Design of the Blast Furnace Wall Structure Made of Efficient Materials. Part 3. Mathematical Model of Heat Transfer Process

This work is the part 3 of a series of articles under the title “Design of the blast furnace wall made of effective materials.” In the part 1 with the subtitle “Problem statement and calculation prerequisites” typical multilayer enclosing structures of the blast furnace are considered. A description of the layers that make up these structures is given. The main attention is paid to the lining layer. The process of cast iron smelting and temperature conditions in the characteristic layers of the internal environment of the furnace are briefly described. On the basis of the theory of A.V. Lykov, the initial equations describing the interrelated transfer of heat and mass in a solid body are analyzed in relation to the set problem – an adequate description of the processes for the further rational design of a multilayer enclosing structure of a blast furnace. A priori, enclosing is considered from a mathematical point of view as an unlimited plate. In the part 2 with the subtitle “Solution of boundary value problems of heat transfer” the boundary value problems of heat transfer in separate layers of the structure with different boundary conditions are considered, their solutions, which are basic when developing a mathematical model of the unsteady heat transfer process in a multilayer enclosing structure, are given. The part 3 presents a mathematical model of the heat transfer process in the enclosing structure and the algorithm for its implementation. The proposed mathematical model makes it possible to solve the following problems: to estimate the thermo-physical condition of the designed structures under different operating conditions and, as a result, to design them rationally for a specific mode or range of modes; calculate the temperature field in structurally complex multilayer structures, for example, when the arrangement of layers is discrete; when measuring the temperature at characteristic points (at the joints of layers and surfaces of the structure), it makes it possible to determine the thermal characteristics of the materials that make up the surveyed structure; in the course of laboratory tests can significantly reduce the test time, the researchers have the opportunity not to wait for the establishment of a regular regime; there is an opportunity to abandon the climate chamber and expensive instrumentation experiments and research; when solving the inverse problem, directly determine the resistance to heat transfer of the entire layered structure and its individual layers from an unsteady temperature field.

S.V. FEDOSOV¹, Doctor of Sciences (Engineering), Academician of the Russian Academy of Architecture and Construction Scien (RAACS), President (This email address is being protected from spambots. You need JavaScript enabled to view it.)
A.M. IBRAGIMOV², Doctor of Sciences (Engineering), (This email address is being protected from spambots. You need JavaScript enabled to view it.)
L.Yu. GNEDINA², Candidate of Sciences (Engineering)

¹ Ivanovo State Polytechnic University (20, 8 Marta Street, Ivanovo, 153037, Russian Federation)
² National Research Moscow State University of Civil Engineering (26, Yaroslavl highway, Moscow, 129337, Russian Federation)

1. Ibragimov A.M., Lipenina A.V., Gnedina L.Yu. Design of the blast furnace wall structure made of efficient materials. Part 2. Solution of boundary problems of heat transfer. Stroitel’nye Materialy [Construction Materials]. 2018. No. 5, pp. 73–76. DOI: https://doi.org/doi.org/10.31659/0585-430X-2018-759-5-73-76 (In Russian).
2. Lykov A.V., Mikhailov Yu.A. Teoriya perenosa energii i veshchestva [The theory of energy and matter transfer]. Minsk: Publishing House Academy of Sciences of the BSSR. 1959. 330 p.
3. Fedosov S.V., Gnedina L.Yu. Non-stationary heat transfer in a multilayered enclosing structure. In the book. Problems of building thermal physics systems for microclimate and energy saving in buildings: Collection of reports of the fourth scientific-practical conference. April 27–29, 1999. Moscow: NIISF. 1999, pp. 343–348. (In Russian).
4. Fedosov S.V., Ibragimov A.M., Gnedina L.Yu., Gushchin A.V. Mathematical model of non-stationary heat transfer in a multilayered enclosing structure. Reports of the XII Russian-Polish seminar “Theoretical bases of construction”. Warsaw. 2003, pp. 253–261.
5. Ibragimov A.M., Lipenina A.V Design of the blast furnace wall structure made of efficient materials. Part 1. Statement of a problem and calculation prerequisites. Stroitel’nye Materialy [Construction Materials].2018. No. 3, pp. 70–74. DOI: http://10.31659/0585-430X-2018-757-3-70-74 (In Russian).
6. Fedosov S.V. Analytical description of heat and moisture transport in the process of drying dispersed materials in the presence of thermal diffusion and internal evaporation of moisture. Zhurnal prikladnoi khimii. 1986. Vol. 59. No. 3, pp. 2033–2038. (In Russian).
7. Fedosov S.V., Kiselnikov V.N. Heat transfer in a spherical particle with convective drying in a suspended state. Izvestiya vuzov. Khimiya i khimicheskaya tekhnologi. 1985. Vol. 28. No. 2, pp. 14–15. (In Russian).
8. Fedosov S.V., Zaitsev V.A., Shmelev A.L. Calculation of temperature fields in a cylindrical reactor with a nonuniformly distributed source of heat. The state and prospects of development of electrical technology. Abstracts of the All-Union Scientific and Technical Conference. Ivanovo. 1987, p. 28. (In Russian).
9. Fedosov S.V., Kiselnikov V.N., Shertaev T.U. Primenenie metodov teorii teploprovodnosti dlya modelirovaniya protsessov konvektivnoi sushki [Application of the methods of the theory of heat conduction for the modeling of convective drying processes]. Alma-Ata: Gylym. 1992. 168 p.
10. Chizil’skii E. Ventilated structures of external walls. Zhilishchnoe Stroitel’stvo [Housing Construction]. 1996. No. 10, pp. 25–27. (In Russian).
11. Shmelev A.L., Fedosov S.V., Zaitsev V.A., Sokolsky A.I., Kiselnikov V.N. Simulation of non-stationary heat transfer in a reactor for the hydrolysis of cyanide-containing polymers. Ivanovo Institute of Chemical Technology. 1988. 10 p.
12. Shmelev A.L. Continuous method of obtaining water-soluble polyacrylonitrile-based polymers with a high content of the basic substance. Diss… Candidate of Sciences (Engineering). Ivanovo. 1998.