About Calculation and Forecast of Temperature in the Layer Cell of Self-Heating of Raw Materials in a Silo

Abstract

The article clarifies an approximate variant for calculating the temperature in an inhomogeneous layer cell without a clear boundary under the assumption of significant distance in its center between the upper and lower ends of the silo when heat exchange conditions have little effect on the development of temperature in the layer cell due to poor thermal conductivity. The normal Gaussian law concerning distribution of thermal sources in the cell on an axis of a silo is accepted. The integral cosine of the Fourier transform is used to construct the analytical solution of the nonstationary thermal conductivity problem. A compact formula for calculating the increase in excess temperature in the center of the self-heating cell over time is derived and used to identify the parameters of the cell. The change in temperature at other points of the raw material is expressed through incomplete gamma function that is reduced to the probability integral. Calculations show that for the selected distribution of thermal sources, the temperature increase slows down rapidly with separation from the center of the cell. The possibility of determining the pattern distribution of the localized field of excess ambient temperature over time is proved. Examples of density identification of thermal sources are given. After identification, the calculation formulas become consistent with the experiment and suitable for the theoretical prediction of temperature rise in the raw material. The approbation of the proposed mathematical expressions to identify the parameters of the self-heating process of raw materials showed high accuracy relative to experimental data with a deviation of 0.01–0.015%. It is possible not only to determine the parameters of the self-heating cell but also to predict the time of reaching a flammable temperature in it.