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### Mathematical modeling of heat exchange processes when heating metal in a furnace

 Назва Mathematical modeling of heat exchange processes when heating metal in a furnace Назва англійською Mathematical modeling of heat exchange processes when heating metal in a furnace Автори Viktor Aulin, Mykola Bosiy, Volodymyr Kropivnyi, Olexandr Kuzyk, Alena Kropivna Принадлежність Central Ukrainian National Technical University, Kropyvnytskyi, Ukraine Бібліографічний опис Mathematical modeling of heat exchange processes when heating metal in a furnace / Viktor Aulin, Mykola Bosiy, Volodymyr Kropivnyi, Olexandr Kuzyk, Alena Kropivna // Scientific Journal of TNTU. — Tern.: TNTU, 2021. — Vol 104. — No 4. — P. 123–130. Bibliographic description: Aulin V., Bosiy M., Kropivnyi V., Kuzyk O., Kropivna A. (2021) Mathematical modeling of heat exchange processes when heating metal in a furnace. Scientific Journal of TNTU (Tern.), vol 104, no 4, pp. 123–130. УДК 620.22 Ключові слова Newton-Richman law, metal heating, variable separation method, Stefan-Boltzmann law, heating furnace. The article presents a mathematical model of the heat transfer process when heating metal in a furnace, which describes the thermophysical processes that occur when using industrial technology for heating castings. A simplified model of convective and radiant heating of metal in a furnace, which is based on conventional differential equations, allows to calculate the heating time of the metal. It allows you to evaluate the process of heating the metal in the furnace and find its optimal parameters. The model is widely used and can be applied to study the process of heating the casting of any metal or alloy in the furnace. The adequacy of the model is confirmed by comparing the obtained results of estimating the parameters of the model with experimental data. ISSN: 2522-4433 Перелік літератури Sabirzyanov T. G. (2007). Mathematical modeling of technological processes of casting. Kirovograd: KNTU. [In Ukrainian]. Sabirzyanov T. G., Kropivny V. M. (2005) Heat engineering of livarny processes. Kirovohrad: KNTU. [In Ukrainian]. Sabirzyanov T. G. (2007) Foundry furnaces. Kirovograd: KNTU. [In Ukrainian]. Krivandin V. A., Markov B. L. (1977) Metallurgical furnaces. M: Metallurgy. [In Russian]. Tkachenko V. N. (2008). Mathematical modeling, identification and control of technological processes of heat treatment of materials. Kiev: Naukova Dumka. Vol. 13. 243 р. [In Ukrainian]. Revun M. P., Zinchenko V. Yu., Ivanov V. I., Moseiko Yu. V. (2016). Model of metal heating dynamics in chamber-type flame furnaces. Zaporizhia State Engineering Academy, Zaporizhia. Mathematical modeling. No. 1 (34) P. 32–34. [In Ukrainian]. Kayukov Yu. M., Ivanov V. I., Cheprasov O. I., Radchenko Yu. M. (2018). To control of low-oxidative heating of metal in chamber-type furnaces. Metallurgy. Issue 2 (40). P. 106–110. [In Ukrainian]. Revun M. P., Ivanov V. I., Moseiko Yu. V. (2016). Model of metal heating in chamber type furnaces. Scientific works SWORLD LLC Scientific World (Ivanovo). Vol. 2. No. 2 (43). P. 85–92. [In Russian]. Zinchenko V. Y., Ivanov V. I., Cheprasov O. I., Kayukov Y. M. (2018). Zaporozhye State Engineering Academy. Zaporizhzhia. To optimize the control of thermal work of flame thermal furnaces of chamber type during heating of massive ingots. Mathematical modeling. No. 1 (38). P. 88–94. [In Ukrainian]. Revun M. P., Zinchenko V. Yu., Ivanov V. I., Cheprasov O. I. (2016). Development of a mathematical model and algorithm for calculations of heating of thermally massive bodies in flame thermal furnaces of chamber type Metallurgy. Issue 1 (35). P. 72–77. [In Ukrainian]. Revun M. P., Zinchenko V. Yu., Ivanov V. I., Cheprasov O. I. (2016). Development of a mathematical model and algorithm for heating calculations for heat treatment of ingots in flame chamber furnaces. Metallurgy. Issue 2 (34), P. 93–97. [In Ukrainian]. Budnik A. F. Heat and mass transfer in processes and materials to materials design. Navchalnyy posibnik. Sumi: View of Sumy Department, 2008. 158. [In Ukrainian]. Timoshpolsky V. I., Trusova I. A., Mendelev D. V., Ratnikov P. E. (2012). Analysis of methods for mathematical modeling of heat transfer processes in industrial furnaces for heating metal. BNTU. Casting and metallurgy. No. 2 (65). P. 102–107. [In Belarus]. Revun M. P., Sokolov A. K. (2000). Simulation of metal heating in computer-aided design and control. Zaporozhye: ZGIA. 351 p. [In Ukrainian]. Cherevko O. O., Shcherbakov S. V., Ermilin A. I., Titku V. V. (2020). Mathematical modeling of thermal work of the methodical furnace. Science and production. Issue 22. Р. 218–224. [In Ukrainian]. Mnykh I. M. (2015). Development of a mathematical model of metal heating and study of temperature fields in the chamber recirculation of the furnace. Energy saving. Energy. Energy audit. No. 5 (136). P. 59–66. [in Ukrainian]. References: Sabirzyanov T. G. (2007). Mathematical modeling of technological processes of casting. Kirovograd: KNTU. [In Ukrainian]. Sabirzyanov T. G., Kropivny V. M. (2005) Heat engineering of livarny processes. Kirovohrad: KNTU. [In Ukrainian]. Sabirzyanov T. G. (2007) Foundry furnaces. Kirovograd: KNTU. [In Ukrainian]. Krivandin V. A., Markov B. L. (1977) Metallurgical furnaces. M: Metallurgy. [In Russian]. Tkachenko V. N. (2008). Mathematical modeling, identification and control of technological processes of heat treatment of materials. Kiev: Naukova Dumka. Vol. 13. 243 р. [In Ukrainian]. Revun M. P., Zinchenko V. Yu., Ivanov V. I., Moseiko Yu. V. (2016). Model of metal heating dynamics in chamber-type flame furnaces. Zaporizhia State Engineering Academy, Zaporizhia. Mathematical modeling. No. 1 (34) P. 32–34. [In Ukrainian]. Kayukov Yu. M., Ivanov V. I., Cheprasov O. I., Radchenko Yu. M. (2018). To control of low-oxidative heating of metal in chamber-type furnaces. Metallurgy. Issue 2 (40). P. 106–110. [In Ukrainian]. Revun M. P., Ivanov V. I., Moseiko Yu. V. (2016). Model of metal heating in chamber type furnaces. Scientific works SWORLD LLC Scientific World (Ivanovo). Vol. 2. No. 2 (43). P. 85–92. [In Russian]. Zinchenko V. Y., Ivanov V. I., Cheprasov O. I., Kayukov Y. M. (2018). Zaporozhye State Engineering Academy. Zaporizhzhia. To optimize the control of thermal work of flame thermal furnaces of chamber type during heating of massive ingots. Mathematical modeling. No. 1 (38). P. 88–94. [In Ukrainian]. Revun M. P., Zinchenko V. Yu., Ivanov V. I., Cheprasov O. I. (2016). Development of a mathematical model and algorithm for calculations of heating of thermally massive bodies in flame thermal furnaces of chamber type Metallurgy. Issue 1 (35). P. 72–77. [In Ukrainian]. Revun M. P., Zinchenko V. Yu., Ivanov V. I., Cheprasov O. I. (2016). Development of a mathematical model and algorithm for heating calculations for heat treatment of ingots in flame chamber furnaces. Metallurgy. Issue 2 (34), P. 93–97. [In Ukrainian]. Budnik A. F. Heat and mass transfer in processes and materials to materials design. Navchalnyy posibnik. Sumi: View of Sumy Department, 2008. 158. [In Ukrainian]. Timoshpolsky V. I., Trusova I. A., Mendelev D. V., Ratnikov P. E. (2012). Analysis of methods for mathematical modeling of heat transfer processes in industrial furnaces for heating metal. BNTU. Casting and metallurgy. No. 2 (65). P. 102–107. [In Belarus]. Revun M. P., Sokolov A. K. (2000). Simulation of metal heating in computer-aided design and control. Zaporozhye: ZGIA. 351 p. [In Ukrainian]. Cherevko O. O., Shcherbakov S. V., Ermilin A. I., Titku V. V. (2020). Mathematical modeling of thermal work of the methodical furnace. Science and production. Issue 22. Р. 218–224. [In Ukrainian]. Mnykh I. M. (2015). Development of a mathematical model of metal heating and study of temperature fields in the chamber recirculation of the furnace. Energy saving. Energy. Energy audit. No. 5 (136). P. 59–66. [in Ukrainian]. Завантажити ﻿
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