Boundary-value Problems Of Heat Transfer Research Articles

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

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.

Heat Transfer in the Enclosing Structures of a Blast Furnace. Part 4. Examples of Calculation

The article is part of 4th 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. Part 4 gives a number of examples of calculation of the heat transfer process in a multiwalled fencing of a blast furnace, which show the effectiveness of the proposed calculation procedure.

Heat Transfer in the Enclosing Structures of a Blast Furnace. Part 2. Solution of boundary-value problems of heat transfer

This work is the second part out of a series of articles with a shared name “Heat transfer in the shielding structure of the blast furnace”. In the first part with the subtitle “Problem Statement and background for calculation” multilayer shielding structures of the blast furnace were examined. A description of the layers that are a part of these structures is presented. The lining layer is focused on. The process of cast iron smelting and the temperature zones of the individual layers of the blast furnace internal environment are briefly described. Based on A.V.Lykov’s theory original equations were analyzed, they describe interconnected heat and mass transfer in a solid object as applied to the given problem – appropriate process depiction aimed at the further rational development work on the multilayer shielding structures of the blast furnace. A priori the shielding mathematically is considered as an unlimited plate. In the second part boundary problems of heat transmission are examined in separate layers of the structure with different boundary conditions, solutions for them are introduced which are the basis of development of the mathematical model of the nonstationary process of heat transfer in the multilayered shielding structure. The mathematical model will be introduced in the third part of the series of articles.

ВЫЧИСЛИТЕЛЬНАЯ ИДЕНТИФИКАЦИЯ ГРАНИЧНОГО УСЛОВИЯ В ЗАДАЧАХ ТЕПЛОПЕРЕНОСА

Граничные обратные задачи теплопереноса имеют важное прикладное значение, и их численным методам решения посвящены работы многих авторов. В работе рассматривается такой прямой метод решения граничных обратных задач для одномерного параболического уравнения, что на каждом временном слое производится декомпозиция конечно-разностного аналога поставленной задачи. С помощью предлагаемого численного метода решены граничные обратные задачи: с фиксированной границей, с подвижной границей и задача Стефана. Обсуждаются результаты численных расчетов. The inverse boundary-value problems of heat transfer are of great practical importance, and the work of many authors is devoted to the numerical methods of their solution. We consider a direct method for solving inverse boundary-value problems for a one-dimensional parabolic equation that decomposes a finite-difference analogue of the problem at each time layer. With the help of the proposed numerical solution, we solve the inverse boundary-value problems with a fixed boundary, with a moving boundary, and the Stefan problem. The results of numerical calculations are discussed.

The possibility of anomalous heat transfer in flows with nonequilibrium boundary conditions

The kinetic Boltzmann equation has been solved for the boundary-value problem of heat transfer with boundary conditions in the form of nonequilibrium distributions. Modes with anomalous heat transfer have been revealed in the spatial zones where the signs of the heat flux and temperature gradient coincide (in the classical statement of the problem with equilibrium conditions, heat transfer conventionally occurs in the entire range of physical parameters). Possible experiments aimed at verifying these effects are discussed.

MODELING OF TEMPERATURE FIELD DISTRIBUTION OF THE FOAM GLASS BATCH IN TERMS OF THERMAL TREATMENT OF FOAM GLASS

Applications of foam glass is currently quite wide. This material is applied directly to construction and other human activities. Recent years the attention of scientists aimed at modeling the thermal processes in the production of foamed glass. Appear works in which the developed mathematical model allows to predict the distribution of temperature fields in the foam glass material at various stages of heat treatment of the material. The emergence of these models reveals a number of promising directions in the improvement of technology of producing foamed glass. Within the phenomenological formulation of the problem it is necessary to consider three-dimensional temperature field in the charge of foam-glass and inside the metal mold for foaming. It is necessary to consider the nonstationarity of the process and dynamics of change in macrovisiontm values. It is also worth noting that in the conditions of heat treatment of charge materials occurs difficult the heat transfer. The distribution of temperature fields in the foam glass material is from near-surface regions of the charge to the center. The first objective of the study is to find and describe the distribution of temperature fields in the volume of the foam glass of the charge to reflect changes in microphysically parameters in foam glass batch due to the gradual formation of porosity of the material of the charge from the periphery to the center. The second task is to find conditions for the uniform formation of the pore volume of the material. The paper presents a boundaryvalue problem of heat transfer in foam glass material for the metal mold on the x coordinate. This illustration of temperature field distribution inside the metal mold for foaming.

Modelling of heat transfer in composite bodies reinforced with tubes with incompressible liquid coolant moving in laminar regime

The equations were obtained for description of heat transfer in composite bodies with reinforcement with a set of smooth tubes with pumping of incompressible liquid coolant. The appropriate boundary-value problem of heat transfer was formulated with the following qualitative analysis. The steady temperature fields in cylindrical shells with spiral-shaped tube reinforcement (with liquid coolant flow) were simulated. The influence on the temperature fields from the side of reinforcement geometry parameters, flow direction and velocity, tubes cross sections was studied. It was found that these characteristics allow significant variation of temperature field in its gradients within the composite item: this open ways for effective control of temperature fields.

Determination of the relaxation time of a heat flux

A method for determining the relaxation time of a heat flux is suggested for some nonlinear boundary-value problems of heat transfer. Modern representations of the applied theory of dynamical systems are employed.