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Автор: Grafiati

Опубліковано: 30 травня 2022

Оновлено: 31 травня 2022

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1

Levchenko, V., M. Kascheev, S. Dorokhovich, and A. Zaytsev. "NON-STATIONARY THREE-DIMENSIONAL TEMPERATURE FIELD IN A MULTILAYER CYLINDER." PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. SERIES: NUCLEAR AND REACTOR CONSTANTS 2020, no. 4 (December 26, 2020): 138–47. http://dx.doi.org/10.55176/2414-1038-2020-4-138-147.

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Анотація:

The problem of determining a non-stationary three-dimensional temperature field in a k-layer cylinder of length is solved. There is a symmetrically located cylindrical cavity in the center of this body. The absence of a cavity is a special case of the problem. In each layer, there are heat sources, depending on the coordinates and time. The initial temperature of the layers is a function of the coordinates. In the center of the body the symmetry condition is fulfilled. At the boundary of contact of the layers - ideal thermal contact: continuity of temperatures and heat flows. On the inner and outer side surfaces and ends, heat exchange occurs according to Newton's law with environments whose temperatures change over time according to an arbitrary law. The periodicity condition is set for the angle φ. The problem in this statement is solved for the first time. For the solution of the problem the following approach is used: by means of the method of finite integral transformations differential operations on longitudinal coordinate, angle and transverse coordinate are sequentially excluded, and the determination of time dependence of temperature is reduced to the solution of the ordinary differential equation of the first order.

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2

Anishchenko, Galina Ottovna, Vladimir Ivanovich Konokhov, and Denis Vladimirovich Lavinsky. "Heat generation in devices for magnetic-pulse processing of materials." Bulletin of the National Technical University «KhPI» Series: Dynamics and Strength of Machines, no. 2 (December 31, 2021): 123–26. http://dx.doi.org/10.20998/2078-9130.2021.2.249735.

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The problem of analysis of non-stationary heat generation due to the flow of electric current in devices for magnetic-pulse processing of materials is considered. An analysis of the available information sources led to the conclusion that a large number of studies in this area are devoted to the study of heat transfer processes during technological operations of induction heating. In other technological operations of magnetic-pulse processing of materials, heat release is also significant. In this case, a non-stationary inhomogeneous temperature field can lead to significant temperature deformations. This, in turn, can cause a loss in the performance of the device due to destruction or irreversible deformation. Adequate modeling of non-stationary temperature propagation in this case is an obligatory step in carrying out computational analysis in the process of designing technological devices. A general strategy is proposed for determining the propagation of a non-stationary temperature field in the presence of a non-stationary non-uniform electromagnetic field. The proposed strategy presupposes a general solution of the problems of the propagation of the electromagnetic field and the temperature field within the framework of a unified design scheme. The use of the finite element method is proposed as a numerical method. The finite element method, when used in such problems, allows one to draw up iterative procedures that can be used to take into account the nonlinear effects associated with the influence of temperature on the electro-physical properties of materials. The problem of sequential determination of a non-stationary, non-uniform electromagnetic field and a non-stationary temperature field in composite matrices intended for electromagnetic pressing of powders of super-strong refractory materials is considered. The distribution of some quantitative characteristics of the electromagnetic field, as well as the dependence of temperature on time are presented.

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3

Yevtushenko, A., and O. Ukhanska. "Non-stationary temperature field of discrete sliding contact of elastic bodies." Wear 176, no. 1 (July 1994): 19–23. http://dx.doi.org/10.1016/0043-1648(94)90192-9.

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4

MUSII, R. S., N. B. MELNYK, B. J. BANDYRSKII, L. V. HOSHKO, and V. K. SHYNDER. "DETERMINING NON-STATIONARY TEMPERATURE FIELD OF PRE-HEATED INHOMOGENEOUS ISOTROPIC CYLINDRICAL COVER." Applied Questions of Mathematical Modeling 3, no. 2-2 (2020): 202–11. http://dx.doi.org/10.32782/kntu2618-0340/2020.3.2-2.20.

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5

DAVLETSHIN, Filyus F., and Ramil F. SHARAFUTDINOV. "INVESTIGATION OF THE NON-STATIONARY TEMPERATURE FIELD IN A RESERVOIR WITH A HYDRAULIC FRACTURING BASED ON AN ANALYTICAL MODEL." Tyumen State University Herald. Physical and Mathematical Modeling. Oil, Gas, Energy 7, no. 3 (2021): 8–24. http://dx.doi.org/10.21684/2411-7978-2021-7-3-8-24.

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Анотація:

Currently, well temperature studies are widely used to solve various problems of control and monitoring of hydraulic fracturing. Temperature data measured in production wells during and after hydraulic fracturing provide important information about non-stationary filtration and thermal processes that are sensitive to fracture parameters — position and orientation, geometry and filtration characteristics. Mathematical models developed for calculating non-stationary pressure and temperature fields with known geometry and filtration-capacitive properties of the fracture and reservoir, in the general case, can be numerical and analytical. In the quantitative interpretation of temperature measurements and solving inverse problems for estimating fracture parameters, the speed of calculating the temperature field is important, in this regard, the development of analytical mathematical models of non-isothermal filtration in a reservior with a hydraulic fracturing is relevant. The paper presents the results of a study of a non-stationary formation temperature field in a reservoir with a hydraulic fracture based on an analytical model. The developed analytical model takes into account convective heat transfer, heat and mass transfer between the fracture and the formation, thermodynamic (adiabatic and Joule — Thomson) effects. To control the calculation correctness and adequacy of the temperature field, the analytical solution was compared with numerical calculations in the Ansys Fluent software package. The non-stationary temperature formation features of the fluid flowing into the well in the constant withdrawal mode at various parameters of the fracture (width and permeability) are investigated. It was found that the temperature of the fluid flowing into the well increases in inverse proportion to the width and permeability of the fracture, and in the first hour after putting the well into operation, negative dynamics of the flowing liquid temperature is observed, the duration of which increases with the growth of the fracture width.

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6

Kanafin, I. V., R. F. Sharafutdinov, M. F. Zakirov, and A. Sh Ramazanov. "RESEARCH OF NON-STATIONARY THERMAL FIELD IN RESERVOIRAND WELLBORE WITH MULTIPHASE FILTRATION." Oil and Gas Studies, no. 5 (November 1, 2017): 20–25. http://dx.doi.org/10.31660/0445-0108-2017-5-20-25.

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Анотація:

In the paper the mathematical formulation of a task of temperature filed in the wellbore and reservoir sys-tem with multiphase fluid filtration is considered. The mathematical models of two-phase non-isothermal filtration of fluid in porous media are described, which take into account non-stationary thermo hydrodynamic processes, barothermic effect, oil degassing when reservoir pressure lowers below saturation pressure. The mathematical models are developed for two-phase flow in vertical wellbore. The paper shows the results of numerical solution of formation of temperature field in reservoir and wellbore system and testing results on analytical solutions.

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7

Spassov, K. B. "Temperature Field Estimation Using the Kalman Filter in Non-Stationary Thermal Conductivity Problems." IFAC Proceedings Volumes 25, no. 15 (July 1992): 567–72. http://dx.doi.org/10.1016/s1474-6670(17)50693-x.

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8

Tatsii, R., and O. Pazen. "DETERMINATION OF NON-STATIONARY TEMPERATURE FIELD IN THE SYSTEM OF TWO SPHERICAL SHELL." Bulletin of Lviv State University of Life Safety 19 (October 2, 2019): 79–86. http://dx.doi.org/10.32447/20784643.19.2019.08.

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Анотація:

The main classification indicator, in terms of fire safety, is the degree of fire resistance of the house. Depending on this indicator normalize its surface, the area of development and distance to other buildings and structures. The de-gree of fire resistance of the house is determined by the limit of fire resistance of its building structures and the limit of the fire spread by these structures. Therefore, the value of the fire resistance limit of building constructions, which con-sists of a house, significantly affect its architectural solution and the parameters of construction in general. On this ba-sis, taking into account the approaches to ensuring normalized fire resistance limits of the design and the features of their behavior under high-temperature (fire) influence is very relevant.Most research on building constructions. The proposed work is devoted to the application of the direct method to the study of heat transfer processes in the system of two embedded spherical bodies – a ball in a sphere. It is assumed that there is an ideal thermal contact between the balls, and the law of temperature change on the outer surface is an arbitrary function of time, and evenly distributed over the surface of the ball. Consequently, isotherms inside this construction are concentric fields, that is, the problem is symmetric and is solved for the first time in such a statement. To solve such a problem, in parallel, the auxil-iary problem of determining the distribution of a non-stationary temperature field in a two-layer hollow spherical structure with a "extracted" sphere of sufficiently small radius is raised. In this case the symmetry condition of the original problem is replaced by the condition of the second kind on the inner surface of this construction. The implementation of the solution of the auxiliary problem is carried out by applying a reduction method using the concept of quasiderivatives. In the future, the Fourier scheme is used with the use of the modified eigenfunctions method. To find the solution of the original problem, the idea of the boundary transition is used by passing the radius of the withdrawn bullet to zero. It is established that in this approach all the eigenfunctions of the corresponding problem on the eigenvalues have no singularities at zero, which means that the solutions of the original problem are constrained throughout the design. The solution of this problem at zero temperature on the outer surface coincides with those known in the literature. To illustrate the proposed method, a model example of finding the temperature field distribution in a system of two spherical bodies with different thermophysical properties of materials is solved. The results of the calcu-lations are presented in the form of a table and a three-dimensional graph of temperature change, depending on the time and spatial coordinates. The generalization of the results obtained in the event of any finite number of nested balls is a purely technical problem, and not a fundamental one. Note that while changing the boundary condition of the first kind to any other boundary condition (for example, the third kind) does not affect the scheme of solving similar tasks. Since the general scheme of studying the distribution of temperature fields in multi-layered structures with an arbitrary number of layers in the presence of internal sources of heat is studied in detail, the setting and solving of such problems for the system of nested balls does not cause any difficulty.

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9

Latypov, I. I., L. A. Bigaeva, G. S. Mukhametshina, N. A. Shaikhutdinova, and A. Y. Gilev. "Analytical study of the non-stationary temperature field of a thermally thin plate." IOP Conference Series: Materials Science and Engineering 1155, no. 1 (June 1, 2021): 012007. http://dx.doi.org/10.1088/1757-899x/1155/1/012007.

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10

Mustari, Mustari, and Yuant Tiandho. "Thermodynamics of a Non-Stationary Black Hole Based on Generalized Uncertainty Principle." Journal of Physics: Theories and Applications 1, no. 2 (October 29, 2017): 127. http://dx.doi.org/10.20961/jphystheor-appl.v1i2.19308.

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Анотація:

In the general theory of relativity (GTR), black holes are defined as objects with very strong gravitational fields even light can not escape. Therefore, according to GTR black hole can be viewed as a non-thermodynamic object. The worldview of a black hole began to change since Hawking involves quantum field theory to study black holes and found that black holes have temperatures that analogous to black body radiation. In the theory of quantum gravity there is a term of the minimum length of an object known as the Planck length that demands a revision of Heisenberg's uncertainty principle into a Generalized Uncertainty Principle (GUP). Based on the relationship between the momentum uncertainty and the characteristic energy of the photons emitted by a black hole, the temperature and entropy of the non-stationary black hole (Vaidya-Bonner black hole) were calculated. The non-stationary black hole was chosen because it more realistic than static black holes to describe radiation phenomena. Because the black hole is dynamic then thermodynamics studies are conducted on both black hole horizons: the apparent horizon and its event horizon. The results showed that the dominant correction term of the temperature and entropy of the Vaidya-Bonner black hole are logarithmic.

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11

Цоцко, Віталій Іванович, Олександр Йосипович Дідоборець, and Олександр Миколайович Клєцков. "NON-STATIONARY SURFACE TEMPERATURE FIELD LAYER OF METAL WITH PERIODIC ENERGY ACTION ON SURFACE." Математичне моделювання, no. 2(43) (November 26, 2020): 33–43. http://dx.doi.org/10.31319/2519-8106.2(43)2020.219264.

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12

Mukin, Dmitrii, Ekaterina Valdaytseva, and Gleb Turichin. "Analytical Solution of the Non-Stationary Heat Conduction Problem in Thin-Walled Products during the Additive Manufacturing Process." Materials 14, no. 14 (July 20, 2021): 4049. http://dx.doi.org/10.3390/ma14144049.

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The work is devoted to the development of a model for calculating transient quasiperiodic temperature fields arising in the direct deposition process of thin walls with various configurations. The model allows calculating the temperature field, thermal cycles, temperature gradients, and the cooling rate in the wall during the direct deposition process at any time. The temperature field in the deposited wall is determined based on the analytical solution of the non-stationary heat conduction equation for a moving heat source, taking into account heat transfer to the environment. Heat accumulation and temperature change are calculated based on the superposition principle of transient temperature fields resulting from the heat source action at each pass. The proposed method for calculating temperature fields describes the heat-transfer process and heat accumulation in the wall with satisfactory accuracy. This was confirmed by comparisons with experimental thermocouple data. It takes into account the size of the wall and the substrate, the change in power from layer to layer, the pause time between passes, and the heat-source trajectory. In addition, this calculation method is easy to adapt to various additive manufacturing processes that use both laser and arc heat sources.

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13

Élesztős, Pavel, Roland Jančo, Ladislav Écsi, and Gregor Izrael. "Temperature and Stress Field Measurement at Friction-Stir Welding of an Aluminum Alloy Probe." Applied Mechanics and Materials 486 (December 2013): 96–101. http://dx.doi.org/10.4028/www.scientific.net/amm.486.96.

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The presented work is devoted to an experimental determination of a non-stationary temperature field during friction-stir welding using a thermo camera and thermocouples respectively. The aim of the measurements was to tune up the heat source originating from friction between the rotating tool and a stationary probe by finding appropriate parameters of an employed mathematical model. After having identified the parameters, the friction-stir welding simulation was carried out using an aluminium alloy probe. Strain measurements were also performed during welding at selected locations on the probe. The experimentally determined results have been compared with the results of the numerical simulations.

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14

Pankratov, V. M., M. A. Barulina, A. V. Golikov, E. V. Pankratova, and M. V. Efremov. "Practical modeling of non-stationary temperature fields of fiber-optic gyroscopes in space flight conditions." E3S Web of Conferences 224 (2020): 02007. http://dx.doi.org/10.1051/e3sconf/202022402007.

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Based on the mathematical model presented in the first part of this paper, specialized software was created and computer modeling of nonstationary inhomogeneous temperature fields in a fiber-optic gyroscope was performed. The simulation aimed to analyze the temperature distribution in the gyroscope structural elements, especially in the fiber-optic coil and the electronics unit, since temperature fluctuations in them are one of the main sources of device errors. To achieve this goal, a three-dimensional unsteady field was calculated in a fiber-optic gyroscope. Based on the results of computer modeling, comparative data on the temperature distribution in the gyroscope structural elements on earth and orbital flight conditions, and the degree of influence of space and zero-gravity conditions are obtained.

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15

Akhverdashvili, Robert, Aleksandr Gulkanov, and Konstantin Modestov. "Non-stationary temperature field of the heating device in the conditions of unsteady thermal field of the space." IOP Conference Series: Materials Science and Engineering 1030 (January 15, 2021): 012087. http://dx.doi.org/10.1088/1757-899x/1030/1/012087.

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16

Loik, Vasyl, Oleksandr Lazarenko, Taras Bojko, and Sergiy Vovk. "Research into non-stationary temperature field in the protected metallic structure under conditions of fire." Eastern-European Journal of Enterprise Technologies 5, no. 5 (89) (October 30, 2017): 11–20. http://dx.doi.org/10.15587/1729-4061.2017.112370.

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17

Bracun, Drago, Janez Diaci, and Janez Mozina. "Optodynamic measurement of a non-stationary temperature field in air by multiple laser-beam deflection." Measurement Science and Technology 12, no. 11 (October 19, 2001): 2009–14. http://dx.doi.org/10.1088/0957-0233/12/11/334.

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18

Vidin, Yu V., V. S. Zlobin, and A. A. Fedyaev. "Analytical method for calculating a non-stationary temperature field with a variable thermal conductivity coefficient." Systems. Methods. Technologies, no. 1(41) (2019): 57–60. http://dx.doi.org/10.18324/2077-5415-2019-1-57-60.

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19

Chmielowski, W., K. Knast, and S. Kielich. "Hydrodynamical field fluctuations in a non-equilibrium quasi-stationary state due to a temperature gradient." Physica A: Statistical Mechanics and its Applications 154, no. 1 (December 1988): 89–107. http://dx.doi.org/10.1016/0378-4371(88)90182-3.

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20

Chmielowski, W., K. Knast, and S. Kielich. "Hydrodynamical field fluctuations in a non-equilibrium quasi-stationary state due to a temperature gradient." Physica A: Statistical Mechanics and its Applications 170, no. 3 (January 1991): 624–42. http://dx.doi.org/10.1016/0378-4371(91)90010-a.

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21

SHARAFUTDINOV, Ramil F., and Filyus F. Davletshin. "AN ANALYTICAL MODEL OF A NON-STATIONARY TEMPERATURE FIELD IN A RESERVOIR WITH A HYDRAULIC FRACTURING." Tyumen State University Herald. Physical and Mathematical Modeling. Oil, Gas, Energy 7, no. 2 (2021): 75–94. http://dx.doi.org/10.21684/2411-7978-2021-7-2-75-94.

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At the present stage of development of the oil and gas industry, considerable attention is paid to methods of increasing oil recovery of productive reservoirs. One of the most popular methods of intensifying oil production today is hydraulic fracturing. The efficiency and success of hydraulic fracturing largely depends on the parameters of the formed fracture; in this regard, the development of methods for evaluating the parameters of hydraulic fracturing fractures is an urgent task. Non-stationary thermometry is a promising area for monitoring the quality of hydraulic fracturing. To date, thermometry is used to localize the locations of multiple fractures in horizontal wells. In this paper, we study the application of non-stationary thermometry for estimating the parameters of a vertical hydraulic fracturing fracture. An analytical model of non-isothermal single-phase fluid filtration in a reservoir with a vertical fracture is developed. To calculate the temperature field in the formation and the fracture, the convective heat transfer equation is used, taking into account the thermodynamic effects (Joule — Thomson and adibatic), for the fracture, the heat and mass transfer between the fracture and the formation area is also taken into account. To assess the correctness of the model, the analytical solution is compared with the results of numerical modeling in the Ansys Fluent software package. The nonstationary temperature field is calculated for the constant sampling mode. It is established that at the initial moment of time after the well start-up, a negative temperature anomaly is formed due to the adiabatic effect, the value of which increases with a decrease in the fracture width. Over time, the temperature of the fluid flowing into the well increases due to the Joule — Thomson effect, and the value of the positive temperature anomaly increases as the width and permeability of the fracture decreases due to an increase in the pressure gradient in it. The developed analytical model can be used to solve inverse problems for estimating hydraulic fracturing parameters based on non-stationary temperature measurements in the wellbore of producing wells.

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22

BARANGER, JACQUES, and ANDRO MIKELIĆ. "STATIONARY SOLUTIONS TO A QUASI-NEWTONIAN FLOW WITH VISCOUS HEATING." Mathematical Models and Methods in Applied Sciences 05, no. 06 (September 1995): 725–38. http://dx.doi.org/10.1142/s0218202595000401.

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System of equations describing the stationary flow of a quasi-Newtonian fluid, with temperature-dependent viscosity and with a viscous heating, is considered. Existence of at least one appropriate weak solution is proved, i.e. we get existence of at least one velocity field having finite energy and existence of a non-negative temperature field. Its regularity is a consequence of the L1-forcing term generated by the viscous heating.

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23

Mukin, Dmitrii, Ekaterina Valdaytseva, Gleb Turichin, and Artur Vildanov. "An Extended Analytical Solution of the Non-Stationary Heat Conduction Problem in Multi-Track Thick-Walled Products during the Additive Manufacturing Process." Materials 14, no. 23 (November 28, 2021): 7291. http://dx.doi.org/10.3390/ma14237291.

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Анотація:

An analytical model has been developed for calculating three-dimensional transient temperature fields arising in the direct deposition process to study the thermal behavior of multi-track walls with various configurations. The model allows the calculation of all characteristics of the temperature fields (thermal cycles, cooling rates, temperature gradients) in the wall during the direct deposition process at any time. The solution of the non-stationary heat conduction equation for a moving heat source is used to determine the temperature field in the deposited wall, taking into account heat transfer to the environment. The method considers the size of the wall and the substrate, the change in power from layer to layer, the change in the cladding speed, the interpass dwell time (pause time), and the heat source trajectory. Experiments on the deposition of multi-track block samples are carried out, as a result of which the values of the temperatures are obtained at fixed points. The proposed model makes it possible to reproduce temperature fields at various values of the technological process parameters. It is confirmed by comparisons with experimental thermocouple data. The relative difference in the interlayer temperature does not exceed 15%.

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24

Polukhin, O. S., and V. V. Kravchina. "Thermomigration of non-oriented aluminium-rich liquid zones through (110) silicon wafers." Технология и конструирование в электронной аппаратуре, no. 5-6 (2021): 33–40. http://dx.doi.org/10.15222/tkea2021.5-6.33.

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Анотація:

The paper analyzes the reasons and factors that allow avoiding faceting of non-oriented linear zones. It is shown that in the manufacture of semiconductor chips with a large perimeter and a reverse voltage of 2000 V, the conditions sine qua non to create isolating walls on silicon wafers with an orientation different from (111) are to form an ensemble of linear zones by the method of high-temperature selective forced wetting (HSV) and to fulfill a number of requirements to the “thermomigration” photomask and zones immersion stage during TM at high temperatures. It is shown that these factors provide a stable migration of an ensemble of linear zones through wafers (110) even in a stationary temperature gradient field. For the first time in the world, the authors practically demonstrate the possibility of stable migration of an ensemble of non-oriented linear zones through silicon (110) in a stationary temperature gradient conditions, outlining the conditions and factors necessary for this process. It is assumed that when the conditions for the formation of linear zones and their immersion are met, the crystallographic orientation of the silicon wafers does not matter at all.

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25

Kalytka, V. A., A. D. Mekhtiev, P. Sh Madi, and A. V. Bashirov. "Quantum-mechanical model of dielectric losses in nanometer layers of solid dielectrics with hydrogen bonds at ultra-low temperatures." Journal of Physics: Conference Series 2140, no. 1 (December 1, 2021): 012028. http://dx.doi.org/10.1088/1742-6596/2140/1/012028.

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Abstract Upon based the finite difference methods construct the solutions for Liouville quantum kinetic equation linearized by the external field, in complex with the stationary Schrodinger equation and the Poisson operator equation, for an ensemble of non-interacting hydrogen ions (protons) migrating in the field of a crystal lattice perturbed by a variable polarizing field. The influence of the phonon subsystem is not taken into account. The equilibrium (non-balanced) proton density matrix is calculated using quantum Boltzmann statistics. The temperature spectra of dielectric losses tangent angle for hydrogen bonded crystals (HBC) in a wide temperature range (50–550 K) are calculated. At the theoretical level detected the effects of nano-crystalline states (1–10 nm) during the polarization of HBC in the region of ultra-low temperatures (4–25 K).

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26

Ghorbanalilu, Mohammad, and Elahe Abdollahazadeh. "Extension of temperature anisotropy Weibel instability to non-Maxwellian plasmas by 2D PIC simulation." Laser and Particle Beams 36, no. 1 (December 29, 2017): 1–7. http://dx.doi.org/10.1017/s0263034617000842.

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AbstractThe Weibel instability driven by temperature anisotropy is investigated in a two-dimensional (2D) particle-in-cell simulation in non-extensive statistics in the relativistic regime. In order to begin the simulation, we introduced a new 2D anisotropic distribution function in the context of non-extensive statistics. The heavy ions considered to be immobile and form the neutralizing background. The numerical results show that non-extensive parameterqplays an important role on the magnetic field saturation time, the time of reduction temperature anisotropy, evolution time to the quasi-stationary state, and the peak energy density of magnetic field. We observe that the instability saturation time increases by increasing the non-extensive parameterq. It is shown that structures with superthermal electrons (q< 1) could generate strong magnetic fields during plasma thermalization. The simulation results agree with the previous simulations for an anisotropic Maxwellian plasma (q= 1).

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27

Khvesyuk, Vladimir I., and Denis A. Vorobyov. "Method of Heat Balances for Calculating Heat Transfer in Flat Multilayer Nanostructures." Applied Mechanics and Materials 789-790 (September 2015): 407–10. http://dx.doi.org/10.4028/www.scientific.net/amm.789-790.407.

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Анотація:

We suggest method of calculation of one-dimensional temperature field in multilayer nanostructures. Our method allows obtaining non-stationary temperature distribution in the periodical and non-periodical spatial structures with a different degree of periodicity. Comparison temperature distributions in the multilayer nanostructures and equivalent continuous samples are performed in this study. In addition we suggest experimental application of our method for estimation an average value of thermal Kapitza resistance.

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28

Zubenko, Denis, Alexander Petrenko, and Sergii Dulfan. "INVESTIGATION OF THE HEATING PROCESSES AND TEMPERATURE FIELD OF THE FREQUENCY-CONTROLLED ASYNCHRONOUS ENGINE BASED ON MATHEMATICAL MODELS." EUREKA: Physics and Engineering 5 (September 17, 2019): 64–72. http://dx.doi.org/10.21303/2461-4262.2019.00960.

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The study of the temperature field of the engine for non-stationary modes is done. A numerical simulation of a non-stationary thermal process using dynamic EHD, the characteristic of the rate of rise of temperatures is done. An increase in the temperature of individual parts in the idle interval, when the power of heat release is significantly reduced, is established, and the reverse of the heat flow through the air gap is established. It is shown that the EHD method, in contrast to the FEM, is self-sufficient, which determines its practical value. In various parts of the speed control range in the implementation of various laws of regulation. At the same time, the main electrical, magnetic and additional losses associated with the fundamental voltage harmonics (FVH), and mechanical losses, as well as additional electrical and magnetic losses associated with the higher voltage harmonics, change. When using serial asynchronous engines as frequency-controlled. Permissible under the conditions of heating power is significantly reduced by the power of serial engines. Depending on the synchronous speed, the reduction is from 10 % to 20 %. Given the additional overheating due to higher voltage harmonics, as well as the deterioration of the cooling conditions when adjusting the rotational speed "down" from the nominal, it seems very relevant.

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29

Levchenko, V., M. Kascheev, S. Dorokhovich, and A. Zaytsev. "THE TWO-DIMENSIONAL PROBLEM OF NON-STATIONARY THERMAL CONDUCTIVITY IN A MULTILAYER PLATE AND CYLINDER." PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. SERIES: NUCLEAR AND REACTOR CONSTANTS 2020, no. 2 (June 26, 2020): 141–49. http://dx.doi.org/10.55176/2414-1038-2020-2-141-149.

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Анотація:

The problem of determining a two-dimensional non-stationary temperature field in a k-layer cylinder and plate of length l is solved. There is a symmetrically located gap (plate) or cylindrical cavity (cylinder) in the center of these bodies. The absence of a gap or cavity is a special case of the problem. In each layer, there are heat sources, depending on the coordinates and time. The initial temperature of the layers is a function of the coordinates. In the center of the bodies the symmetry condition is fulfilled. At the boundary of contact of the layers - ideal thermal contact: continuity of temperatures and heat flows. On the inner and outer side surfaces and ends, heat exchange occurs according to Newton's law with environments whose temperatures change over time according to an arbitrary law. With the help of the geometric parameter G in the mathematical formulation of the problem, one differential equation for both multilayer bodies is written. The problem in this statement is solved for the first time. For the solution of the problem the following approach is used: by means of the method of finite integral transformations differential operations on longitudinal and transverse coordinates are sequentially excluded, and the determination of time dependence of temperature is reduced to the solution of the ordinary differential equation of the first order.

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30

Pataraya, A. D., and T. A. Pataraya. "Non-linear dynamo waves in an incompressible medium when the turbulence dissipative coefficients depend on temperature." Annales Geophysicae 15, no. 1 (January 31, 1997): 97–100. http://dx.doi.org/10.1007/s00585-997-0097-z.

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Abstract. Non-linear α-ω; dynamo waves existing in an incompressible medium with the turbulence dissipative coefficients depending on temperature are studied in this paper. We investigate of α-ω solar non-linear dynamo waves when only the first harmonics of magnetic induction components are included. If we ignore the second harmonics in the non-linear equation, the turbulent magnetic diffusion coefficient increases together with the temperature, the coefficient of turbulent viscosity decreases, and for an interval of time the value of dynamo number is greater than 1. In these conditions a stationary solution of the non-linear equation for the dynamo wave's amplitude exists; meaning that the magnetic field is sufficiently excited. The amplitude of the dynamo waves oscillates and becomes stationary. Using these results we can explain the existence of Maunder's minimum.

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31

Tepnatim, Wipawee, Witchuda Daud, and Pitiya Kamonpatana. "Simulation of Thermal and Electric Field Distribution in Packaged Sausages Heated in a Stationary Versus a Rotating Microwave Oven." Foods 10, no. 7 (July 13, 2021): 1622. http://dx.doi.org/10.3390/foods10071622.

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Анотація:

The microwave oven has become a standard appliance to reheat or cook meals in households and convenience stores. However, the main problem of microwave heating is the non-uniform temperature distribution, which may affect food quality and health safety. A three-dimensional mathematical model was developed to simulate the temperature distribution of four ready-to-eat sausages in a plastic package in a stationary versus a rotating microwave oven, and the model was validated experimentally. COMSOL software was applied to predict sausage temperatures at different orientations for the stationary microwave model, whereas COMSOL and COMSOL in combination with MATLAB software were used for a rotating microwave model. A sausage orientation at 135° with the waveguide was similar to that using the rotating microwave model regarding uniform thermal and electric field distributions. Both rotating models provided good agreement between the predicted and actual values and had greater precision than the stationary model. In addition, the computational time using COMSOL in combination with MATLAB was reduced by 60% compared to COMSOL alone. Consequently, the models could assist food producers and associations in designing packaging materials to prevent leakage of the packaging compound, developing new products and applications to improve product heating uniformity, and reducing the cost and time of the research and development stage.

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32

Anishchenko, Galina Ottovna, Vladimir Ivanovich Konokhov, and Denis Vladimirovich Lavinsky. "Specific features of thermal deforming of composite inductors during magnetic-pulse processing of materials." Bulletin of the National Technical University «KhPI» Series: Dynamics and Strength of Machines, no. 2 (December 31, 2021): 127–30. http://dx.doi.org/10.20998/2078-9130.2021.2.249751.

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Анотація:

The problem of taking into account a non-stationary inhomogeneous temperature field in the analysis of the stress-strain state of inductor systems for magnetic-pulse processing of materials is considered. It follows from the analysis of open information sources that the problem of analyzing a non-stationary temperature field arising from the presence of a non-uniform electromagnetic field and its effect on deformation has been sufficiently studied in relation to induction heating. At the same time, during other operations of magnetic-pulse processing of materials, heating of equipment can cause additional deformations of a significant magnitude, which, in turn, can lead to a loss of equipment performance due to destruction or irreversible deformation. A general approach to the analysis of such problems is proposed, which involves the determination of the spatial-temporal distributions of the quantitative characteristics of the electromagnetic field, temperature field and stress-strain state. The necessity of using numerical methods for carrying out such an analysis has been substantiated. The most effective numerical method is the finite element method, which makes it possible to analyze the unsteady electromagnetic field, temperature field, and stress-strain state within the same calculation scheme. In this case, within the framework of the finite element method, iterative schemes can be created that allow taking into account nonlinear effects. Here, nonlinear effects can be due to the dependence of the mechanical and electro-physical properties of the material on temperature, the plastic nature of deformation, and the need to take into account contact phenomena. The results of complex analysis for a composite single-turn inductor with a dielectric band are presented. The features of contact interaction were taken into account by introducing layers of contact finite elements. The stress-strain state of the inductor is estimated for two variants of the materials used: copper and non-magnetic steel.

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33

MARKOV, O. I. "INFLUENCE OF THE CURRENT PULSE SHAPE ON THE DYNAMICS OF THE TEMPERATURE FIELD OF THE THERMOELECTRIC COOLER BRANCH." Fundamental and Applied Problems of Engineering and Technology 3 (2021): 161–65. http://dx.doi.org/10.33979/2073-7408-2021-347-3-161-165.

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Анотація:

Numerical simulation of thermoelectric processes in a branch of a solid–state thermoelectric Peltier cooler in a non–stationary mode is performed. Some examples show the effect of changes in the amplitude of the current pulse over time on the temperature in the branch of the thermoelectric element.

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34

Shlyahin, Dmitriy. "Analyzing calculation results of non-stationary axisymmetric thermoelasticity task for a circular isotropic plate." MATEC Web of Conferences 196 (2018): 01007. http://dx.doi.org/10.1051/matecconf/201819601007.

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Анотація:

The paper releases results of numerical calculation of axisymmetric dynamic thermoelasticity task for a fixed circular isotropic plate in case of temperature change on its front faces (boundary conditions of the 1st type). The calculated ratios are obtained by using the GL-theory of thermoelasticity (classical theory), which determines the dependence of the vector of heat flux on the velocity of change and temperature gradient. The mathematical model of the task in question includes differential equations of axisymmetric motion and thermal conductivity, formulated as regard to the component of the movement vector and the function of temperature change. Not self-adjoint system is investigated independently. For its solution, a mathematical apparatus technique of separation of variable in the form of finite integral transformations is used, that is transformations of Fourier, Hankel and generalized integral transformation (GIT). The constructed calculation ratios give an opportunity to define stress and strain state and character of distribution of a thermal field of rigidly fixed circular plate with arbitrary axially symmetrical temperature external influence. It is shown, that elastic inertial characteristics of a plate influence the law of change of movement over time only while investigating very thin plates at high-speed temperature impact.

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35

Bratsun, Dmitry, and Vladimir Vyatkin. "Closed-Form Non-Stationary Solutionsfor Thermo and Chemovibrational Viscous Flows." Fluids 4, no. 3 (September 19, 2019): 175. http://dx.doi.org/10.3390/fluids4030175.

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Анотація:

A class of closed-form exact solutions for the Navier–Stokes equation written in the Boussinesq approximation is discussed. Solutions describe the motion of a non-homogeneous reacting fluid subjected to harmonic vibrations of low or finite frequency. Inhomogeneity of the medium arises due to the transversal density gradient which appears as a result of the exothermicity and chemical transformations due to a reaction. Ultimately, the physical mechanism of fluid motion is the unequal effect of a variable inertial field on laminar sublayers of different densities. We derive the solutions for several problems for thermo- and chemovibrational convections including the viscous flow of heat-generating fluid either in a plain layer or in a closed pipe and the viscous flow of fluid reacting according to a first-order chemical scheme under harmonic vibrations. Closed-form analytical expressions for fluid velocity, pressure, temperature, and reagent concentration are derived for each case. A general procedure to derive the exact solution is discussed.

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36

Dats, Evgeniy, Sergey Mokrin, and Evgeniy Murashkin. "Calculation of the Residual Stress Field of the Thin Circular Plate under Unsteady Thermal Action." Key Engineering Materials 685 (February 2016): 37–41. http://dx.doi.org/10.4028/www.scientific.net/kem.685.37.

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Анотація:

The dimensional problem of a formation of the residual stresses in the thin circular elastoplastic plate under the given thermal action was analytically solved. The generalized Prandtl-Reuss thermoelastoplastic model was used. The effect of the non-stationary temperature gradient on the residual stresses field formation was investigated under the condition that the yield stress depends on a temperature. The borders of the irreversible deformation domain and unloading domain were computed. The level of residual stresses was calculated.

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37

Levin, A. A., and P. V. Khan. "Experimental observation of the maximum bubble diameter in non-stationary temperature field of subcooled boiling water flow." International Journal of Heat and Mass Transfer 124 (September 2018): 876–83. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2018.03.078.

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38

Lausova, Lenka, and Iveta Skotnicova. "Analysis of Experimental Measurements and Numerical Simulations of a Heat Field in the Light Weight Building Structure." Advanced Materials Research 969 (June 2014): 33–38. http://dx.doi.org/10.4028/www.scientific.net/amr.969.33.

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Анотація:

The paper analyses results of the experimental measurements and numerical simulations of the winter and summer temperature response in the light timber structure. In the article there is evaluated the suitability of using of the theoretical numerical methods for a thermal field prediction in a building structure exposed to non-stationary boundary conditions.

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39

Shlyakhin, D. A., and Zh M. Dauletmuratova. "Non-stationary coupled axisymmetric thermoelasticity problem for a rigidly fixed round plate." PNRPU Mechanics Bulletin, no. 4 (December 15, 2019): 191–200. http://dx.doi.org/10.15593/perm.mech/2019.4.18.

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Анотація:

A new closed solution is constructed for the axisymmetric dynamic problem of the classical (CTE) theory of thermoelasticity for a rigidly fixed circular isotropic plate in the case of a temperature change on its face surfaces (boundary conditions of the first kind). The mathematical formulation of the problem under consideration includes linear equations of thermal conductivity and equilibrium in a spatial setting, assuming that their inertial elastic characteristics can be neglected in the structures under study. In constructing a general solution of related non-self-conjugate equations, we use the mathematical apparatus of separation of variables in the form of finite integral transformations i.e. Hankel along the radial coordinate and biorthogonal transformation (FIT) with respect to the axial variable. At each stage of the investigation, a procedure is performed to reduce the boundary conditions to a form that allows the corresponding transformation to be applied. A particular feature of this solution is the application of a FIT based on a multicomponent relation of the eigenvector functions of two homogeneous boundary value problems. An important point in the procedure of the structural algorithm is the separation of the adjoint operator, without which it is impossible to solve non-self-adjoint linear problems of mathematical physics. This transformation is the most effective method for studying similar boundary value problems. The calculated design relationships make it possible to determine the stress-strain state and the character of the distribution of the temperature field in a rigidly fixed circular isotropic plate for an arbitrary external temperature effect with respect to time. Numerical analysis of the strength characteristics of the concrete structure shows that during the period of the unsteady load the maximum values of mechanical stresses are observed. Later, at a constant temperature regime, as a result of heating the entire plate, the displacements increase and the stresses fall.

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40

Tatsii, R. M., O. Y. Pazen, and L. S. Shypot. "DETERMINATION OF THE NON-STATIONARY TEMPERATURE FIELD IN THE SYSTEM OF TWO CYLINDRICAL SHELL UNDER THE FIRE CONDITIONS." Fire Safety, no. 34 (July 19, 2019): 84–90. http://dx.doi.org/10.32447/20786662.34.2019.14.

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Анотація:

The proposed work is devoted to the application of the direct method to the study of heat transfer processes in the system "solid cylinder inside a cylindrical shell". It is assumed that there is an ideal thermal contact between them, and the law of changing the ambient temperature, which rinses the surface of the structure, is an arbitrary function of time, and evenly distributed over the surface. Consequently, isotherms inside this construction are concentric circles, that is, the problem is symmetric and is solved for the first time in such a statement. To solve such a problem, the auxiliary problem of determining the distribution of a non-stationary temperature field in a two-layer hollow cylindrical structure with a "withdrawn" cylinder of sufficiently small radius is raised in parallel. In this case the symmetry condition of the original problem is replaced by the condition of the second kind on the inner surface of this construction. The implementation of the solution of the auxiliary problem is carried out by applying a reduction method using the concept of quasi-derivatives. In the future, the Fourier scheme is used with the use of the modified eigenfunctions method. To find the solution of the original problem, the idea of the boundary transition is used by passing the radius of the withdrawn cylinder to zero. It is established that in this approach all the eigenfunctions of the corresponding problem on the eigenvalues have no singularities at zero, which means that the solutions of the original problem are constrained throughout the design. In order to illustrate the proposed method, a model example of finding the temperature field distribution in a column of a circular cross-section (concrete in a steel shell) is solved under the influence of the standard temperature regime of the fire. The results of the calculations are presented in a bulk schedule of temperature changes, depending on time and spatial coordinates. The generalization of the results obtained in the case of any finite number of cylindrical shells is a purely technical problem, and not a fundamental one. Note that while changing the boundary condition of the third kind to any other boundary condition (for example, the first kind) does not affect the scheme of solving similar tasks. Since the general scheme of studying the distribution of temperature fields in multi-layered structures with an arbitrary number of layers in the presence of internal sources of heat is studied in detail, the setting and solving of such problems for the system of "solid cylinder inside a cylindrical shell" is not without difficulty.

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41

Tsaplin, S. V., and S. A. Bolychev. "THERMAL-CONTROL SYSTEM OF EXPERIMENTAL MODEL OF SPACECRAFT OPTICAL TELESCOPE ASSEMBLY." Vestnik of Samara University. Natural Science Series 19, no. 9.2 (June 6, 2017): 236–43. http://dx.doi.org/10.18287/2541-7525-2013-19-9.2-236-243.

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Анотація:

Software on the base of program package of ANSYS, MathCAD, Zemax for study of influence of thermal factors of space factor on optical characteristics of lens objective of spacecraft is developed. Calculation of non-stationary field of temperature and deformation, output data of lens objective for specific case is carried out.

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42

Yaparova, N. M., and T. P. Gavrilova. "NUMERICAL METHOD FOR DETERMINING TEMPERATURE FIELD OF A LINEAR OBJECT UNDER EXTERNAL THERMAL INFLUENCE." Journal of the Ural Federal District. Information security 20, no. 3 (2020): 49–58. http://dx.doi.org/10.14529/secur200306.

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Анотація:

The use of data analysis technologies for processing the temperature measurement results is aimed at solving the problems of controlling the parameters of controlling thermal modes, monitoring the thermal state of the main industrial equipment, as well as issues of integrity and availability of data circulating in automated control systems for technological processes.The article is devoted to the problem of determining non-stationary temperature fields in-side an object from the noisy results of surface temperature measurements and the parameters of external thermal effect on its surface. Mathematically, the heat transfer process is represent-ed by a parabolic equation, includes initial conditions, as well as boundary conditions formed from temperature measurements on the object’s surface and in accordance with the character-istics of the external thermal regime.

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43

Gryzunov, V., A. Zaycev, Yu Kim, and D. Tkhai. "EFFECTS OF COLLAPSING CAVITATION ON HIFU-EXPOSED BIOLOGICAL OBJECTS." East European Scientific Journal 3, no. 10(74) (November 22, 2021): 22–25. http://dx.doi.org/10.31618/essa.2782-1994.2021.3.74.140.

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Анотація:

Therapeutic significance in the studies of HIFU-induced effects of is attached to the local heating of tissues, but the role of the mechanical component caused by non-stationary cavitation is practically not taken into account. Calculations show that the temperature inside cavitation bubbles can differ significantly from the temperature in the thermal ablation zone, and the developing temperature gradient can change the formation of the thermal field. Collapsing bubbles can cause mechanical destruction of tissues.

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44

Lugantsev, L. D. "Computer analysis of unsteady creeping of construction rod elements." Izvestiya MGTU MAMI 8, no. 1-3 (May 10, 2014): 50–56. http://dx.doi.org/10.17816/2074-0530-67573.

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Анотація:

The article considers the method and algorithm of the computer analysis of viscoelastic deformation of a beam in a non-stationary temperature field. The data of program realization of the offered method of calculation are presented. The example of calculation of process of unsteady creep of a beam is adduced at thermomechanical influence.

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45

Kreisl, P., A. Helwig, G. Müller, E. Obermeier, and S. Sotier. "Detection of hydrocarbon species using silicon MOS field-effect transistors operated in a non-stationary temperature-pulse mode." Sensors and Actuators B: Chemical 106, no. 1 (April 2005): 442–49. http://dx.doi.org/10.1016/j.snb.2004.09.004.

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46

Levin, Anatoliy A., A. S. Safarov, V. M. Chudnovskii, and Andrey A. Chernov. "MODELING OF NON-STATIONARY TEMPERATURE FIELD IN THE NEIGHBORHOOD OF THE OPTICAL FIBER END UNDER LASER PULSE HEATING." Interfacial Phenomena and Heat Transfer 8, no. 1 (2020): 25–32. http://dx.doi.org/10.1615/interfacphenomheattransfer.2020032806.

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47

Glebov, A. O., and S. V. Karpushkin. "A method of designing equipment for heat processing of polymer workpieces." Journal of Physics: Conference Series 2094, no. 2 (November 1, 2021): 022016. http://dx.doi.org/10.1088/1742-6596/2094/2/022016.

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Анотація:

Abstract The paper describes a method of designing heating equipment that maintains a predetermined temperature field. The method consists in sequential solution of two problems. At the first stage, the heat generation field was calculated using the stationary heat conduction equation. At the second stage, parametric optimization of the temperature field was performed with reference to the power and configuration limits of the heaters. To test this method, the problem of maintaining a predetermined non-uniform temperature field was solved. A practical example of the application of the method for designing a uniform heating plate used in vulcanizing presses was given. To assess the efficiency of the plate, the results of modeling the heat processing of a workpiece from a rubber mixture were presented.

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48

Kalis, Harijs, Maksims Marinaki, Uldis Strautins, and Maija Zake. "ON NUMERICAL SIMULATION OF ELECTROMAGNETIC FIELD EFFECTS IN THE COMBUSTION PROCESS." Mathematical Modelling and Analysis 23, no. 2 (April 18, 2018): 327–43. http://dx.doi.org/10.3846/mma.2018.020.

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Анотація:

This paper deals with a simpliﬁed model taking into account the interplay of compressible, laminar, axisymmetric ﬂow and the electrodynamical eﬀects due to Lorentz force’s action on the combustion process in a cylindrical pipe. The combustion process with Arrhenius kinetics is modelled by a single step exothermic chemical reaction of fuel and oxidant. We analyze non-stationary PDEs with 6 unknown functions: the 3 components of velocity, density, concentration of fuel and temperature. For pressure the ideal gas law is used. For the inviscid ﬂow approximation ADI method is used. Some numerical results are presented.

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49

Mestnikov, Alexey, Gavril Turantaev, and Valeriy Fedorov. "Mathematical modeling of temperature fields and concrete strength during winter concreting of building structures." MATEC Web of Conferences 245 (2018): 03009. http://dx.doi.org/10.1051/matecconf/201824503009.

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Анотація:

In this paper we present a mathematical model of a three-dimensional non-stationary temperature field for concrete that hardens in winter conditions. The developed mathematical model describes heat transfer processes basing on the differential heat equation. We also consider the classical boundary conditions of the I, II, III and IV kinds. We compiled a computer interpolation of the family of nomograms in the second order regression equation in order to calculate the relative theoretical strength of concrete after heat treatment.

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50

Skotnicova, Iveta, Lenka Lausova, and Jiri Brozovsky. "Dynamic Heat Transfer through the External Wall of a Timber Structure." Applied Mechanics and Materials 617 (August 2014): 162–66. http://dx.doi.org/10.4028/www.scientific.net/amm.617.162.

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Анотація:

The article compares results of temperature and heat flux measurements in the external wall of a real timber structure with results obtained by numerical modeling using the finite element method in the ANSYS software. The measured temperature values are compared with results obtained from numerical simulation of dynamic heat transport using non-stationary boundary conditions. In the article there is evaluated a suitability of theoretical numerical calculations for a thermal field and heat flux prediction in a building structure.

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