On the calculation and forecast of the temperature in the core hearth by self-heating of raw materials in the silo

Abstract

An approximate method for calculating the temperature in an inhomogeneous core hearth without a clear boundary is presented, assuming a significant distance from its center from the walls of the silo, when the conditions of heat exchange on them have little effect on the temperature process in the center of the hearth. Gauss's law is adopted regarding the distribution of thermal sources along the radial coordinate. To construct analytical solutions of the unsteady axisymmetric problem of unsteady heat conduction, the integral Hankel transform is used. This solution makes sense when the center of the self-heating hearth is significantly sepa-rated from the walls of the silo and the influence of their thermal exchange on the temperature distribution in the hearth can be neglected. A compact formula is derived for calculating the increase in excess temperature in the center of the self-heating center over time. The change in temperature at other points is expressed using an integral exponential function. Calculations show that for the selected distribution of thermal sources, the excess temperature grows most rapidly in the center of the focus and its vicinity. A method of using the de-rived formulas for identification of the density of thermal sources in the hearth is proposed. It provides for the experimental measurement of the excess temperature in the center of the hearth at two points in time at the beginning of self-heating. Thus, the research is based on the theoretical and experimental method. Examples of identification of the density of thermal sources are given. After identification, the calculation formulas that are consistent with the experiment become suitable for the calculated forecast of the temperature development in the raw material. The stated method is simple in practical implementation. It does not require the compila-tion of special computer programs, although it is associated with the solution of the inverse problem of heat conduction, which belongs to mathematically incorrect problems. The obtained dependences make it possible to identify the density of thermal sources in the cell and then become suitable for predicting the development of the temperature of self-heating of raw materials over time. The adequacy of the obtained theoretical results is confirmed by the calculations.