To calculation and forecast of the temperature of formation self-heating of plant raw materials

Abstract

An analytical solution to the problem of non-stationary thermal conductivity in the formation of self-heating of plant raw materials by a focus without a clear boundary is obtained. A normal distribution law of thermal sources in the hearth is adopted, under the assumption that the center of the cell is remote from the ends of the silo. Heat transfer to the side walls of the silo is taken into account. An integral cosine transform is used to construct an analytical solution to the heat equation. Improper integrals and the distribution of excess temperature in the raw material are expressed through the integral of probability, and then, using a known approximation, reduced to elementary functions. It is shown that the increase in excess temperature slows down during the self-heating process. To identify the parameters of the distribution of thermal sources in the hearth, graphs of the type of nomograms were built. Their use is shown to determine these parameters from the results of measuring the excess temperature at two points in time at the beginning of the self-heating process. After identification, the calculation formulas, as consistent with the experiment, become suitable for predicting the development of the temperature of raw materials over time within the framework of the chosen theoretical model. An example of identification of the source parameters and the forecast of the temperature rise is given.
The stated theoretical and experimental method of calculation is convenient in practical implementation, since it does not require the compilation of special computer programs, but is limited to the variant of localized temperature fields that are possible in plant raw materials due to its weak thermal conductivity. The obtained analytical solution to the problem of non-stationary thermal conductivity makes it possible not only to calculate the temperature of self-heating of the reservoir, taking into account heat transfer to the silo racks, but also to identify the parameters of the source, which is necessary to predict the development of temperature. The solutions are convenient and do not require special computer programs associated with solving the inverse problem of heat conduction, which are mathematically incorrect problems. The adequacy of the obtained analytical dependences is confirmed by calculations.