Mathematical modeling of the process of vacuum drying of corn cobs

Abstract

Purpose. To determine the effect of vacuum on the process of drying corn seeds on the cob using mathematical modeling. Methods. Differential calculus methods were used, in particular, methods for solving differential diffusion equations with time-varying boundary conditions, as well as methods of differential and analytical geometry. The mathematical model was analyzed using graphs constructed by the computer program MathCad 13 from the solutions of differential equations and methods of technical analysis. Results. On the basis of the differential diffusion equation with variable boundary conditions in time, the processes of moisture removal from corn seeds in the cob were described. These processes are described by analytical dependencies that describe the kinetics of drying corn seeds and the entire cob, while taking into account diffusion processes both inside the seed and in the cob core. They are used to construct graphs that describe the dynamics of the moisture field inside a single seed and all the seeds along the cob. They show that the part of the seed that is outside the cob takes the longest to dry. The graphs also show the unevenness of drying along the cob: the ends of the cob dry the fastest, and the middle dries the slowest. Conclusions. The vacuum drying of corn cobs consists of 3 processes that take place in parallel: evaporation of moisture from the end surface of the cob, diffusion of moisture to the outer surface of the cob, and diffusion of moisture from the seed to the cob. The outer part of the seed takes the longest to dry, resulting in a moisture gradient that moves toward the core. Reducing the pressure inside the drying chamber reduces the time for moisture equalization, both over the volume of the seed and along the length of the cob, and increases the drying speed of the cob. To increase the uniformity of drying, the distribution of the heating temperature of the seeds along the length of the cob should correspond to a parabolic relationship with the highest temperature in the middle of the cob length, or it is necessary to divide the cob into parts to reduce the length of the moisture path. Keywords: seeds, moisture diffusion, drying time, moisture evaporation, vacuum, humidity, corn cob, cob, drying kinetics, drying chamber.