Nonstationary Temperature Field Research Articles

Analysis of the thermomechanical behavior of a three-layer rectangular plate of the ceramic-metal-ceramic structure due to non-stationary convective heating

A rectangular isotropic layered plate is considered, which is convectively heated by the external environment. The thermal stress state of the plate is determined in two stages. At the first stage, the nonstationary temperature field is determined from the ratios of the non-stationary thermal conductivity problem. At the second stage, using the five-modal mathematical model of the shear theory of thermoelasticity, the parameters of the stress-strain state are determined.

RESIDUAL - STRESS AND TEMPERATURE FIELDS IN SURFACE TESTING: FINITE-ELEMENT ANALYSIS

Numerous advancements have been made to treat part surfacing, however, the presence of surface imperfections resulting from finishing processes has raised concerns about their potential to serve as stress concentrators. To address this concern, the present study utilized the power of the finite element method and cutting-edge software applications. The main aim of the study is to evaluate the stress-strain condition of material surfaces post-finishing, leveraging the comprehensive capabilities offered by these software systems. A significant component of the investigation centered on the influence of non-stationary temperature fields, as monitored by dynamic thermoelements, on the stress-strain dynamics within material surfaces. Visualization techniques were employed to depict the specified field functions, revealing notable variations in temperature distribution. The findings demonstrated that the standard function identified the highest temperature area within the 3-7-4 node segment, while the alternative function pinpointed it within the 4-node segment, indicated by the red area. These outcomes highlight the valuable role of non-stationary temperature fields in balancing the mechanical and physical aspects of the finishing process. This study contributes significant insights into the post-finishing stress-strain state of material surfaces, emphasizing the potential advantages of using modern software systems for in-depth exploration.

MATHEMATICAL MODELING OF THE NON-STATIONARY THERMAL STATE OF A COMPOSITE COATING OF CLOSE TO EQUIMOLAR COMPOSITION DURING LASER REMELTING

Based on assumptions and limitations, a mathematical model of the non-stationary thermal state of a composite coating during laser remelting on a metal substrate to obtain an alloy of equimolar or close to equimolar composition has been developed. The model includes the boundary value problem of calculating the nonstationary thermal state of the temperature distribution in the solid, two-phase and liquid regions, considering the heat release of crystallization according to the theory of a quasi-equilibrium two-phase zone in the presence of porosity of a mixture of metal powders. Based on the mathematical model, the computer program “Composite coating thermal state” was created, which allows to determine the non-stationary temperature distribution in the formed coating and substrate, the depth of penetration of the high-entropy coating layer, to evaluate the shrinkage of the molten coating under different technological conditions: laser power, the diameter of its focal spot, as well as the speed of movement along the surface of the processed material. The created program also allows to determine the dynamics of the position of two-dimensional liquidus and solidus lines for each metal included in the mixture. Using the created program, a computer simulation of the process of unsteady heating of a mixture of three metal powders in the same mass fractions: nickel, chromium and iron was carried out. Non-stationary temperature fields in the composite coating are obtained, considering its penetration and heating of the substrate. The depth of penetration of all metals, including the most low-melting one, was determined during laser remelting on a metal substrate in the production of a high-entropy alloy. The practical significance of the developed computer model lies in its use to predict the penetrationdepth of a composite coating under specified technological modes of laser remelting. At the same time, its adaptation is necessary, based on experimental data on the porosity and thickness of the coating before and after melting of simple metal systems with similar thermophysical properties.

Mathematical Modeling of the Heat Transfer Process in Spherical Objects with Flat, Cylindrical and Spherical Defects

This paper proposes a method for determining the optimal parameters for the thermal testing of plant tissues of fruits and vegetables containing surface and subsurface defects in the form of areas of plant tissues with different thermophysical characteristics. Based on well-known mathematical models for objects of predominantly flat, cylindrical and spherical shapes containing flat, spherical and cylindrical regions of defects, numerical solutions of three-dimensional, non-stationary temperature fields were found, making it possible to measure the power and time of the thermal exposure of the sample surface to the radiation from infrared lamps using the finite element method. This made it possible to ensure the reliable detection of a temperature contrast of up to 4 °C between the defect and defect-free regions of the test object using modern thermal imaging cameras. In this case, subsurface defects can be detected at a depth of up to 3 mm from the surface. To determine the parameters of mathematical models of temperature fields, such as thermal conductivity and a coefficient of the thermal diffusivity of plant tissues, a new method of a pulsed heat flux from a flat heater is proposed; this differs in the method of processing experimental data and makes it possible to determine the required characteristics with high accuracy during the active stage of the experiment in a period not exceeding 1–3 min.

Qualitative Properties of the Solution of a Conjugate Problem of Thermal Convection

The joint convection of two viscous heat-conducting liquids in a three-dimensional layer bounded by flat solid walls was studied. The upper wall is thermally insulated, and the lower wall has a non-stationary temperature field. The liquids are immiscible and separated by a flat interface with complex conjugation conditions set on it. The evolution of this system in each liquid was described by the Oberbeck–Boussinesq equations. The solution of the problem was sought for velocities that are linear in two coordinates and temperature fields that are quadratic functions of the same coordinates. Thus, the problem was reduced to a system of 10 nonlinear integro-differential equations. Its conjugate and inverse nature is determined by the four functions of time. Integral redefinition conditions were set to find them. The physical meaning of the integral conditions is the closeness of the flow. The inverse initial-boundary value problem describes convection near the temperature extremum point on the lower solid wall in a two-layer system. For small Marangoni numbers, the problem was approximated linearly (the Marangoni number is analogous to the Reynolds number in the Navier–Stokes equations). Using the obtained a priori estimates, sufficient conditions were identified for the non-stationary solution to become a stationary one over time.

Analysis of non-stationary temperature field generated by a shaftless screw conveyor heated by Joule–Lenz effect

Analysis of non-stationary temperature field generated by a shaftless screw conveyor heated by Joule–Lenz effect

Constructing a physical-mathematical model of grain mass self-heating by a rod site of rectangular cross-section

This paper considers the issue related to improving the energy and resource efficiency of the process of storing raw materials of plant origin, namely, preventing self-heating of grain masses in elevator silos. It was noted that the effectiveness of the analysis of self-heating of grain mass increases with the use of mathematical models of temperature fields of grain mass during storage together with data obtained experimentally. A physical-mathematical model has been built that describes a two-dimensional localized non-stationary temperature field of seed material generated by a homogeneous rod cell with a rectangular cross-section. A technique for accelerating the convergence of the series is proposed for the constructed analytical solution, which is based on the selection and analytical calculation of the sum of the component of slow convergence. The adequacy of the physical-mathematical model has been proven by calculations and by comparing the temperature of the self-heating site, obtained theoretically, and the temperature obtained under industrial setting. The established temperature kinetics of grain mass volumes during storage, obtained experimentally and theoretically, correlate with each other in the duration range from 0 to 30 days with a correlation coefficient of at least 0.98. This proves the possibility of applying forecasts of the temperature of self-heating sites in the volume of grain mass, obtained by using the physical-mathematical model built, under industrial setting. A limitation of the study is that the model is not universal. It is another stage on the way to a universal model. A limitation of the study is that for storage periods of more than 30 days, a new excess temperature forecast must be made

Нестаціонарна математична модель розподілу температур в шарах соняч-ної панелі

This paper presents the results of mathematical modeling of non-stationary temperature fields in a typical solar panel under real environmental conditions. The mathematical model is based on a system of nonlinear ordinary differential equations with corresponding initial and boundary conditions. The model takes into account radiation losses from the surface of the panel, which are determined by the Stefan–Boltzmann law, and convective losses due to free and forced convection. The solar flux density was considered constant, but its value depended on the solar panel setting angle. The temperature dependence of the solar cell efficiency was calculated using a standard method. A computational algorithm was developed in C++ using standard mathematical libraries with a linearization of the system of ordinary differential equations. The results were visualized using the gnuplot graphing utility. The temperature distribution in each of the solar panel layers was obtained as a function of the ambient temperature. It was found that an increase in the ambient temperature leads to a significant decrease, up to 40%, in the solar panel efficiency. With increasing ambient temperature, the time of transition to steady operation increases. The solar panel temperature was related to the blackness degree of the protective glass. It was shown that in the Kirchhoff approximation it is necessary that the blackness degree of the selective coating of the protective glass be a maximum, which reduces the temperature of the system and increases its efficiency. The solar panel temperature was related to the wind speed. It was shown that the convective losses increase with the wind speed, which has a favorable effect on the solar panel temperature regime. The results of the study showed the effect of various external environmental factors on the temperature regime of a solar panel and a way to maximize its efficiency by optimizing its parameters. The results may be used in the development and production of improved solar panels with minimum temperature effects on their efficiency.

METHOD OF CALCULATING THE UNSTATIONARY TEMPERATURE FIELD PARTS OF THE SPHERICAL FORM OF THE STRUCTURE FLIGHT APPARATUS OF UNMANNED AVIATION COMPLEXES

The design of unmanned aircraft vehicles during operation is exposed to significant temperature effects, which causes changes in the dielectric characteristics of radio technical elements and can lead to failures of on-board radio electronic equipment, as a result of which the task of determining the amount of temperature change in the compartments where the radio electronic equipment is located is performed. At the same time, some external elements of the aircraft vehicle can have complex structures with shapes close to spherical and different thicknesses in each cross-sectional structure.
 There is a need to develop a method for calculating the non-stationary temperature field with the purpose of finding out the real conditions in which all the elements of the aircraft structure work, which would help to determine how the temperature of the structure changes during any flight. At the same time, it is necessary to take into account the three dimensions of temperature gradients on spherical parts of structures of various shapes, namely nose part, rounded wing and others. In them, as a rule, each cross-section of the wall has its own thickness and, according to each cross-section, the temperature distribution along the thickness of the wall will correspond, that is, it is necessary to ensure the redistribution of temperature along the structural element, the calculation of which month. In addition, it is necessary to note that the wall of the aircraft can be multi-layered and the properties of its material can change along with the change in temperature. Considering the fact that it is impossible to take into account all the listed features by analytical methods, when choosing a calculation method, it will be advisable to stop at numerical methods.
 One of the most well-known numerical methods is the finite difference method with an implicit calculation scheme, which has an indisputable advantage for modeling - absolute stability with sufficient changes in time and coordinate steps. We will use the level of thermal conductivity in spherical coordinates in order to increase the accuracy of the calculation, for which solution, after finding out the boundary conditions, we will perform a one-dimensional calculation of the temperature by thickness in each mesh section of the structure, and also perform a calculation of the two-dimensional "heat flow" along the solid between the points, that are located on the same thickness, but have a temperature difference. Thus, when calculating the temperature field, the sphericity and multi-lay redness of the structural elements is taken into account, and the property of the material of the aircraft structure changes depending on the temperature.

The Influence of Pressure on Local Heat Transfer Rate under the Vapor Bubbles during Pool Boiling

This paper presents the results of an experimental study on the evolution of a nonstationary temperature field during ethanol pool boiling in a pressure range of 12–101.2 kPa. Experimental data were obtained using infrared thermography with high temporal and spatial resolutions, which made it possible to reconstruct the distribution of the heat flux density and to study the influence of pressure reduction on the local heat transfer rate in the vicinity of the triple contact line under vapor bubbles for the first time. It is shown that, for all studied pressures, a significant heat flux density is removed from the heating surface due to microlayer evaporation, which exceeds the input heat power by a factor of 3.3–27.7, depending on the pressure. Meanwhile, the heat transfer rate in the area of the microlayer evaporation significantly decreases with the pressure reduction. In particular, the local heat flux density averaged over the microlayer area decreases by four times as the pressure decreases from 101.3 kPa to 12 kPa. Estimates of the microlayer profile based on the heat conduction equation were made, which showed the significant increase in the microlayer thickness with the pressure reduction.

Measurement of the thermal diffusivity of optical materials and products by a new thermographic express method that does not require cutting samples from bulk

Thermal diffusivity a and thermal conductivity λ are important for many building, structural and functional material applications. They determine the intensity of heat transfer, the quality of thermal insulation, the rate of heating / cooling, reaching a stationary mode, and the efficiency of power equipment. In laser technology, the radiation strength of the optical components of the system depends upon them, and in laser technologies with material removal they determine the speed and quality of processing. Most methods for measuring a and λ in solid materials require cutting out samples of a certain geometry, which makes them unsuitable for testing finished products. The paper proposes and describes an express method for determining a and λ in translucent materials, which does not require cutting a sample from a controlled object. It consists in the analysis of a non-stationary temperature field on the surface of the test object using a high-speed thermal imaging camera. The unsteady heating spot was created by a focused laser beam. It was switched on abruptly and operated in the mode of continuous irradiation with a constant intensity during the entire time of measurements. Heat propagated from this spot to the periphery, creating a non-stationary temperature field containing information about a and λ. The a value was extracted from the primary data using original algorithms and software. A thermal imager, as a recorder of a dynamic temperature field, provides a number of advantages – non-contact, high speed and a large amount of information (each of the many hundreds of thousands of pixels of a professional thermal imager matrix is a temperature sensor in a small surface area). Measurements of a and λ in semitransparent materials of laser optics have their own specifics. The low radiation absorption coefficient and the possible curvature of the surface (for example, in lenses) require special measures, which are described in the article. Due to the large amount of information contained in the dynamic patterns of the thermal field and the possibility of averaging over a large data array, the RMS of the thermal diffusivity measurement does not exceed 2 %.

Study of the Thermomechanics of the Additive Manufacturing Process of Biocompatible Products Subject to the Viscoelastic Behavior of the Functional Material Polyetheretherketone

This study considers the problem of numerical modeling of the PEEK product’s 3D printing using the FDM technology. The aim of the study is to verify the adequacy of the use of a thermoviscoelastic model for numerical computations of the PEEK deposition process and to develop an algorithm for calculating this process. The Prony model is used to describe the thermoviscoelastic behavior of the material under study; the temperature-time shift is described by the Williams–Landel–Ferry function (WLF). To obtain the values of the material constants of the relaxation function, first, we used data from other authors; however, after their substitution into the numerical simulation, it was not possible to obtain results close to the full-scale experiment. Therefore, realized our own DMA experiment. The algorithm was developed and implemented in the ANSYS package to calculate non-stationary temperature fields and the stress–strain state of the structure during its layer-by-layer deposition. To solve these problems, the technology of “killing” and subsequent “aliving” of the PEEK material, implemented in the ANSYS package, is used. The numerical algorithm is verified with the results of an experiment on printing samples from PEEK. A good consistency of the calculated data with the experiment is shown.

Determination of non-stationary temperature fields in a thermosensitive half-space

Determination of non-stationary temperature fields in a thermosensitive half-space

Development of a Methodology for Calculating the Stress State and Resource of a Hydrogen Generator Using the Finite Element Method

An experimental stand was created to study the thermobaric and chemical influence of hydrogen on the identification of hydrocarbon production. The said stand allows to reproduce chemical-technological processes as close as possible to real formation ones. This stand makes it possible to study the kinetics of not only hydrogen, thermobaric and chemical effects, but also other thermal gas chemical processes, including hydrogen generation. The main element of the experimental stand is a hydrogen generator, the components of which work at high pressures and temperatures under conditions of hydrogen embrittlement of mechanical properties and an aggressive environment that causes corrosion of its inner surface. Based on this, the development of a methodology for calculating the thermal stress state of the generator, its strength under hydrogen embrittlement conditions, and its resource becomes relevant. Based on the finite element method, a methodology for calculating non-stationary temperature fields and the thermal stress state that occur in the hydrogen generator during thermobaric and chemical processes of varying intensity is proposed. The methodology allows to take into account the features of the geometry of the structure, the time-varying temperature and pressure distributions of the reaction products, the temperature dependence of the thermophysical and mechanical properties of the hydrogen generator material. Thanks to the application of the developed software, a study of the hydrogen generator thermal stress state during two real thermobaric and chemical processes of different intensity was carried out. Graphs of temperature and pressure changes of the reaction products of hydroreactive substances in the generator over time, which were registered during the experiment conduction, were used. The distribution of non-stationary temperature fields and stresses in the hydrogen generator elements was obtained. Areas of maximum load of generator elements are defined. It was established that during the flow of the studied thermobaric and chemical processes, pressure makes a greater contribution to the thermal stress state. The obtained results and the developed theory and software can be used in the study of generators of other designs with other thermobaric and chemical processes occurring in them.

Three-dimensional phase separation under a nonstationary temperature field

Pattern formation via nonequilibrium dynamical paths has been the focus of much recent attention. An example is phase separation under the action of a nonstationary temperature field. Under directional quenching (DQ), where a region at some ``quenched'' temperature spreads in one direction over time, it has been found that a variety of patterns (random droplet, lamellar, and columnar patterns) may be formed by controlling the dynamics of the quenching front in two dimensions. Although a similarly rich phenomenology may be expected in three dimensions (3D), DQ in 3D would require temperature control in bulk, which is difficult to realize. Instead of DQ, we fix the temperature gradient through the slab, and control of the surface temperature of both sides of the slab (gradient cooling, GC). It seems similar to DQ and it is significantly easier to realize experimentally. Here, we compare the mechanism of the phase separation in DQ with that in GC. It is found that no columnar pattern is formed in GC. It is also revealed that a pattern formation mechanism in GC is clearly different from conventional DQ.

Nonstationary Temperature Fields in Piecewise Homogeneous Strips with Regard for the Frictional Heat Generation

Nonstationary Temperature Fields in Piecewise Homogeneous Strips with Regard for the Frictional Heat Generation

Analyzing the fire performance of concrete columns and slabs under loading and using options, preventing explosive spalling to ensure the pre-set fire resistance

Introduction. The authors focus on preventing the explosive spalling of concrete and the fireproofing of reinforced concrete structures. The relevance of this issue is explained by the insufficient number of fire tests of such structures under loading and thermal engineering calculations, needed for an objective analysis of testing results.Goal and objectives. The authors analyze the results of a series of fire tests, involving concrete columns and slabs with and without polypropylene microfiber, if no fireproofing is applied, as well as the results of the same tests involving the same items fireproofed by plates or plaster.Methods. The fire resistance of full-scale specimens of concrete was evaluated according to a standardized testing in a fire furnace under loading. It encompasses additional thermocouple measurements used to make a thermal engineering analysis. The analysis entailed both one- and two-dimensional problem formulations, methods and programmes for the numerical computation of non-stationary temperature fields in fireproof structures.Results. New data, obtained in the course of the fire experiments, show the efficiency of the polypropylene microfiber used to prevent the explosive spalling of concrete. The fire resistance limit is R 120 and R 150 under constant static loading. The fire resistance limit of similar structures, fireproofed by PROSASK Firepanel plates or IGNIS LIGHT plaster, was demonstrated. The specimens show the efficiency of methods and programmes for the one- and two-dimensional numerical analysis of non-stationary temperature fields in fireproof structures. The calculation results are presented for various fireproofing options.Conclusions. The testing results and their thermal analysis represent important items of information necessary to ensure the fire safety and the pre-set fire resistance of concrete structures under loading. They can also be used to outline the development pattern of this experimental and theoretical research project. The efficiency of thermal engineering calculations as a tool for evaluating fire protection parameters and the fire resistance of concrete structures is demonstrated, also as an option to reduce the number of expensive fire tests.

Modeling the Temperature Field in Frozen Soil under Buildings in the City of Salekhard Taking into Account Temperature Monitoring

Most residential buildings and capital structures in the permafrost zone are constructed on the principle of maintaining the frozen state of the foundation soils. The changing climate and the increasing anthropogenic impact on the environment lead to changes in the boundaries of permafrost. These changes are especially relevant in the areas of piling foundations of residential buildings and other engineering structures located in the northern regions since they can lead to serious accidents caused by the degradation of permafrost and decrease the bearing capacity of the soil in such areas. Therefore, organization of temperature monitoring and forecasting of temperature changes in the soil under the buildings is an actual problem. To solve this problem, we use computer simulation methods of three-dimensional nonstationary thermal fields in the soil in combination with real-time monitoring of the temperature of the soil in thermometric wells. The developed approach is verified by using the temperature monitoring data for a specific residential building in the city of Salekhard. Comparison of the results of numerical calculations with experimental data showed good agreement. Using the developed computer software, nonstationary temperature fields under this building are obtained and, on this basis, the bearing capacities of all piles are calculated and a forecast of their changes in the future is given. To avoid decreasing the bearing capacity of piles it is necessary to prevent the degradation of permafrost and to supply the thermal stabilization of the soil. The proposed approach, based on a combination of the soil temperature monitoring and computer modeling methods, can be used to improve geotechnical monitoring methods.

Modeling and Investigation of Nonstationary Pressure and Temperature Fields in a Deformable Formation During the Filtration of a Gas–Condensate Mixture

Modeling and Investigation of Nonstationary Pressure and Temperature Fields in a Deformable Formation During the Filtration of a Gas–Condensate Mixture

The effect of thermal insulation of the lining on the heat exchange of rotating apparatuses

Rotary kilns are used in many industries to process bulk raw materials. In the building materials industry, rotary kilns are widely used for heat treatment. However, the fuel utilization factor in rotary kilns is extremely low. Thus, the bulk of cement clinker is fired in furnaces, the thermal efficiency of which does not exceed 55-60%. Therefore, the task of increasing the efficiency of such units is extremely relevant. In operating furnaces, heat losses to the environment only through the furnace body reach 20-25% of the total heat of combustion. In this case, one of the main factors determining the thermal efficiency of furnace operation is the value of thermal resistance of lining.
 The aim of the work is to study the evolution and temperature changes in the rotary kiln lining made of shaped refractory to reduce heat losses to the environment and improve the efficiency by increasing the thermal resistance of the lining. The increase in thermal resistance is achieved by changing the shape of the refractory by creating appropriate cells and introducing additional fibrous insulating material into them.
 A mathematical model and software have been developed and numerical calculations have been carried out to determine non-stationary temperature fields in the lining with a thermal insulating element and to substantiate the choice of an appropriate thermal insulating fibrous material.
 Analyzing the calculation results, it is possible to conclude about the expediency of using a lining with increased thermal resistance. The use of this technical solution makes it possible to reduce heat losses through the housing by 18-24%, to increase the amount of transferred material in the working zone by 1.5-8% due to the creation of an appropriate temperature field in the working volume, and to reduce the mass of the lining and the furnace as a whole. and increase the energy efficiency of the thermal unit.
 The presence of cells with additional thermal insulation contributes to the emergence of thermal pulsations having oscillatory character and affecting the intensification of heat and mass exchange processes, which in general contributes to the performance of the thermal unit.
 A significant advantage of this method is also the fact that increasing the energy efficiency of the furnace does not require additional fuel consumption, increasing the temperature or increasing the enthalpy of the combustion products.