that when using a vacuum in the process of drying seeds, the exposure time and the proportion of thermal energy used directly to heat the seeds are reduced. Reducing the initial absolute humidity of the air inside the drying chamber also reduces the exposure time and equilibrium humidity. Therefore, drying in a vacuum reduces the negative impact of the heater on the seeds. Keywords: seeds, seed moisture, seed temperature, vacuum, absolute humidity, drying kinetics, drying chamber, equilibrium humidity.