Heat Transfer in the Enclosing Structures of a Blast Furnace. Part 3. Mathematical Model of the Heat Transfer Process

Abstract

The article is part of 3rd cycle of articles under the general title “Heat transfer in the enclosing structures of a blast furnace”. In Part 1, with the subheading “Statement of the problem and the prerequisites for calculation”, typical multiwalled enveloping structures of a blast furnace are considered. The description of the layers in these structures is given. The main attention is paid to the lining layer. Briefly described the process of smelting cast iron and temperature conditions in the characteristic layers of the internal environment of the furnace. Based on the theory of A.V. Lykov, the initial equations describing the interconnected transfer of heat and mass in a solid are analyzed in relation to the problem posed (a proper description of the processes for the purpose of further rational design of the multilayered enclosing structure of the blast furnace). A priori enclosure from the mathematical point of view is considered as an unlimited plate. In Part 2 with the subtitle “Solving the boundary-value problems of heat transfer,” the boundary-value problems of heat transfer in separate layers of the design with various boundary conditions are considered, and their solutions are given that are basic in the development of the mathematical model of the nonstationary heat transfer process in a multilayered enclosing structure. Part 3 presents a mathematical model of the process of heat transfer in the enclosure and an algorithm for its implementation.The proposed mathematical model allows to solve the following problems: - assess the thermophysical state of the designed structures under different operating conditions and, as a consequence, rationally design them for a particular mode or range of modes; - to calculate the temperature field in complex multi-layer constructions, for example, when the arrangement of the layers is discrete;- when temperature is measured at characteristic points (at the joints of layers and structural surfaces), it is possible to determine the thermophysical characteristics of the materials constituting the surveyed structure; - in laboratory tests it is possible to significantly shorten the test time, the researchers have the opportunity not to wait for the establishment of a regular regime;- it becomes possible to abandon the climate chamber and expensive instrumentation for 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 the unsteady temperature field.