Abstract
The use of linear graphs in the development of a mathematical model of metal melting in an induction crucible furnace allows to determine the metal melting temperature and control the excess temperature in the main parts of the furnace. In addition, if it is necessary to optimize the thermal mode of operation of the furnace according to the presented graph conversion method, a graph model of any part of the furnace with the desired thermal parameters can be obtained.
Highlights
Due to the difficulty of calculating the process of heating the molten metal and the main structural parts of induction crucible furnaces from the point of view of engineering practice, it is of great interest to develop a mathematical model based on linear graphs used in the analysis of linear electric circuits.[4]
We exclude the node Θ4 from the graph presented in Fig.2 and get two loops with the following transmissions Λ34Λ43/Λ33Λ44 and Λ24Λ42/Λ22Λ44 (Fig.3)
After removing the node Θ4, the graph model of the thermal process has the form with three unknowns (Fig.4)
Summary
Due to the difficulty of calculating the process of heating the molten metal and the main structural parts of induction crucible furnaces from the point of view of engineering practice, it is of great interest to develop a mathematical model based on linear graphs used in the analysis of linear electric circuits.[4]. The induction crucible furnace can be represented as a thermal circuit consisting of four interconnected thermal bodies.[1] The system of thermal balance equations for the steady state of such a scheme is as follows: Λ11Θ1 − Λ12Θ2 − Λ13Θ3 = P1,
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