ON PARABOLIC APPROXIMATION OF THE TEMPERATURE FIELD OF SLABS DURING HEATING IN CONTINUOUS FURNACES

Abstract

In the conditions of increasing requirements for the quality and efficiency of metal heating before rolling, the task of creating and improving the mathematical support of automated process control systems (APCS) for heating furnaces is quite relevant. Purpose of the study. To establish the specifics of the implementation of the parabolic approach mentioned in the literature to the description of the temperature fields of billets during heating in continuous furnaces. Materials and methods. A physi-cal, mathematical and numerical analysis was carried out of the question of how much the parabola method sa¬tisfies the well-known mathematical description of the heating process, the core of which, as is well known, is the heat conductivity equation. Results. An ordinary differential equation for determining the desired parameters of the parabola is obtained. A general solution to this equation and its specification for the case of a constant temperature of the furnace working space are given. A method for finding the initial condition for the obtained solution is proposed. Computational experiments were carried out to assess the acceptability of the approach under consideration for calculating the temperature fields of billets. It is shown that when using the parabola method, the greatest error in determining the temperature occurs for the center and surface of the slab, while there is practically no error in calculating the average mass tempe-rature. Conclusion. The results of the work can be used in the development and improvement of algorith-mic support for automated process control systems for continuous furnaces.