Nonstationary Heat 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.

Effects of Solidification Thermal Variables on the Microstructure and Hardness of the Silicon Aluminum Bronze Alloy CuAl6Si2

The properties of the final product obtained by solidification directly result from the thermal variables during solidification. This study aims to analyze the influence of thermal solidification variables on the hardness, microstructure, and phases of the CuAl6Si2 alloy. The material was solidified using unidirectional solidification equipment under non-stationary heat flow conditions, where heat extraction is conducted through a water-cooled graphite base. The thermal solidification variables were extracted using a data acquisition system, and temperature was monitored at six different positions, with cooling rates ranging from 217 to 3 °C/min from the nearest to the farthest position from the heat extraction point. An optical microscope, scanning electron microscope (SEM), and X-ray diffraction (XRD) were used to verify the fusion structure and determine the volumetric fraction of the formed phases. The XRD results showed the presence of β phases, α phases, and possible Fe3Si2 and Fe5Si3 intermetallics with different morphologies and volumetric fractions. Positions with lower cooling rates showed an increased volume fraction of the α phase and possible intermetallics compared to positions with faster cooling. High cooling rates increased the Brinell hardness of the alloy due to the refined and equiaxed β metastable phase, varying from 143 HB to 126 HB for the highest and lowest rates, respectively.

Identification of the Characteristics of Thermal Engineering Materials Under Conditions of Nonstationary Heating With Changes in Pressure by Solving Inverse Heat Exchange Problems. 1. Development of Computing Algorithms

Identification of the Characteristics of Thermal Engineering Materials Under Conditions of Nonstationary Heating With Changes in Pressure by Solving Inverse Heat Exchange Problems. 1. Development of Computing Algorithms

Experimental setup for comprehensive study of non-stationary heat transfer in complex liquid media.

This paper presents a setup for studying non-stationary heat exchange in liquid media on a scale of small times and sizes at high heat flux densities created using a high-speed precision power controller. A platinum wire with a diameter of 20μm and a length from 0.5 to 1cm is used as a probe. The heating time ranged from 1 to 300ms, and the heat flux densities from 1 to 20 MW/m2 were achieved in the experiments. Strictly specified conditions for heat release in the probe are confirmed by maintaining a constant power in a series of pulses with an accuracy of 0.05%. Acquiring a primary electrical signal of thermograms is synchronized with high-speed video recording, allowing an accurate relationship between the applied thermal load and the mechanics of processes in the studied liquid. The setup capabilities were shown by comparing the boiling patterns of a simple substance, such as ethanol, and a solution with a lower critical solution temperature, a 30 vol.% solution of polypropylene glycol-425 in water, which have similar thermograms. As a result, a qualitative difference between the heating and boiling patterns observed using high-speed video and the presented setup fitting its purpose has been shown.

MATHEMATICAL MODELS OF THE THERMAL PROTECTION COATING OF THE GAS GENERATOR OF THE HYDROGEN STORAGE AND SUPPLY SYSTEM

The article describes the properties of the thermal protection coating of the gas generator of the hydrogen storage and supply system by two transfer functions with Hurwitz polynomials of the third order. Obtaining such transfer functions is based on the solution of the non-stationary heat conduction equation, represented in operator form using the integral Laplace transform, and in which approximating spline functions in the form of second-order polynomials are used. The article gives the solution of the non-stationary thermal conductivity equation, which describes the thermal processes in the heat-protective coating of the gas generator of the hydrogen storage and supply system under the thermal effect of a fire. This solution comes in the operator form for the surface temperature of the heat-protective coating on the side of the gas generator wall. The peculiarity of this decision is the presence of hyperbolic functions of an irrational argument in its composition. The structural and dynamic scheme of the thermodynamic system ‘gas generator wall – heat-protective coating’ is presented, the feature of which is the presence of two entrances. The signal at the scheme’s first input reflects the thermal effect of the fire, and the signal at the second input reflects the thermal state of the gas generator cavity. An equivalent mathematical transition to the description of thermal processes in the heat-protective coating of the gas generator of the hydrogen storage and supply system was carried out. This transition happened due to the use of spline functions, which approximate the hyperbolic functions of the irrational argument and are polynomials of the second order. The article gives a verbal interpretation of the algorithm for determining the transfer functions of the heat-protective coating of the gas generator of the hydrogen storage and supply system and also an example of its implementation. Furthermore, it shows that for the given conditions of functioning of the gas generator heat-protective coating, the relative errors in approximation of hyperbolic functions by second-order polynomials do not exceed 1.7 %, and the average relative error when equivalent replacement of transfer functions does not exceed 3.8 %. Keywords: gas generator, hydrogen storage and supply system, thermal protection coating.

Comparison of the Position of the Maximum Humidification Zone when Using the Methods of Stationary and Non-Stationary Heat and Humidity Regime

The basic formulas for mathematical modeling of the heat and moisture regime of building envelopes in stationary and non-stationary settings are given. It is noted that the mathematical model uses third kind boundary conditions. Objective of the study: to check whether the moisture maximum plane position in the thickness of building envelopes is confirmed assessing non-stationary moisture conditions. Two methods for verification are used: the graphical method for determining the plane of maximum moisture and the method for assessing the non-stationary moisture regime, based on the Gagarin and Kozlov moisture potential. It was found that the maximum moisture is confirmed both for facade systems with mineral wool insulation and for facade systems with expanded polystyrene insulation. In the case of mineral wool, the maximum moisture is located outside the insulation layer. For expanded polystyrene insulation, the maximum moisture is determined inside the insulation layer. Thus, it was confirmed that the maximum moisture in the thickness of the enclosing structure, determined by the graphical method, is confirmed by mathematical modeling of a non-stationary heat and moisture regime.

Prediction of thermal regime and frost heave deformations of subgrade soils during non-stationary heat and moisture transfer

In order to ensure the safe operation of high-speed trains in cold regions, frost heave is one of the basic problems in the research for prediction and control roadbed deformation in such regions. In this paper, based on the classical hydrodynamic model we developed a method of studying thermal regime of soils and predicting frost heave deformations of subgrade soils. Our coupling model takes into account the mutual influence of temperature and soil moisture during non-stationary processes of heat and moisture transfer, calculation of frost heave deformation based on calculated result of the temperature and moisture fields of the roadbed. We have also observed the change of the soil temperatures and frost heave deformation in a freezing-thawing cycle at the geodesic center of PGUPS. The field observation results show that the soil temperature variations amplitude decreases with depth. The simulation verification results and the field observation data show good reproducibility, thus the reliability of the model is confirmed. At last, the paper presents the application of the method in improving high speed railway lines (HSRL) subgrade design in order to reduce frost heave deformations. Based on the results of calculations, it is recommended to lay a thermal insulation layer at the depth of 0.2 m below the subgrade and on the slopes to reduce frost depth and frost heave deformations of subgrade soils.

Numerical modeling of discharge modes and evaluation of the major characteristics of latent heat thermal energy storage at a nuclear power plant

Under conditions of uneven power consumption schedules, construction of renewable power plants and low maneuverability of nuclear power plants (NPPs), combining NPPs with latent heat thermal energy storage systems (LHTES) can improve efficiency and maneuverability of NPPs. Combination of the LHTES with an additional low-capacity steam turbine will allow not only meeting peak electricity loads, but also increase the NPP safety by additional reservation of its own needs using this multifunctional turbine in emergency situations of complete blackouts. A scheme for combining a PCM-based thermal storage system with a two-circuit nuclear power plant is proposed, where the LHTES is charged with part of fresh steam from steam generators in the night hours of off-peak loads in the power grid and heating feed water above the nominal temperature during the peak loads. Non-stationary heat transfer between the heat storage material and feed water during the LHTES discharge was modeled using the finite volume method. The design characteristics of the LHTES as part of the NPP and the weight-size parameters of the thermal accumulator have been determined. The rational phase change material and the types of finned tubes have been determined. A solution has been proposed to ensure stable water temperature at the outlet of the PCM-based thermal accumulator during its discharge within the NPP that will significantly increase efficiency of its performance. Heat losses from the LHTES to the environment during the day have been calculated.

An Approach to Improving the Accuracy and Efficiency of the ROMB Method for Solving the Nonstationary Heat Equation

An Approach to Improving the Accuracy and Efficiency of the ROMB Method for Solving the Nonstationary Heat Equation

Расчеты сжатия сферической слоистой системы ударными волнами с учетом переноса тепла излучением в различных приближениях

Numerical modeling is one of the basic tools to investigate physical phenomena that occur in materials compressed by shock waves. A study of the behavior of shock waves using simplified models is helpful in the analysis of more complex systems, for instance, in the problems of inertial thermonuclear fusion on laser facilities. Mathematical simulation of the nonstationary radiative heat transfer in a spectral kinetic statement is rather complicated because the system of equations is nonlinear and large in size. Generally, the kinetic transport equation is solved in 7D phase space, which requires huge computational resources. The initial system is often approximated under certain assumptions but this immediately causes questions as to whether the simplified model is applicable to particular calculations. In this study, several economic radiative heat transfer models were implemented in a 2D hydrodynamic code. Based on these models, test calculations were performed to simulate the compression of a layered spherical system by shock waves, taking into account radiative heat transfer. When the shock wave reaches the center of the sphere, it is focused and reflected. In the neighborhood of the focal point of a converging wave, temperature gradients increase; therefore, thermal conduction and radiation become the main mechanisms of energy dissipation to be considered when taking into account heat transfer. Maximum densities and temperatures at the center of the sphere and their average values in its regions were calculated. In addition, the time when shock and heat waves cross the sphere center was determined, and their behavior before and after focusing at the sphere center was estimated. It is shown that solutions to such problems can be found much faster and with adequate accuracy when applying simplified models.

Modeling of Non-stationary Heat Transfer of Floor Structures of Rooms with Artificial Ice

Statement of the problem. The purpose of the scientific article is to develop an adjusted methodology and program for calculating the non-stationary heat exchange of floor structures with artificial ice, taking into account the asymmetric radiation cooling of heat exchange surfaces to determine the time they reach the critical temperature. Results. An important characteristic of the adjusted technique is the use of the average coefficient of irradiation of the surfaces of the structure, as well as taking into account the displacement of the thermal center during its asymmetric heating. The technique takes into account the radiant component from the ice surface in the determining generalized heat transfer coefficient. Conclusions. The considered features make it possible to increase the accuracy of calculating the cooling time of the surface of the structure to critical values, which can be used to adjust the operating modes of microclimatic systems of rooms with artificial ice.

Freezing and Thawing of Enclosing Structures and Foundation Soils Taking into Account the Effects of Solar Energy: Part 2. Problem Statement

Part 1 provides general information about some of the physical properties of water, ice, and snow necessary to understand the non-stationary processes of freezing and thawing of enclosing structures of wet foundation soils. Part 2 presents the physical and mathematical formulation of the problem of freezing of wet soil, the solution of Lyame and Clapeyron, the solution of Stefan, the physical and mathematical formulation of the problem of freezing of the ribbon foundation. The following are considered: description of the process of freezing of a single-layer enclosing structure considering the phase transformations of moisture in the material of the structure according to V.N. Bogoslovsky and the process of freezing of an unlimited plate considering the phase transformations of moisture in the material of the structure according to A.V. Lykov. Mathematical model of non-stationary heat transfer process in wet layered media. Based on the method of small-time intervals, solutions of boundary value problems for frozen and thawed zones in the region of large and small Fourier numbers are given. Prospects for the application of the proposed mathematical models to describe the processes of freezing and enclosing structures and foundation soils are outlined.

Modeling of heat transfer and fluid flow in the metal being welded during DC and HFPC TIG spot welding

A mathematical model of non-stationary electromagnetic, heat and mass transfer processes in the metal during high frequency pulsed current (HFPC) TIG spot welding has been proposed. A computational algorithm for the the numerical solution of the corresponding mathematical problems has been developed and implemented in Wolfram Language. A comparative analysis of the hydrodynamic and heat transfer processes in the specimen of steel S-235JR during HFPC TIG welding with 10 kHz square wave pulse current modulation and direct current (DC) TIG welding with current equal to the mean current of HFPC mode has been carried out. As simulations showed, the HFPC modulation results to appreciable weld penetration with minor influence on the radius of the fusion zone compared to the DC process.

The effect of porous coatings obtained by various methods on heat transfer and crisis phenomena during nitrogen boiling including non-stationary heating and cooling

The paper presents the main results of experimental investigation of the influence of porous coatings obtained by various methods on heat transfer and crisis phenomena during nitrogen boiling, including unsteady heating and cooling regimes. Modification of heater surfaces was carried out by the methods of directed plasma spraying, additive 3D printing and micro-arc oxidation. For all types of porous coatings, a significant intensification of heat transfer at atmospheric pressure relative to smooth heaters was obtained (maximum degree of heat transfer increase up to 6 times). The mechanisms playing a determining role in the process of heat transfer coefficients increase are suggested. The essential influence of structured capillary-porous bronze coatings on the dynamics of transient processes and development of crisis phenomena of non-stationary processes is shown, leading to degeneration of the heat transfer crisis at pulse supply of heat load and significantly reducing the time of complete cooling of the heater in the process of rewetting.

Thermophysical model of a thermonic cathode with induction heating

A thermophysical model was built and the temperature field of a cylindrical thermionic cathode with induction heating was calculated, taking into account the initial and boundary conditions, based on the adoption of assumptions to simplify the mathematical model. During the induction heating of the cathode, a non-stationary heat conduction process is established, which is described by the differential equation of heat conduction with internal sources of Joule heat. The distribution of internal heat sources in the volume of the cathode is determined by the distribution of the ring induced current. The cylindrical design of the inductive thermionic cathode, due to spatial symmetry, allows to reduce the number of spatial variables, significantly simplify functional dependencies, and limit the algorithm for solving the problem. The problem was solved in the cylindrical coordinate system. The obtained approximate solutions were assessed for the correctness of the accepted simplifications when finding the distribution of the temperature field with a sufficient degree of accuracy. Despite the high thermal conductivity of the cathode material, when the cathode is inductively heated, there can be a significant temperature difference between its outer and inner surfaces. The article shows the permissible temperature difference on the surface of the cathode, which limits the choice of geometric dimensions of the cathode. The temperature difference on the surfaces of the induction thermionic cathode is most affected on the end (annular) surfaces of the cathode, so it is better to apply emitting coatings to the side surfaces of the cylindrical cathode, thus complicating the design of the cathode. The application of induction heating of the thermionic cathode allows to simplify the heating unit, increase the reliability and service life of powerful electronic devices. The obtained results are planned to be used in further research as test data for the analysis of more complex problems of numerical calculation of the thermal regimes of the cathode unit with heat shields and focusing elements of thermoelectron flows.

Связанная неосесимметричная нестационарная задача термоупругости для длинного цилиндра

Inhomogeneous non-stationary heating of constructions of various purposes induces thermal strains and stresses that should be considered in the comprehensive analysis of elastic systems. The mathematical formulation of the considered linear threedimensional thermoelasticity problems includes coupled non-self-adjoint differential equations of motion and thermal conductivity. Due to their integration difficulty, axisymmetric problems are usually analyzed instead. The purpose of this work is to develop a solution algorithm for the coupled nonaxisymmetric non-stationary problem of the thermoelasticity of a long cylinder. On the internal surface of the hollow anisotropic cylinder, the temperature variation function is known; on the external surface, the convective heat transfer and environmental temperature are given. The rate of the temperature load does not affect the inertial characteristics of the cylinder. Therefore, the equilibrium and heat equations can be added to the initial system of linear equations. The finite Fourier sine and cosine transforms and general biorthogonal transforms are used to study a non-self-adjoint system of differential equations and to develop a closed solution. The obtained solution allows one to determine the temperature field and the stress-strain state of a cylinder with its internal surface affected by non-stationary nonaxisymmetric loading in terms of the temperature variation function.

Review of methods and devices for determining the resistance to heat transfer under natural conditions

The purpose of this study is to review modern methods of determining the resistance to heat transfer of building envelopes under natural conditions using experimental equipment. Methods for experimental determination of the resistance to heat transfer given in regulatory documents have been considered. Golunov S.V. and co-authors developed a method of determining the resistance to heat transfer based on thermal imaging examination with the placement of sensors on the surfaces of the building envelopes. Abramova E.V. together with other researchers created a method of thermal non-destructive testing using a thermal imaging system, temperature and heat flow sensors. The possibility of experimentally determining the reduced resistance to heat transfer of external building envelopes under summer operating conditions using the device developed by A.E. Rusanov’s with co-authors has been described. Wang Xin et al. proposed a device for determining the resistance to heat transfer of building envelopes with improved accuracy. As a result of the analytical review, it was concluded that the presented methods make it possible to measure the resistance to heat transfer of external building envelopes when modeling various stationary and non-stationary heat transfer processes.

Analysis of the process OF non-stationary heat transfer through the wall of a cylindrical container

Analysis of the process OF non-stationary heat transfer through the wall of a cylindrical container

Termostressed state of a three-layer rectangular plate under non-stationary convective heating conditions

The study considers a rectangular isotropic plate with a layered irregular structure. It is convectively non-stationarily heated by an external environment. The initial relationships of the non-stationary heat conduction and thermoelasticity problem are formulated using a five-mode mathematical model based on the shear deformation theory of thermoelasticity. Using the methods of Fourier and Laplace integral transforms, general solutions have been obtained for the non-stationary heat conduction problem and the quasi-static thermoelasticity problem for a hinge-supported plate along its edges. A numerical analysis of the temperature field, radial deflections, normal forces, bending moments, and normal stresses, depending on geometric parameters and the Bi criterion, has been performed for a three-layer plate. The materials of its layers are made of ceramics and metal. The temperature and mechanical parameters have been analyzed for the layering configuration of the plate: metal-ceramic-metal.

DETERMINATION AND ANALYSIS OF THE TEMPERATURE FIELD IN A THREE-LAYER ISOTROPIC PLATE WITH A GIVENINITIAL TEMPERATURE DISTRIBUTION

An approximate system of two-dimensional heat conduction equations for a multilayer isotropic plate is written down. Boundary conditions for a rectangular plate of finite dimensions are formulated. A general solution of the non-stationary heat conduction problem for this plate was found using integral Fourier transforms in spatial variables and Laplace transform in time.On the basis of the obtained general solutions, the solution of the thermal conductivity problem for a three-layer plate, which at the initial moment of time is heated by a temperature field linear in its thickness, which is uniformly distributed over the surface of the plate in a rectangular region, was analyzed.The numerical analysis of the temperature field was performed for a three-layer plate, the middle layer of which is made of metal, and the outer layers are made of ceramics.