Modeling Of Heat Transfer Processes Research Articles

Design of the Blast Furnace Wall Structure Made of Efficient Materials. Part 4. Calculation Examples

This work is part of a series of articles under the general title The structural design of the blast furnace wall from efficient materials [1–3]. In part 1, Problem statement and calculation prerequisites, typical multilayer enclosing structures of a blast furnace are considered. The layers that make up these structures are described. The main attention is paid to the lining layer. The process of iron smelting and temperature conditions in the characteristic layers of the internal environment of the furnace is briefly described. Based on the theory of A.V. Lykov, the initial equations describing the interrelated transfer of heat and mass in a solid are analyzed in relation to the task – an adequate description of the processes for the purpose of further rational design of the multilayer enclosing structure of the blast furnace. A priori the enclosing structure is considered from a mathematical point of view as the unlimited plate. In part 2, Solving boundary value problems of heat transfer, boundary value problems of heat transfer in individual layers of a structure with different boundary conditions are considered, their solutions, which are basic when developing a mathematical model of a non-stationary heat transfer process in a multi-layer enclosing structure, are given. Part 3 presents a mathematical model of the heat transfer process in the enclosing structure and an algorithm for its implementation. The proposed mathematical model makes it possible to solve a large number of problems. Part 4 presents a number of examples of calculating the heat transfer process in a multilayer blast furnace enclosing structure. The results obtained correlate with the results obtained by other authors, this makes it possible to conclude that the new mathematical model is suitable for solving the problem of rational design of the enclosing structure, as well as to simulate situations that occur at any time interval of operation of the blast furnace enclosure.

Search the optimal ratio of system’s component reliability parameters and the heat capacity of prosumers in the district heating system

The paper presents a methodology for ensuring the reliability of heat supply to prosumer connected to a district heating system, by using the heat capacity of its own heat source and optimization of failure rates of system components. To solve this problem, a mathematical formalization is developed, within which a markov random process, a flow distribution model of the theory of hydraulic circuits, nodal reliability indices, and simplified models of heat transfer processes in heat supply to consumers are used. A case study is considered based on a test scheme of district heating system with prosumer, an analysis of the results obtained is carried out, conclusions and directions for the further research on the subject are formulated.

Basic model of heat transfer process in a solid with spherical inclusion absorbing penetrating radiation

Basic model of heat transfer process in a solid with spherical inclusion absorbing penetrating radiation

Лабораторное моделирование в задачах городской климатологии

The paper presents a new approach to the problems of urban climatology, which is based on a laboratory modeling of heat transfer processes in the urban landscape conditions. As an experimental model, we used a three-dimensional layout of the central part of Perm, which takes into account the complex terrain, location and height of buildings on an area of five square kilometers. As an idealized model configuration we considered the nocturnal cooling process of megapolis. The process of cooling of the city model surface after prolonged heating by infrared radiation was studied. The key issue is dependence of the heat transfer on the type of urban structure. The influence of the building density on the cooling process of the layout surface was studied. The comparison was made for two areas with 70 and 90 percent of open area. It was shown that an increase in the number of buildings has influence on the cooling process, which is probably connected with variation of convective circulation and decreasing of the ventilation efficiency. However, stagnant zones with high temperatures in areas of high building density were found for both cases.

Генерация суперконтинуума в режиме филаментации в водяной капле с наночастицами серебра при низкой температуре

The supercontinuum generation in water droplets with nanoparticles of citrate silver in the temperature range of 2–22 °C, as well as in the ice droplets frozen to −15.0 °C, has been studied. It was found that the intensity of the supercontinuum emission under the excitation by a train of femtosecond laser pulses exponentially decays along the droplet diameter and it increases linearly with increasing NP concentration. The emission spectrum of supercontinuum in water droplet with NPs and the generation of localized plasmons with fluorescence at the 430 nm wavelength was studied. The movement of a heat wave along the diameter of a small frozen drop with a speed of 190 mm / s accompanying exponentially decaying supercontinuum radiation was recorded. The modeling of heat transfer processes in the frozen droplet during the formation of a heat wave has been carried out.

Modelling of heat transfer process in non-vacuum electron beam additive manufacturing with CuSi3 alloy wire

Non-vacuum electron beam wire feed deposition is a new technology in the family of additive technologies. It has some advantages in comparison with the laser one, especially for materials with great reflection ability, such as copper alloys. The suggested model is for assist determination of the optimal modes of processing. It considers heat transfer processes in the substrate and wire and also surface formation of the deposited layers. A wire can be feed along the process direction as well as from a side position. The equation of the liquid phase equilibrium in the gravity field is used to analyze the mechanism of formation of the bead surface profile. The proposed method allows determining the shape of the wall surface of the product with satisfactory accuracy. The position of the wire tip greatly affects both the shape and the size of the melt pool and its temperature. Increasing the wire feed rate leads not only to an increase in the cross-sectional area and the height of the deposited layers but also to a decrease in the width of the wall. Therefore, special attention should be paid to the selection of the wire feed rate.

Математичне моделювання процесів теплообміну при дискретно-імпульсному введенні енергії

Математичне моделювання процесів теплообміну при дискретно-імпульсному введенні енергії

Non integer order, discrete, state space model of heat transfer process using Grünwald-Letnikov operator

Non integer order, discrete, state space model of heat transfer process using Grünwald-Letnikov operator

Numerical Modelling of Heat Transfer in Convector’s Pipes by ABAQUS

The paper presents method for implementation of numerical modelling of heat transfer process between the water flow and the internal surface of a “water-air” convector’s pipes. The convector is a heat consumer in a reversible heat pump installation. To implement the CFD simulations, which are part of the numerical modelling of the processes, the ABAQUS software has been used. The main features and results from the simulations have been analysed. The method includes experimental investigations aiming determination of the boundary conditions for CFD simulation. The distribution of temperature, pressure and velocity in the fluid flowing through the pipe have been investigated. The results of the investigation of the temperature distribution present reduced heat transfer intensity in pipe’s sections, characterized by higher local hydraulic resistances.

Experimental validation data for CFD of heat transfer processes in a heat exchanger thermosyphon type with complex geometry

The paper explores the validation of experimental studies by means of numerical modelling of heat transfer processes occurring in a two-phase thermosyphon air heater. The object analysed is an air heater, used for the utilisation of the heat from flue gases emitted by a steam generator running on solid fuel with nominal load of 125 t/h, and temperature of the flue gases at nominal load 220C. The experimental study performed shows heat transfer coefficients of the evaporation and condensation zones of hfgas = 104.9 and hfgas = 84.9 W(m2 · K) respectively, and a reduction of the exhaust gas temperature down to 184°C. The numerical study pertains to a thermosyphon tube with complex geometry. Three zones can be distinguished for the air heater in question. In the evaporation zone the tube is inclined at 30 degrees in the direction of the flue gasses, in addition to the inclines of the adiabatic zone – 30 degrees, and the evaporation zone of the thermosyphon – 90 degrees to the horizon. The commercial software Ansys Fluent was used to perform the numerical calculations.

НОВЫЙ ПОДХОД К МОДЕЛИРОВАНИЮ ПРОЦЕССА ФОРМИРОВАНИЯ ТЕПЛОВОГО РЕЖИМА ТЕРМОСИФОНОВ БОЛЬШИХ РАЗМЕРОВ ДЛЯ ИСПОЛЬЗОВАНИЯ ГЕОТЕРМАЛЬНОЙ ТЕПЛОТЫ

Актуальность исследования обоснована необходимостью разработки математических моделей теплофизических процессов, протекающих в термосифонах, существенно менее сложных, по сравнению с известными (в которых решаются сложные задачи гидродинамики для парового канала), но в то же время обеспечивающих возможность адекватного прогностического моделирования процессов теплопереноса в термосифонах и определения их основных характеристик (температур, тепловых потоков, скоростей испарения), необходимых для создания систем теплоснабжения с использованием геотермальной и петротермальной энергии глубинных слоев земли при передаче теплоты системой термосифонов большой высоты. Цель: апробация нового подхода к описанию процессов теплопереноса в термосифонах, являющихся основными элементами системы извлечения теплоты глубинных слоев земли (геотермальной и петротермальной энергии) путем сравнения результатов математического моделирования температур в рамках новой модели в характерных точках слоя теплоносителя и результатов экспериментальных исследований. Объект: замкнутый двухфазный термосифон. Метод. Краевая задача математической физики решалась методом конечных разностей. Результаты. На основании анализа и обобщения результатов экспериментальных исследований разработан новый подход к математическому моделированию процесса формирования теплового режима термосифонов большой высоты для использования геотермальной теплоты. Сформулирована математическая модель, описывающая теплоперенос в слое теплоносителя на нижней крышке термосифона и обеспечивающая возможность достоверного прогноза скоростей испарения (или кипения) теплоносителя. Модель отличается от известных описанием не только теплопроводности, но и процесса естественной конвекции в слое теплоносителя. Численные исследования выполнены на пространственной сетке 36×101, шаг по времени изменялся в диапазоне от 10–3 до 10–6 с. Рассматривался диапазон тепловых потоков q, соответствующих условиям интенсивного испарения на свободной поверхности слоя теплоносителя. Проведено сравнение температур в точке, расположенной на оси симметрии термосифона на расстоянии 6 мм от поверхности его нижней крышки, полученных при проведении численного анализа и установленных в экспериментах. В качестве теплоносителя рассматривался Н-пентан – низкокипящая жидкость, которая может использоваться в термосифонах при относительно низкой (до 40 °С) температуре скальных пород или воды. Установлено хорошее соответствие результатов численного моделирования температурных полей в области анализа и экспериментов. Установлено, что свободная конвекция в слое теплоносителя при достаточно высоких тепловых потоках к нижней поверхности термосифона играет важную роль в формировании температурного поля жидкости и скорости ее испарения со свободной поверхности. Разработанный подход может быть использован при анализе систем геотермального и петротермального теплоснабжения при извлечении теплоты из глубинных слоев земли с использованием группы термосифонов большой высоты.

On the issue of mathematical modeling of rotary kiln operation in order to reduce fuel consumption

In accordance with the operation principle of the rotary kiln of limestone and its shortcomings, the authors developed the foundations of a mathematical model. The ultimate goal of building algorithms for the proposed method is to reduce fuel consumption when using a rotary kiln. The paper proposes to use a mathematical model based on the method of energy balances. The scientific novelty is that for a rotary kiln for the first time it is proposed to use the method of energy balances by heating zones, depending on the type of fuel burned. The procedure of inputting initial data for mathematical modeling of heat transfer processes allows us to identify the largest heat fluxes in various zones of the furnace. After that, an optimization procedure is carried out using, among other things, objective functions, as well as nonlinear programming. In the end, such calculation algorithms allow us to make recommendations to reduce heat losses in a rotary kiln and a refrigerator, as well as to reduce specific fuel consumption.

Application of mathematical modeling to optimize the operation of a tubular oil heating furnace

An energy balancing scheme has been developed for building a mathematical model of a tubular furnace for heating oil in accordance with the principle of its operation. This will allow taking into account all the heat fluxes, and the result of the work will be a reduction in fuel consumption for the tube furnace. The use of a particular calculation scheme depends on the nature of the task and the features of the boundary conditions of heat transfer. The main factors when choosing a calculation scheme are the accuracy and duration of the calculation. The scientific novelty is that for a tubular heating furnace for the first time it is proposed to use the method of energy balances in the chambers of radiation and convection. The practical significance of the work is to reduce fuel consumption for a tube furnace, as well as the possibility of utilizing the heat of oil refining products when building a mathematical model of a distillation column. The calculation algorithm using the energy balances method for mathematical modeling of heat transfer processes allows balance equations for all furnace sections, including the radiation chamber and the convection chamber. After which several successive approximations are carried out using linear programming. In addition, there are technological solutions to optimize fuel use.

INVESTIGATION OF THE EFFECT OF A THERMAL ISLAND IN KHARKIV

Problem. One of the main problems that attracts the attention of researchers is a change in the urban microclimate, which is commonly referred to as the «effect of the urban heat island». Such an effect has already been investigated in many cities, but for cities in post-Soviet countries they have not yet been conducted. Goal. The goal of this work is to detect the effect of the heat island in Kharkiv and its research. Methodology. A mathematical modeling was carried out to evaluate design decisions aimed at improving the heat island's appearance in the city, including simulation of air flow, heat transfer and radiation equation. The flow of buildings and constructions within the city with allowance for heat transfer is characterized by unsteadiness, energy non-equilibrium, and large-scale diffusion, which is conditioned by the presence of large coherent structures. The calculation is made on the basis of solving the non-stationary Reynolds-averaged Navier–Stokes equations. Results. The picture of changes in the temperature of air at different times during the day is obtained. The confirmation of the presence of the effect of the "heat island" in Kharkiv, with a temperature increase of 2-4 C , in comparison with the rural, has been obtained. The influence of roughness on the patterns of the flow in the field of urban development is analyzed. The roughness was given by the value of ks=29,6 m. There are changes in temperature near the surface of the earth and buildings, which apparently is associated with a decrease in velocity near the surfaces. Originality. For the first time, calculations were made for Kharkiv, which made it possible to determine the heat island manifestation and to improve the microclimate research. Practical value. Mathematical modeling of heat transfer processes taking into account solar radiation allows us to investigate the interrelated problems of urban physics. In particular, the optimization of air temperature in large cities should be based on the results obtained, which will allow to more accurately determine the temperature fields and reduce their impact on human health.

Second-order two-temperature model of heat transfer processes in a thin metal film subjected to an ultrashort laser pulse

Thermal processes in domain of thin metal film subjected to an ultrashort laser pulse are considered. A mathematical description of the process discussed is based on the system of four equations. Two of them describe the electrons and lattice temperature, while third and fourth equations represent the generalized Fourier law, it means the dependencies between the electrons (lattice) heat flux and the electrons (lattice) temperature gradient. In the generalized Fourier law the heat fluxes are delayed in relation to the temperature gradients which consequently causes the appearance of heat fluxes time derivatives in the appropriate equations. Depending on the order of the generalized Fourier law expansion into the Taylor series, the first- and the second-order model can be obtained. In contrast to the commonly used first-order model, here the second-order two-temperature model is proposed. The problem is solved using the implicit scheme of the finite difference method. The examples of computations are also presented. It turns out that for the low laser intensities the results obtained using the first- and the second-order models are very similar.

Investigations of heat transfer and hydrodynamics in heat exchangers with compact arrangements of tubes

The paper presents the main results of theoretical and experimental investigation of hydrodynamics and heat transfer processes in heat exchangers with a compact arrangement of small diameter tubes. A new design of heat exchangers is proposed, in which there are no gaps and shifting in the direction of transverse to the flow between adjacent tubes.Numerical modeling of heat transfer processes and hydrodynamics for turbulent flow of heat-carrier and experimental investigations of hydrodynamic and heat transfer characteristics of new designs of heat exchangers with compact bundles of small diameter tubes are carried out. The analysis results demonstrated that the proposed designs of shell-and-tube heat exchangers have dimensions of 1.7–2 times smaller and mass is 10–15% lower compared to heat exchangers of traditional designs with the same heat power. The findings in this work may provide a theoretical basis for the selection of optimal designs of shell-and-tube heat exchangers with tube bundles.

Improving Recuperative Air Heater to Enlarge its Application Area Provided that the Dust-Laden Heat Carrier is Used

The aim of the work is the development of highly efficient heat exchange equipment with an optimal flow of heat transfer media for heating air with the smudged flue gases that are released during various technological processes. To achieve this goal, the following work was used in the work: calculation methods for studying heat transfer; physical modeling of heat transfer processes; methods of mathematical statistics; methods of the theory of similarity; mathematical modeling of heat exchange between flue gases and air through loop tubes using an object-oriented programming environment Borland C++ Builder.The obtained results show that, with the correct choice of the coolant flow pattern, it is possible to heat air up to 500 ºС with a dusty coolant. The choice of the optimum design of the recuperator allows prolonging the period of effective operation. Advantage of the heater of the proposed design is the ability to carry out a stable heating of the combustion air, catching process dust, and prolong the effective operation of the air heater. The results of the solution of the tasks set in the work can be used to develop energy-saving complexes in the sphere of metallurgy and power engineering, for the development of energy-efficient complexes, highly efficient heat exchange equipment and systems for utilization of thermal secondary energy resources of high-temperature energy technological processes.

A Memory–Efficient Noninteger–Order Discrete–Time State–Space Model of a Heat Transfer Process

Abstract A new, state space, discrete-time, and memory-efficient model of a one-dimensional heat transfer process is proposed. The model is derived directly from a time-continuous, state-space semigroup one. Its discrete version is obtained via a continuous fraction expansion method applied to the solution of the state equation. Fundamental properties of the proposed model, such as decomposition, stability, accuracy and convergence, are also discussed. Results of experiments show that the model yields good accuracy in the sense of the mean square error, and its size is significantly smaller than that of the model employing the well-known power series expansion approximation.

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.

Modelling of heat transfer processes in film liquid devices when obtaining fresh water

Modelling of heat transfer processes in film liquid devices when obtaining fresh water