Mathematical Model Of Thermal Processes Research Articles

Mathematical modeling of thermal processes during "cassette" crystallization of chalcogenides

A new, relatively simple and highly efficient modification of the directional melt crystallization method in the form of a multi-cassette process has been considered. This study is based on Russian Patents and technological studies conducted at National Research and Technological University MISiS. As a result, mathematical models of a multi-cassette method have been developed for 3D radiation and conduction analysis of thermal processes in the entire volume of the heating unit and 2D analysis of convection and conduction heat exchange in a separate cassette. Parameters have been calculated on the basis of these mathematical models for clarifying the effect of heating unit component arrangement and dimensions on the formation of thermal fields in cassette units, the effect of vertical homogeneity of heat supply to the cassette unit and heating power reduction rate during crystallization on the shape of the crystallization front, as well as the effect of small asymmetry in cassette design and violation of cassette bottom cooling homogeneity on convection and asymmetrical heat transfer. Application of the conductive and radiative heat exchange model to the entire heating unit has allowed us to calculate process parameters on the basis of which we have analyzed the effect of heating unit components, their arrangement and temperature on the heat exchange conditions at the cassette unit boundaries. Application of the convective and conductive model to one growth cassette has shown that asymmetrical design and boundary thermal conditions as well as unstable vertical temperature gradient lead to the formation of convection vortices and substantial crystallization front deviation from planar shape. Calculations on the basis of the convective mass exchange model have shown that an increase in the crystallization rate by one order of magnitude greatly increases the tellurium flow into the crystal thus substantially altering the melt composition in the vicinity of the crystallization front and hence serving as a potential origin of dendrite growth. The authenticity of the calculation results has been verified in a number of tests aimed at analyzing the effect of heat and mass transport on crystallization front shape for cassette cooling rates that are typical of polycrystalline bismuth telluride growth processes.

Temperature modes of the contactor contacts during the test for the limiting breaking capacity

The processes of electric arc quenching of an electromagnetic contactor during testing for ultimate breaking capacity are considered. The conditions for facilitating the successful arc quenching when turning off the limiting currents are shown: by reducing the phase shift between current and voltage, by reducing the amplitude of the restriking and recovery voltages. The processes of anode heating during arcing (heat saturation mode), after the change of polarity and transition of the current through zero, processes on the cathode in the temperature equalization mode are considered. The mathematical models of cathode thermal processes adressed the heat fluxes of the ionic component and evaporation. The mathematical models of anode thermal processes in the temperature equalization mode took into account the heat fluxes of the ionic component, thermionic emission, and evaporation. The calculations were carried out for the averaged values of thermophysical coefficients for copper, since the arc base moves from the contacts to the contact holders, which are made of copper or its alloys. The calculation results showed that the used mathematical models of thermal processes are appropriate both for the cathode and for the anode. This was confirmed by the results of previously performed and published experimental and theoretical studies of thermal processes at the switching contacts of electrical devices.

A method for solving a boundary value problem in a multilayered area

A mathematical model of thermal process in an electrical machine was built as an example, presented as a three-layer cylinder where internal heat sources operate in one of the layers and heat is submitted to the other two by means of heat conduction. A method of solving the boundary-value problems for heat conduction equation in a complex area – a multi-layered cylinder with internal heat sources operating in one part of the layers and external ones in another part, is proposed. A method of problem solution in conditions of uncertainty of one of the boundary condition at the layers interface with conductive heat exchange between the layers is reviewed. The principle of method lies in the averaging of temperature distributions radially in the internal layers. As a result of transformations at the layers interface a boundary condition of the impedance-type conjugation appears. The analytical and numeric-analytical solutions of simplified problems were obtained.

Mathematical modeling of thermal processes in small-size DC electric machines

This article considers small-size electric machines used in various fields of technology, from medical electrical equipment to complex mechatronic systems as part of spacecraft. To obtain satisfactory weight and size parameters of electric machines, it is necessary to take into account many factors that limit the possibility of reduction the machine size. The high energy of modern permanent magnets (250 - 300 kJ/m3) makes it possible to obtain the best weight and dimensons indicators in the designs of brushless direct current machines with excitation from permanent magnets, taking into account the influence of thermal processes.

Unsteady model of the hydration process of a reinforced concrete product at software-controlled heating

The development of mathematical models for design of the thermal technology equipment intended for accelerated hydration of concrete products is an urgent task of industrial heat power engineering. The introduction of mathematical modeling methods can reduce the time and the resources spent for the development of technological regimes that reduce energy consumption in the production of building structures and, ultimately, in the construction of buildings and structures for various purposes. There is not yet a generally accepted mathematical model of thermal processes occurring in thermal technological installations in the case of accelerated hardening of a three-dimensional concrete object. The purpose of this work is to develop an unsteady model of the concrete hydration process applied to a symmetrical three-dimensional reinforced concrete product at software-controlled heating. By using the numerical finite-volume method in the case of a 0.3 × 0.3 ×0.3 mcube, a three-dimensional feld of hydration in a concrete object at a given operation mode of a heater is calculated. The following heating mode was used: “heating–maintaining at a constant temperature–cooling”. The dependences of a temperature difference between reinforced and non-reinforced cubic products on the hardening time at the corresponding space points in the direction from the surface to the center of the product have been obtained. By the example of the numerical simulation results, it is shown that the evolution of the hydration degree at these points during the hardening of non-reinforced concrete differs from the hardening of reinforced concrete. The time dependences of heat treatment of a rate of temperature change and the hydration coefficient at the selected points of a product are presented. The obtained results are analyzed.

Optimization of a Hybrid Power Plant on the Basis of the Modeling of Thermal Processes in it

Consideration has been given to the problem of optimization of the structure and parameters of an autonomous hybrid power plant operating from renewable energy sources (sun and wind) and methanol fuel cells using mathematical models of thermal processes in it. Examples of practical application of the developed models have been provided. Results of simulation experiments on development of the indicated power plant have been given.

Identification of mathematical models of thermal processes with reconciled measurement results

One of the basic issues in science and technology is modelling. The mathematical model can be developed on the basis of physical laws (analytical model) and as an approximation of the measured data (empirical model). The advantage of using analytical models is the ability to accurately understand the process mechanism. Most often, these processes are characterized by a high degree of complexity which makes it impossible to develop a model using only the process laws of physics. In such cases, empirical models are most frequently used, which, compared to analytical models, are easier to develop. However, the scope of their applicability is limited to the operating parameters for which the model was calibrated. Good results are obtained by combining analytical and empirical models. The prediction quality may be enhanced by the use of Advanced Data Validation and Reconciliation method (DVR) in order to increase the reliability of the measurements which were used for identification of model parameters. The article presents the examples of identification of the analytical–empirical models on the basis of reconciled measure results. The identification of mathematical models was presented with example of double-pressure HRSG and multi-fuel boiler. Appropriate conclusions have also been formulated.

Creation of Model and Calculation of Thermal Processes in the Ring Graphite Electrode of the Plasmatron

This paper presents the theoretical and experimental material obtained in the study of the erosion and thermal state of the ring graphite electrode for a plasmatron. Thermal processes in graphite electrodes of plasmatrons are quite complex and multifaceted. A mathematical model of thermal processes that occur at the ring electrodes of plasmatrones has been developed. The mathematical model is based on the differential heat conduction equation for a ring electrode in cylindrical coordinates. With the use of this mathematical model, the inverse problem of heat conduction is solved: determination of the regularities of the heat exchange process by the temperatures of individual points on a solid surface. An experimental study of the temperature distribution at the end of the electrode and along the length of the electrode was carried out. Experiments have shown that the temperature on the side surfaces drops sharply towards the cold end of the electrode. When reducing the length of the electrode, the maximum temperature at the end decreases, and the temperature on the inner and outer edges of the electrode increases slightly. The most significant factors determining the temperature field at the end of the ring electrode are the power and size of the heat source. Comparison of the results of experimental studies and mathematical modeling showed a match with an acceptable degree of accuracy.

ENERGY EFFICIENCY OF LIFE PROTECTION OF SYSTEMS FOR RAILWAY VEHICLES

Passenger cars consume a fairly significant share of electricity to create comfortable conditions, when transporting passengers. The conducted studies of energy efficiency improvement taking into account the results of mathematical modeling of thermal processes it was established that during the design of passenger cars designers do not take into account a number of factors, affecting energy efficiency life support systems for passenger cars. In the calculations of the thermal balance of the car only heat is taken into account, supplied by heating pipes for more accurate calculations thermal balance of a passenger car the given heat must be taken into account in the thermal balance of the car. Experimental measurements confirmed presence zones of temperature fields with different temperature modes, separated by a decorative ceiling in which the zone of constructive ceiling cavity overheats over the normative indicators. This leads to increased heat loss through the roof of the carriage. In particular, it has been established that the proposed modernization on increasing the energy efficiency of the heating system can be implemented at relatively low cost, in the conditions of existing carriages depot, which will reduce energy consumption for heating 13.4% or UAH 25.9 million for a year. Improved mathematical model non-stationary thermal regime of a passenger car allows comprehensive analysis thermal processes of a passenger car, taking into account its constructive changes by mathematical experiment. Thus, this study will allow not only to increase energy efficiency but also provides grounds for reducing the power of the heating system by at least 10%, which will reduce the metal content of the heating system and, as a consequence of the reduction of the wagon's packaging, reduction of power of electric devices, wires, and the number of electrically heated TENs will decrease.

Математичне моделювання теплових процесів двохшнекового прес-екструдера з індукційним нагріванням

Математичне моделювання теплових процесів двохшнекового прес-екструдера з індукційним нагріванням

Investigation of approximate models of experimental temperature characteristics of machines

This work is devoted to the investigation of various approaches to the approximation of experimental data and the creation of simulation mathematical models of thermal processes in machines with the aim of finding ways to reduce the time of their field tests and reducing the temperature error of the treatments. The main methods of research which the authors used in this work are: the full-scale thermal testing of machines; realization of various approaches at approximation of experimental temperature characteristics of machine tools by polynomial models; analysis and evaluation of modelling results (model quality) of the temperature characteristics of machines and their derivatives up to the third order in time. As a result of the performed researches, rational methods, type, parameters and complexity of simulation mathematical models of thermal processes in machine tools are proposed.

Development of the technique for restricting the propagation of fire in natural peat ecosystems

In order to reduce the scale of peat fires, we suggest using fire barriers made of mineralized materials. The incombustible materials are proposed, specifically sand and bentonite clay, to be used for filling up artificial slits cut in a peat layer. Construction of anti-fire barriers requires a one-time expenditure, in contrast to the existing techniques for fire prevention that require continuous pumping of water in order to increase moisture content in peat. Mathematical modeling of thermal processes in the system peat layer–fire barrier was performed. The time of reaching the dangerous temperature by the protected layer, for the barriers made of river sand with a thickness of 300 mm, and for those made of bentonite clay with a thickness of 180 mm, is not less than 1 day. Given this, we have proven the effectiveness of the proposed barriers. By using mathematical modeling of the processes of fire development, a parabolic dependence was built of the thickness of fire protection barrier b, mm, on time τ, hours, required to protect an object. We established parameters for regression dependences of thickness of a barrier on the time required to protect a peat layer. The result of present research is the proposed technique for designing fire protection barriers made of river sand and bentonite clay, based on the obtained patterns and regression dependences. Research results could be used in the process of designing fire protection barriers for actual peatlands

Mathematical modelling of thermal processes by the use of regression and neural models

Mathematical modelling of thermal processes by the use of regression and neural models

Mathematical modelling and analysis of thermometric diagnostics of electrical products

The actual problem is the diagnosis and monitoring of the technical condition of the machines in operation, as well as the forecasting of their technical condition. The complexity of the problem of condition controlling is that the most informative characteristics of the electrical products can not be accurately determined without the use of special measuring transducers, which considerably increases the test time and makes it difficult to carry out continuous monitoring. A promising direction in solving this problem is the use of sensorless methods. Implementing these methods is based on using as a source of information the working winding of the electrical product, the active component of the resistance of which is determined just before the measurement of the magnetic characteristic and then used as a constant value. In the process of testing, there is heating and, as a consequence, a change in the active component of the winding resistance, which causes an unacceptable errors in determining the electrical products state. In this article the mathematical model of thermal processes are developed and analysis of thermometric diagnostics of electrical products is carried out.

Mathematical model of thermal processes in a biogas plant

One of the promising areas of processing poultry and livestock waste is anaerobic digestion, which helps to prevent pollution of the natural environment, as well as to receive processing products such as gaseous fuel, biogas and highly effective biofertilizer. The use of plants for the production of biological gas as alternative sources of energy is largely determined by its design characteristics and the worked out technological regimes. The study was conducted with the aim of obtaining data on the effect of the main parameters of the biogas plant and the heat exchanger-agitator on the quality of its operation. This paper considers the thermal processes taking place in the biogas plant in which the mixing device and the heating element are combined into one unit, which allows heating and maintaining the given temperature regime more evenly due to the rotation of the heat exchanger and the transfer of biomass heat throughout the whole volume of the methane. As a result of theoretical studies of the processes of heat exchange and heat transfer taking place in the biogas plant, a mathematical model has been obtained that allows determining the distribution of the temperature of the biomass throughout the entire volume of the methane. It is established that the theoretical temperature homogeneity of the stirred medium is achieved by combining the heat exchanger and the mixing device into one unit, the design and technological parameters of which characterize the intensity of the forced motion of fermentable manure, while changing the value of thermal conductivity.

MODELING OF AN ADVANCED HEAT EXCHANGE UNIT WITH MICROCHANNELS FOR A COMBINED PHOTOENERGY SYSTEM

Purpose. Mathematical modeling of the heat exchange unit main parameters for photoenergy system based on general models with forced circulation of heat transfer fluid. Methodology. To determine the coefficient of heat transfer at a given coolant temperature and surfaces temperature necessary to determine the temperature gradient in the wall of the heat exchanger. Temperature gradients can be determined by solving the equation of energy, which depends on the distribution of the flow rate in the flow. In general, a solution of convective heat transfer fluid to flow along the plane comes to solution of the system of differential equations. Results. In the paper features of the selection of theoretical basis and mathematical modeling of thermal processes in the heat exchange unit for combination photoenergy system are presented. As a result of the simulation conducted we improve and develop high-efficiency heat exchange unit with microchannels. Testing of the proposed unit proved its high efficiency through the implementation of turbulent flow of coolant with heat transfer coefficient at 18 kW/(m 2 ×K). Analytical testing of the heat exchanger allowed showing that heat exchanger unit provides a stable operating temperature at less than 50 °C with the coolant flow rate is less than 0.3 m/s. Originality. Novelty of the proposed heat exchanger is in the optimal design of microchannels to improve the heat transfer coefficient. Practical value. The use of this heat exchanger will improve the quality and uniformity of cooling solar panels and reduce energy costs for circulation of fluid.

Математическое моделирование тепловых процессов и расчетная оптимизация режимов лазерной поверхностной обработки

Математическое моделирование тепловых процессов и расчетная оптимизация режимов лазерной поверхностной обработки

A simplified model for dynamic analysis of the indoor thermal environment of rooms with a Chinese kang

This paper uses thermodynamics equilibrium theory to develop a mathematical model for dynamic thermal processes pertaining to rooms with a Chinese kang (a heatable brick bed). The model is developed through analysis of the dynamic thermal equilibrium of indoor air temperature and the temperature of interior and exterior surfaces of the building envelopes of rooms with a kang. It is developed and solved using a thermal reaction coefficient. Based on data from a field test, a simplified mathematical model of thermal processes in such a room is presented. The model only takes into account the radiation heat transfer between the exterior surface of the kang's faceplate and the other interior surfaces of the building envelope, while ignoring the reciprocal radiation heat transfer between all other interior surfaces. A simplified mathematical model pertaining to the Chinese kang is also put forward. This model does not take into account the reciprocal radiation heat transfer between the interior surfaces of the Chinese kang. By combining these two models, the hourly values pertaining to indoor air temperature and exterior temperature of the kang's faceplate can be predicted for different burning modes of the Chinese kang. MATLAB was used for calculating the target temperatures and solving the thermal reaction coefficient. The model was validated by error analysis and correlation analysis, the result of which shows that this mathematical model can accurately predict various characteristics concerning the temperatures in a room with a Chinese kang.

THE DIAGNOSIS TECHNIQUE OF ABNORMAL HEATING OF POWER CAPACITORS

The existing system of protection and diagnostics are not able to detect abnormal heating of the power capacitors caused by its internal malfunction formation. The paper contains a proposal of a technique that enables to detect such heat at its early study. This technique consists of a hardware and an algorithms. The hardware consists of a microprocessor-based instrument developed by the author, of measuring transformers of current and of temperature sensors. This equipment must be connected to the condenser unit with a rated voltage of 380 V. In operation, the device performs continuous measurement of the surface temperature of the casing of each condenser, the temperature of the external environment, voltage and current from the power source. The measured values are used in the mathematical model of thermal processes that enables to calculate the temperature of the hottest point of each capacitor in real-time. Then the calculation of the intrinsic difference ΔΘ1° between the average temperature values of the dielectric and the base average value of this temperatures during the second day from the start of the measurements. If the Dq1 value exceeds the value of the absolute error of simulation, diagnostic signals of abnormal levels of heating, viz. low, medium, high and very high, are generated. It is also necessary to calculate the rate of change of ΔΘ1° and to consider the values obtained in the formation of hazard levels. For the low level and the average level of hazard the operation of diagnostic system with a visual signal is recommended, while for the high level of hazard it is recommended to use both visual and sound signals, and for the very high hazard level the capacitor ought to be turned off from the source. The algorithms have been developed heuristically. The final formation of the algorithms is possible only after the long-term operation of the proposed diagnosis system on real objects. The implementation of the developed system will reduce the probability of sudden failure of capacitor units and, correspondingly, will increase the reliability of power supply system of enterprise.

Thermal Features of the Module with Parabolic-Cylindric Solar Irradiation Concentrator

The work researched the thermal performance of the photovoltaic-thermal (PVT) cogeneration module with solar radiation parabolic-cylindrical concentrator. The advantage of this cogeneration module design is the possibility of both photovoltaic power generation and obtaining the thermal energy. These factors allow to increase the overall efficiency of solar energy conversion and to reduce the cost of produced energy. Research of PVT module thermal power characteristics using mathematical modeling of thermal processes and experimental measurements was carried out. Theoretical analysis of the module operation was based on the balance of incoming (solar), power dissipation, and utilizable energy flows and using similarity numbers (Nusselt, Prandtl, Reynolds). Experimental characteristics were studied under natural solar radiation. Parameters calculated by the balance of energy flows were consistent with the experimental data and have compliance with the accuracy better than 10% with similarity numbers calculations. The solar module showed in the experiment the maximum thermal power of 205 watts at 40 oC and thermal efficiency of 60%; when the water output temperature was 60 oC, the module delivers maximum output of 167 watts with thermal efficiency of 47 %.