Constructing a physical-mathematical model of grain mass self-heating by a rod site of rectangular cross-section

Abstract

This paper considers the issue related to improving the energy and resource efficiency of the process of storing raw materials of plant origin, namely, preventing self-heating of grain masses in elevator silos. It was noted that the effectiveness of the analysis of self-heating of grain mass increases with the use of mathematical models of temperature fields of grain mass during storage together with data obtained experimentally. A physical-mathematical model has been built that describes a two-dimensional localized non-stationary temperature field of seed material generated by a homogeneous rod cell with a rectangular cross-section. A technique for accelerating the convergence of the series is proposed for the constructed analytical solution, which is based on the selection and analytical calculation of the sum of the component of slow convergence. The adequacy of the physical-mathematical model has been proven by calculations and by comparing the temperature of the self-heating site, obtained theoretically, and the temperature obtained under industrial setting. The established temperature kinetics of grain mass volumes during storage, obtained experimentally and theoretically, correlate with each other in the duration range from 0 to 30 days with a correlation coefficient of at least 0.98. This proves the possibility of applying forecasts of the temperature of self-heating sites in the volume of grain mass, obtained by using the physical-mathematical model built, under industrial setting. A limitation of the study is that the model is not universal. It is another stage on the way to a universal model. A limitation of the study is that for storage periods of more than 30 days, a new excess temperature forecast must be made