Mathematical Model of Temperature Distribution over the Length of the Furnace Taking into Account the Mutual Influence of its Zones

The authors analyzed works on the development of mathematical models for external heat exchange in through-type furnaces of rolling mills. They identify two key research areas for the mathematical models of external heat exchange. The first area includes the development of heat exchange models where heat transfer is described with a system of analytical or numerical equations based on physical laws of heat transfer taking into account the hydrodynamic parameters of combustion gas movement. The second research area includes the development of empirical mathematical models based on monitored process parameters that describe the correlations between these parameters. This paper presents the research results for the development of an empirical mathematical model of a through-type furnace taking into account the dynamic parameters of the process. The developed mathematical model determines the correlations between the consumption of the fuel distributed across furnace zones and the operating area temperature in these zones. The mathematical model accounts for the mutual influence of adjacent zones, furnace efficiency in terms of workpiece heating, and the dynamic parameters of the zones. The authors use the operation statistics of the wide-strip hot rolling mill furnace as the initial data to calculate equation coefficients. Equation coefficients for the mathematical model were determined using amoeba method. The developed mathematical model allows for automatic adaptation based on the measured heating parameters, which makes it suitable for the development of adaptive cyber-physical control systems for rolling mill furnaces.