Mathematical model of heating seeds with stirring in a drying drum of vacuum drying of seeds

Abstract

Annotation Purpose. To increase the uniformity of seed heating by substantiating the transitional modes of a vacuum drum dryer through a mathematical model of heating seeds with mixing in a drying drum. Methods. The solutions of the heat equation were used with the use of the Fourier method for parabolic partial differential equations and the analysis of the motion of a material point on a rough surface. The adequacy of the mathematical model was verified on the basis of statistical methods. Results. Based on the solution of the heat conductivity equation and the analysis of the movement of seeds along the inner surface of the drying drum, the dependence of the temperature of the seeds on the layer thickness, heating time and the number of cycles was obtained. The analysis of this dependence made it possible to determine the number of cycles (number of revolutions) at which a uniform temperature distribution is observed over the entire thickness of the seed layer. This dependence shows that the number of revolutions at which a uniform temperature distribution is observed is directly proportional to the thickness of the seed layer and inversely proportional to the thermal diffusivity and the duration of one cycle. The resulting dependence of the number of cycles, at which a uniform temperature distribution over the layer thickness is achieved, was comparable to a similar experimental dependence. Conclusions. It was found that the mathematical model adequately describes the transient process of seed heating during its mixing with the blades of a drying drum for vacuum drying seeds and can be used to calculate the modes of a vacuum drum dryer for seeds. Keywords: seeds, drying drum, seed temperature, stirring, vacuum dryer, thermal conductivity, layer thickness.