Abstract
The chapter describes two mathematical optimization models for research and improving the efficiency of modern industrial and muffle furnaces on an electrical basis. The first mathematical model involves finding the temperatures of internal spot heaters, the location of which is known in advance. It is necessary to find such temperatures of these heaters so that during their operation the temperature of the object, which is in the furnace itself, is close to the specified one. A description of the linear and nonlinear cases is given. The second mathematical model assumes finding the locations of the furnace spot heaters, the temperatures of which are already known. It is necessary to find the optimal arrangement of these heaters, provided that the deviation from the temperature at the furnace object as a result of the operation of these heaters should be as close as possible to the set temperature at this object. The chapter presents a general nonlinear case of this mathematical model. The numerical solution of the optimization models is obtained using high-speed optimization methods that are derived from the classical Newton’s method. Also, a comparative analysis of the work of the methods by the number of calls to the procedure for solving the direct problem of heat conduction is given. The largest number of calls to this procedure was taken by 100%.
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Zaporozhets, A., Khaidurov, V., Tsiupii, T. (2021). Optimization Models of Industrial Furnaces and Methods for Obtaining Their Numerical Solution. In: Zaporozhets, A., Artemchuk, V. (eds) Systems, Decision and Control in Energy II. Studies in Systems, Decision and Control, vol 346. Springer, Cham. https://doi.org/10.1007/978-3-030-69189-9_7
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