Modeling Of Heat Transfer Processes Research Articles

Mathematical modeling of heat exchange for efficient automated control systems

The article deals with the problem of mathematical modeling of heat transfer processes, taking into account a large number of factors affecting these processes and a variety of mathematical modeling methods. The article discusses the idea of developing a universal and flexible model that could quickly adapt to different initial modeling conditions and take into account various parameters for further use of the mathematical model in the synthesis of automatic control systems. The paper discusses the main aspects of mathematical modeling of heat transfer and the creation of a mathematical model in distributed heat exchanger parameters with the possibility of changing the properties and parameters of the equipment. The paper analyzes previous studies and identifies the problems of existing methods of mathematical modeling of heat transfer, such as lack of versatility, complexity, and insufficient accuracy. The paper goes on to review different approaches to mathematical modeling of heat transfer, such as models with a group of parameters, models in distributed parameters, and models based on artificial intelligence. The article provides an overview of model implementation methods and their advantages and disadvantages. Based on this analysis, the authors propose a new mathematical model of heat transfer in distributed parameters, which should be universal, easy to use, and accurate in accordance with the requirements of synthesizing automated control systems. The authors also outline the methodology for achieving this goal, which includes the implementation of the geometry of the heat exchanger, the implementation of conditions and mathematical modeling, as well as the study of the influence of parameters and the formation of transients. The general conclusion of the article is that the developed mathematical model of heat transfer can be used to synthesize automatic control systems for heat exchange processes in various industries.

Study the influence of the environment on heat transfer processes in sewing sheaths with heat-accumulating properties

In the article research results are presented, which aim to modeling of heat transfer processes in a system for evaluating the heat storage effect of combined cooling shells. Clothing and equipment corresponding to the type and activity of movements and work performed by a person are considered as a shell. To a certain extent, the task of compensating for excessive heat load is solved by special materials that are used in the manufacture of such shells. Such shells are multicomponent structures of materials from various fiber systems with the inclusion of ice modules. The main means of processes for evaluating and improving such technologies are mathematical modeling tools, in particular, heat transfer modeling in multilayer shells. The structure of a heat transfer model with the inclusion of a heat storage module in a fibrous sheath. To describe the heat transfer the mean radii of curvature of the geometric system “manheat-shielding shell” were calculated. The problem is considered when layers of various materials separate the external environment from ice. For the “man-clothing” section, the temperature field is calculated. The data obtained make it possible to evaluate the heat storage effect in combined cooling shells.

Concentration of CO2 in the Local Working Area during the Joint Operation of a Gas Infrared Heater and an Air-Exchange System

The formation of local areas in large buildings with regulated thermal conditions is an urgent task. The use of gas infrared heaters for this purpose raises questions on the utility of an air-exchange system and the monitoring of the combustion product concentration. In this study, the modeling of heat transfer processes on premises with a gas infrared heater and an air-exchange system was conducted. The carbon dioxide concentration in the local working area when using a light-type gas infrared heater was determined. The regularities of current formation for circulating air and combustion products on the premises at various air-exchange rates were analyzed. The profiles of CO2 temperatures and concentrations in the local working areas on the left and right of the equipment model are shown. The article makes a conclusion about the influence of air velocity from the air-exchange system based on average values of carbon dioxide concentration on the premises and in the local working area. The possibility of increasing the temperature in the local working area without exceeding the permissible CO2 concentrations (less than 1000 ppm) has been identified. The formulated approach allows us to predict the available modes of the air-exchange system to create the highest possible comfort heating parameters while maintaining an acceptable degree of air pollution from combustion products.

Symmetry Properties of Models for Reversible and Irreversible Thermodynamic Processes

The problem of formulating variational models for irreversible processes of media deformation is considered in this paper. For reversible processes, the introduction of variational models actually comes down to defining functionals with a given list of arguments of various tensor dimensions. For irreversible processes, an algorithm based on the principle of stationarity of the functional is incorrect. In this paper, to formulate a variational model of irreversible deformation processes with an expanded range of coupled effects, an approach is developed based on the idea of the introduction of the non-integrable variational forms that clearly separate dissipative processes from reversible deformation processes. The fundamental nature of the properties of symmetry and anti-symmetry of tensors of physical properties in relation to multi-indices characterizing independent arguments of bilinear forms in the variational formulation of models of thermomechanical processes has been established. For reversible processes, physical property tensors must necessarily be symmetric with respect to multi-indices. On the contrary, for irreversible thermomechanical processes, the tensors of physical properties that determine non-integrable variational forms must be antisymmetric with respect to the permutation of multi-indices. As a result, an algorithm for obtaining variational models of dissipative irreversible processes is proposed. This algorithm is based on determining the required number of dissipative channels and adding them to the known model of a reversible process. Dissipation channels are introduced as non-integrable variational forms that are linear in the variations of the arguments. The hydrodynamic models of Darcy, Navier–Stokes, and Brinkman are considered, each of which is determined by a different set of dissipation channels. As another example, a variational model of heat transfer processes is presented. The equations of heat conduction laws are obtained as compatibility equations by excluding the introduced thermal potential from the constitutive equations for temperature and heat flux. The Fourier and Maxwell–Cattaneo equations and the generalized heat conduction laws of Gaer–Krumhansl and Jeffrey are formulated.

BOUNDARY VALUE PROBLEM FOR THE EQUATION OF UNSTEADY THERMAL CONDUCTIVITY IN A NON-CYLINDRICAL REGION

The application of the method of decomposition by eigenfunctions of a self-adjoint differential operator to solving a non-stationary heat transfer problem with a phase transition in a non-automatic formulation under special initial conditions is presented for the example of the solidification process in a continuous medium. The one-dimensional problem is solved in spherical coordinates. Solving of the problem begins with its transformation to a problem in a domain with fixed boundaries, then a finite integral transformation with an unknown kernel is constructed to solve the transformed problem, the finding of which is associated with the formulation and solving of the corresponding spectral problem through degenerate hypergeometric functions. The eigenvalues and eigenfunctions are found, as well as the inversion formula for the introduced integral transformation, which makes it possible to write out an analytical solution to the problem. In the course of solving the problem, the parabolic law of motion of the interface of the two phases is established. Problems of this type arise in the mathematical modeling of heat transfer processes in construction, especially in permafrost areas, in oil and gas production during drilling and operation of wells, in metallurgy, etc.

BOUNDARY VALUE PROBLEM FOR THE EQUATION OF UNSTEADY THERMAL CONDUCTIVITY IN A NON-CYLINDRICAL REGION

The application of the method of decomposition by eigenfunctions of a self-adjoint differential operator to solving a non-stationary heat transfer problem with a phase transition in a non-automatic formulation under special initial conditions is presented for the example of the solidification process in a continuous medium. The one-dimensional problem is solved in spherical coordinates. Solving of the problem begins with its transformation to a problem in a domain with fixed boundaries, then a finite integral transformation with an unknown kernel is constructed to solve the transformed problem, the finding of which is associated with the formulation and solving of the corresponding spectral problem through degenerate hypergeometric functions. The eigenvalues and eigenfunctions are found, as well as the inversion formula for the introduced integral transformation, which makes it possible to write out an analytical solution to the problem. In the course of solving the problem, the parabolic law of motion of the interface of the two phases is established. Problems of this type arise in the mathematical modeling of heat transfer processes in construction, especially in permafrost areas, in oil and gas production during drilling and operation of wells, in metallurgy, etc.

Preparation of wells using an electrohydraulic drill and modeling of heat transfer processes in heat transfer elements of a heat pump

The article discusses the use of innovative electrohydraulic technology in the preparation of vertical ground heat exchangers to create heat supply using heat pumps. The discharge energy in the operating range varied E=900÷2600 J. The most economical mode of operation of the electrohydraulic installation is carried out with the following parameters: discharge voltage 30÷51 kV, capacitor bank capacity 2 µF and interelectrode distance 8÷15 mm. It is determined that the optimal energy of destruction of natural materials depends on their thickness. Based on the research, the limits of the electrophysical parameters of the approach were established, at which the concentrated destruction of hard rocks – the main stones ‒ begins. The effective amount of energy for the destruction of stones with a thickness of 53 mm is 900 J. For stones with a thickness of 78 mm, there should be 2600 J. If to increase the energy of the discharges to 1837 J, the process of complete destruction of the stones is underway. Using an electro hydraulic drill, we have prepared vertical wells up to 25 m deep. In the future, we have installed special temperature sensors along the length of the pipes, inside the well. Using a software product (Temp Keeper), data from temperature sensors are received in real time. This program allows to visually monitor temperature changes occurring at a local point. Temperature and time dependences are also obtained at coolant velocities of 0.2÷0.4 m/s. A significant decrease in the temperature in the well and at the outlet was observed at a coolant velocity of 0.35 m/s for one hour. The study conducted on the basis of the data obtained enables to achieve higher optimal drilling performance compared to conventional installations

Fractional discrete-continuous model of heat transfer process

Fractional discrete-continuous model of heat transfer process

MATHEMATICAL MODELING AND EXPERIMENTAL INVESTIGATION OF THE PROCESS OF NON-STATIONARY HEAT TRANSFER IN A BLOCK FOAM GLASS SAMPLE AT THE ANNEALING STAGE

The specifics of the technology for the production of block foam glass are presented, the results of experimental studies of the properties of the material are presented, a method for improving production based on mathematical modeling of heat transfer processes is proposed. It is shown that the processes of high-temperature processing of foam glass make a key contribution to the formation of a high-quality porous structure, therefore, this area of ​​research needs the development of adequate methods for calculating the main macrophysical parameters based on the theory of heat transfer. A technique for checking the adequacy of the mathematical model of heat transfer is presented using the example of spontaneous cooling of a foam glass block. The entire procedure for checking the adequacy of the mathematical model was carried out in three stages. At the first stage, the degree of validation of the model is assessed, functional dependencies with the results of an experimental study based on the Pearson determination coefficient. The main stage includes the evaluation of the confidence intervals of the experimental data and the discussion of the convergence of the results of the analytical calculation with the results of the experimental data. The final stage, at which a comprehensive assessment of the adequacy of the mathematical model is given, includes both the results of the preparatory and the main stages. The results of the study showed that it can be concluded that the calculated data have sufficient convergence with the experimental data and indicate the adequacy of the developed mathematical model of heat transfer.

Numerical modelling of heat transfer processes in coal-fired vortex furnace with bottom-port secondary blowing: ecological performance comparison for two types of coal fuel

The work is devoted to numerical 3D modelling of aerodynamics and pulverized-coal combustion processes in a novel vortex furnace of a boiler unit for thermal power stations. A prospective retrofitting design of this furnace, featuring additional tangential blowing at the bottom part of the vortex combustion chamber, has been studied. The firing regimes using two types of siberian coal (black coal, brown coal) are considered. Numerical results for the studied combustion regimes in the modified vortex furnace are presented, including the fields of velocity, temperature, species and dispersed phase concentrations, and the comparative analysis of NOx emissions for two types of coal.

Analysis of the Influence of the Gas Infrared Heater and Equipment Element Relative Positions on Industrial Premises Thermal Conditions

The creation of local heated areas in large-sized premises using systems based on gas infrared heaters has recently become the most rational alternative in terms of energy efficiency. However, the lack of information about the thermal characteristics in such areas limits the effective application of these systems. To determine the main thermal parameters characterizing the scheduled thermal conditions in heated local working areas of industrial premises, experimental and mathematical modeling of heat transfer processes in a closed area with the presence of equipment in it was carried out. The experimental area was equipped with a gas infrared heater and a model of the equipment (a horizontally oriented panel). The system of equations of thermal conductivity, radiant heat transfer, as well as energy and Navier–Stokes was solved by the finite element method. A significant influence of the equipment position on the temperature field and the air movement hydrodynamics in the local working area has been established. The equipment presence in the room intensifies the air movement due to thermal convection and, as a result, a more uniform temperature distribution over the local working area was obtained. Analysis of the obtained results shows the possibility to control the temperature fields’ formation in local working areas during the gas infrared heater operation by varying the position and configuration of the equipment in the room.

The micro-explosive fragmentation criteria of two-liquid droplets

This research work presents the results of the modeling of heat transfer processes before micro-explosion of two-liquid droplets under intense heating in a gaseous medium. The work relies on three formulations that differ in the disintegration criteria: (i) overheating of the water/fuel interface above the temperature of the onset of explosive boiling; (ii) the critical radius of the bubble before disintegration; (iii) overpressure in the vapor film. The droplet disintegration delay times were determined as functions of the temperature of the external gaseous medium, the initial droplet size and the components concentration. The theoretical values of the droplet disintegration delay times were compared with those recorded in the experiments. The limits of applicability of the three approaches to the estimation of the delay times of micro-explosion of two-liquid droplets were singled out.

Free Convection and Heat Transfer in Porous Ground Massif during Ground Heat Exchanger Operation.

Heat pumps are the ideal solution for powering new passive and low-energy buildings, as geothermal resources provide buildings with heat and electricity almost continuously throughout the year. Among geothermal technologies, heat pump systems with vertical well heat exchangers have been recognized as one of the most energy-efficient solutions for space heating and cooling in residential and commercial buildings. A large number of scientific studies have been devoted to the study of heat transfer in and around the ground heat exchanger. The vast majority of them were performed by numerical simulation of heat transfer processes in the soil massif–heat pump system. To analyze the efficiency of a ground heat exchanger, it is fundamentally important to take into account the main factors that can affect heat transfer processes in the soil and the external environment of vertical ground heat exchangers. In this work, numerical simulation methods were used to describe a mathematical model of heat transfer processes in a porous soil massif and a U-shaped vertical heat exchanger. The purpose of these studies is to determine the influence of the filtration properties of the soil as a porous medium on the performance characteristics of soil heat exchangers. To study these problems, numerical modeling of hydrodynamic processes and heat transfer in a soil massif was performed under the condition that the pores were filled only with liquid. The influence of the filtration properties of the soil as a porous medium on the characteristics of the operation of a soil heat exchanger was studied. The dependence of the energy characteristics of the operation of a soil heat exchanger and a heat pump on a medium with which the pores are filled, as well as on the porosity of the soil and the size of its particles, was determined.

MODELING OF HEAT EXCHANGE PROCESSES IN THE TECHNOLOGICAL SYSTEM FOR THE RECYCLING OF METALLIC TUNGSTEN RODS

A computational experiment was carried out to study heat exchange processes. They flow in the installation for the production of metal powders, by spraying tungsten rods. This unit uses a special cooling system. The thermophysical problem is solved by one of the numerous methods of mathematical modeling of heat transfer processes. The finite element method was used, which is implemented in the CFD software package. The design and principle of operation of the spindle unit of the installation for sputtering tungsten rods are analyzed. It is represented by the object of mathematical modeling of heat transfer processes. The temperature distributions in the characteristic studied working areas of the parts of the installation units are obtained. Based on the simulation results in the CFD software package, the calculation results were analyzed. The results showed the high efficiency of the developed cooling system for the installation for spraying metal powders.

Impact of complex relief on heat transfer in urban area

The paper presents results of a laboratory modeling of heat transfer processes in the idealized urban landscape conditions. As an experimental model, we used a three-dimensional layout of the central part of Perm city (the area of five square kilometers) at the scale of 1:4000. The estimation of governing parameters was done using eddy transfer coefficients which are common for the atmospheric boundary layer. The process of cooling of the city model surface after prolonged heating by infrared radiation was studied. The key issue is the time dependence of the surface temperature on the type of urban structure. We focused on the influence of building density and artificial relief on the cooling process of the layout surface. Two separate stages of cooling were revealed, namely, relatively short period of a fast cooling and long time relaxation period. On the base of correlation coefficients it was shown that a buildings density has substantial influence on the fast stage and during this stage the correlation coefficient is larger than 0.4. The correlation at the late stage of cooling is weak. The duration of the fast cooling stage shows even stronger correlation (above 0.5) with building density.

Mathematical simulation of heat transfer in nonaccessible channels of heat supply system network

High values of standard heat losses in the heating networks of central heat supply systems indicate an opportunity to increase their energy efficiency. Сurrently available mathematical models of heat networks are described in the scientific studies of Polovnikov V.Yu., Kuznetsov G.V., Tarasevich E.I. But they do not solve the problem of assessing changes of the thermal networks state when energy-saving measures are used. The purpose of the study is to determine the permissible heat perception of the device collector for utilization of heat losses in the heating main channel. The study is based on the development and research of mathematical models of heat exchange processes in the heat supply network. A mathematical modeling method is chosen to search for acceptable operating modes of this device. The method can help to determine properly changes in the operation of the heat network. A descriptive mathematical model with distributed parameters based on differential equations with partial derivatives is used in modeling heat transfer processes in the heat network. The model is implemented using the finite element method. The authors propose a device for the utilization of heat losses in the heating channel. The authors have developed mathematical models of heat transfer processes in heat networks of underground trench laying in nonaccessible channels in a traditional design with the use of a heat-reflecting screen and combined action of the network and the device for the utilization of heat losses in the heat channel. Based on the comparison of the calculation results, the permissible heat perception value of the device collector for the utilization of heat losses has been determined. It equals to 90 % of the initial thermal losses. Mathematical models have been verified by comparing the results obtained and the experimental data with an error of less than 6 %. The developed mathematical models allow us to study the influence of heat perception of the device collector and the heat-reflecting screen on the operating mode of the heat network. It can be used to determine the geometric parameters of the collector of the device.

ВИКОРИСТАННЯ ВКЛАДЕНИХ АДАПТИВНИХ СІТОК ДЛЯ МОДЕЛЮВАННЯ ПРОЦЕСІВ ТЕПЛОПЕРЕДАЧІ В ІНФОРМАЦІЙНО-КЕРУЮЧИХ СИСТЕМАХ СКЛАДНИХ ЗРАЗКІВ ТЕХНІКИ

Modeling of processes on the use of adaptive grids for information and control systems of complex samples of equipment is offered. Application in the simulation of various natural phenomena and processes have obtained differential equations with partial derivatives. The principle of replacing the continuous domain of the unknown function by a discrete set of points (grid) is the basis of numerical methods for solving such equations. The complex solution of such problems is a definite scientific problem, the solution of which determines the accuracy of the numerical solution in areas where the gradient of the desired function reaches large values, significantly affects the accuracy of the solution throughout the region. The study considers the method of constructing nested adaptive difference grids for modeling heat transfer processes in information-control systems of complex samples of equipment, which are condensed in zones of rapid change of the desired function to solve two-dimensional nonstationary equation of thermal conductivity. Existing methods of constructing non-uniform grids before calculations, based on finding possible zones of high gradients are not effective in non-stationary problems, where these zones can change their position over time. The proposed algorithm for finding zones with significant gradients of the desired function in the process of the task analyzes the behavior of the function, controls the error and builds a time variable and a non-uniform difference grid. This significantly reduces the machine time required to solve problems with significant gradients in some areas of the computational domain. The solution of the problem for the main and nested grids can be performed in parallel, which will further reduce the time to solve when using multi-core systems. Keywords: computer model, finite difference method, difference mesh, nested mesh, modeling of heat transfer processes, information and control systems.

Formation of a dendrite structure in crystals NiFeGaCo alloy in the process of growing by the Stepanov method

The process of growing crystals of the NiFeGaCo alloy by the Stepanov method has been developed. It was found that the structural perfection is disturbed by the formation of dendrites, which are distributed inhomogeneously both along the length and in the cross sections of the crystals. The blocking effect of the dendrites on growth crystals of the martensite phase, which appears when the samples are cooled to the temperature of the transition of the crystal to the martensite state, is found. The elemental composition of dendritic formations was studied and it was shown that the iron content in the dendrite is approximately 30% higher, and the gallium content is 40% lower than in the matrix. Based on the modeling of heat transfer processes in the real growth zone, taking into account the experiments performed, recommendations were obtained for suppressing the formation of dendrites Keywords: Dendritic structure, shape memory alloys, Stepanov's method.

Modelling of Heat Transfer Processes in Heat Exchangers for Cardiopulmonary Bypass

A model of the heat exchange process in the heat exchanger of the cardiopulmonary bypass device is proposed which allows for automation of the process of temperature regulation in the cardiopulmonary bypass with an accuracy of ±1 °C during cardiac surgery under controlled cooling and warming of the patient’s heart and brain. The purpose of this research is to create a concept and model of the temperature control circuit using the MSC Easy5 system, the creation of mathematical models of blocks of the temperature control circuit, and the description of the principle of temperature control in the cardiopulmonary bypass circuit. The model of the temperature control loop in the heat exchanger of the heart-lung machine was created using the MSC Easy5 system with a programmable microcontroller. The microcontroller implements a specialized temperature control algorithm in the C language. The model allows the creation of a full-fledged virtual prototype of a temperature control device in a heat exchanger, and helps to conduct virtual tests of the developed device at the design stage. The model identifies control system flaws and influences decisions made before producing an official prototype of the product.

Numerical Model for Heat Transfer Processes in Dry Ash Conveyors

Abstract The dry handling of bottom ash from coal-fired power plants has become more and more important in recent years due to a lack of water availability at the location of power plants or for environmental reasons. Hence, it is crucial that a sufficient cooling of the bottom ash can be ensured by the dry cooling air. In this work, a numerical model for the assessment of heat transfer processes in dry ash conveyors is developed and implemented via the software wolframmathematica. The model uses a newly introduced representative geometric quantity for ash particle geometry. In addition to the ash, cooling air is considered as an own phase for which a temperature solution is obtained. A numerical example, considering geometrical and operational data of an existing facility, shows that the main heat transfer between the ash and the cooling air takes place in the ash hopper, where convective heat transfer from ash to cooling air outweighs the effects from coke combustion and radiation from the boiler outlet area. The convective heat transfer in the ash hopper predominantly depends on the geometrical appearance, i.e., size and shape, of the particles, the grain density, as well as on the falling time/velocity. Conservatism of the calculation approach is indicated based on comparison of computed temperatures with measured data and literature values. The derived model can be used in future designs and projections of dry ash handling systems.