Thermal Conductivity Equation Research Articles

Simulating Thermal Interaction of Gas Production Wells with Relict Gas Hydrate-Bearing Permafrost

The thermal interaction of a gas production well with ice-rich permafrost that bears relict gas hydrates is simulated in Ansys Fluent using the enthalpy formulation of the Stefan problem. The model admits phase changes of pore ice and hydrate (ice melting and gas hydrate dissociation) upon permafrost thawing. The solution is derived from the energy conservation within the modeling domain by solving a quasilinear thermal conductivity equation. The calculations are determined for a well completion with three casing strings and the heat insulation of a gas lifting pipe down to a depth of 55 m. The thermal parameters of permafrost are selected according to laboratory and field measurements from the Bovanenkovo gas-condensate field in the Yamal Peninsula. The modeling results refer to the Bovanenkovo field area and include the size of the thawing zone around wells, with regard to free methane release as a result of gas hydrate dissociation in degrading permafrost. The radius of thawing around a gas well with noninsulated lifting pipes operating for 30 years may reach 10 m or more, while in the case of insulated lifting pipes, no thawing is expected. As predicted by the modeling for the Bovanenkovo field, methane emission upon the dissociation of gas hydrates caused by permafrost thawing around producing gas wells may reach 400,000–500,000 m3 over 30 years.

POSSIBLE RISKS CONTROL METHODOLOGY IN SOLVING APPLIED PROBLEMS

The article deals with developed mathematical models and improved computational methods in terms of taking into account the specifics of the simulated processes to predict and control possible risks in order to increase the efficiency of solving applied problems. The authors propose a method of technological innovations managing to improve the efficiency of complex systems. As a demonstration of its universality, the article calculates and optimizes the technical parameters of laser emitters to increase the speed and accuracy of laser separation of the embryo. Due to the technical characteristics of the emitters and the geometry of the embryo, nonlocal boundary value problems of systems of multidimensional, non-linear differential equations of thermal conductivity are used to describe the state of the simulated system. Methods from the theory of differential equations in the space of generalized functions are used to prove the conditions of existence and the uniqueness of their solution. This allowed to guarantee the correctness of computational and applied optimization mathematical models. The authors have formed a grid model of discretization of optimized parameters, solved boundary value problems using the method of directed search of local extremums, compared to the trauma of cells, which is achieved at the nodes of the grid model. In order to increase the accuracy of optimization, the steps of the grid model were ground. Grinding and spot analysis of embryonic cell injury continues until the time allotted for optimization is exhausted or the specified optimization accuracy is achieved. According to the authors of the article, the research allowed to expand the range of tasks of economic and mathematical modeling for forecasting and control of possible risks to improve the efficiency of calculation and optimization of control parameters of complex systems.

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

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

Mapping of Western Siberian heat flow (southeast)

This paper maps the heat flow density from the pre-Jurassic basement within a large territory of oil accumulation (circa 120 thousand sq. km) in the South-East of Western Siberia. Values of heat flow, calculated for 201 deep wells, comprise a dataset for developing the map with contour lines for every 2 mW/m2. These values were calculated by solving the inverse problem of Geothermy — one-dimensional initial-boundary value problem for equation of thermal conductivity in a solid with the moving upper boundary. The accepted mathematical statement is sufficiently accurate for modeling near horizontal bedded sedimentary section: existence of heat flow convectional component is taken into account via calculation of an effective heat flow value. The map shows different types of anomalous features of heat flow density distribution. Previously it was stated for Western Siberian Plate that values of deep heat flow within positive tectonic structures of sedimentary cover are 5—20 % higher than within negative tectonic structures. As it is, combined analysis of deep heat flow density distribution and location of tectonic structures (Kaimysov arch, Parabelmegaarch, especially Alexandrov arch and Pudino mega swell) shows tendency among positive tectonic structures for increasing deep heat flow value. However, it is not always so. For example, there is the utterly different correlation for the Srednevasyugan mega swell. This structure is characterized with lower heat flow. The location of the Nizhnevartovsk arch is almost untraceable in the deep heat flow density distribution. Concerning oil-and-gas potential ... (?) A large positive anomaly has formed in the zone around the Traigorodsko-Kondakov field in the north. Two positive anomalies are in the central part of the map: around the Snezhnoe field and close by the Lomovoe, the Ozernoe and the Katylgin fields. Such fields as the Rybalnoe, the Pindzhin and the Mirnoe surround a positive anomaly in the southeastern part of the map.
 This paper contains a catalogue of discrete values (by wells) and a map of heat flow, which may be used as a «framework» in basin modeling. Upcoming research concerning origin of heat flow density anomalies — graded assessment of possible influence of tectonics, material composition and oil-and-gas potential of basement rocks has theoretical and practical significance.

Introducing hydrogen bonding contribution to the Patel-Teja thermal conductivity equation of state for hydrochlorofluorocarbons, hydrofluorocarbons and hydrofluoroolefins

The hydrogen bonding contribution has been added to the Patel-Teja thermal conductivity equation of state for the first time to compute the thermal conductivity of the liquid mixtures containing hydrochlorofluorocarbons, hydrofluorocarbons and hydrofluoroolefins. The coefficients of the pure fluids are determined by using 4 strategies. Then an appropriate mixing rule and the cross association terms have been used, and the present model is used for binary and multicomponent mixtures of the liquid phase. The accuracy of this model has been determined through the thermal conductivities of 12 binary liquid mixtures and 1 ternary liquid mixture. Furthermore, the model is used with and without binary interaction parameters to test the predictions of the present thermal conductivity equation of state. The predictions of this model show that the application of hydrogen bonding contribution and the first strategy results in generally low deviations for the liquid mixtures (Overall AAD% is 7.15% and 6.18% without and with binary interaction parameters, respectively).

A weakly nonlinear wave equation for damped acoustic waves with thermodynamic non-equilibrium effects

The problem of propagating nonlinear acoustic waves is considered; the solution to which, both with and without damping, having been obtained to-date starting from the Navier–Stokes–Duhem equations together with the continuity and thermal conduction equation. The novel approach reported here adopts instead, a discontinuous Lagrangian approach, i.e. from Hamilton’s principle together with a discontinuous Lagrangian for the case of a general viscous flow. It is shown that ensemble averaging of the equation of motion resulting from the Euler–Lagrange equations, under the assumption of irrotational flow, leads to a weakly nonlinear wave equation for the velocity potential: in effect a generalisation of Kuznetsov’s well known equation with an additional term due to thermodynamic non-equilibrium effects.

МАТЕМАТИЧНІ ПРОСТОРОВІ МОДЕЛІ ВИЗНАЧЕННЯ ТЕМПЕРАТУРНОГО ПОЛЯ ІЗ ЛОКАЛЬНО ЗОСЕРЕДЖЕНИМ ТЕПЛОВИМ НАГРІВАННЯМ

Linear and nonlinear mathematical models for determining the temperature field, and later the analysis of temperature regimes in isotropic spatial inhomogeneous media exposed to internal and external thermal loads have been developed. To do this, the thermal conductivity for such structures is described as a whole using symmetric unit functions, which allows us to consider boundary thermal conductivity problems with one linear and nonlinear differential equation of thermal conductivity with discontinuous coefficients and linear and nonlinear boundary conditions on boundary surfaces. In the case of a nonlinear boundary value problem, the Kirchhoff transform is applied, which linearizes the initial nonlinear equation of thermal conductivity and nonlinear boundary conditions and results in a second-order linear differential equation with partial derivatives and singular coefficients with respect to the Kirchhoff function with linear conditions. To solve the obtained linear boundary value problem, the method of integral Fourier transform was used, as a result of which an analytical solution was obtained, which determines the Kirchhoff linearizing function. As an example, the linear and cubic dependences of the thermal conductivity of structural materials on the structure, which are often used in many practical problems, are chosen. As a result, analytical relations in the form of quadratic and biquadratic equations are obtained to determine the temperature distribution in the thermosensitive layer with foreign inclusion at external local heating. Numerical analysis of temperature behavior as a function of spatial coordinates for given values of geometric and thermophysical parameters is performed. The influence of foreign inclusion on the temperature distribution was studied if the material of the medium was selected ceramics VK94-I, and the inclusion – silver, aluminum and silicon. To determine the numerical values of temperature in these structures, as well as the analysis of heat transfer processes in the middle of these structures due to internal and external heat loads, developed software that uses a geometric representation of temperature distribution depending on spatial coordinates. The obtained numerical values of temperature testify to the correspondence of the developed mathematical models of the analysis of heat exchange processes in spatial inhomogeneous media with internal and external heating to the real physical process. Software also allows you to analyze this type of environment, which are exposed to internal and external heat loads, in terms of their heat resistance. As a result, it becomes possible to increase it and protect it from overheating, which can lead to the destruction of not only individual elements but also the entire structure.

МОДЕЛЬ ОБНАРУЖЕНИЯ И ОЦЕНКИ ПОЖАРООПАСНОСТИ ЭЛЕКТРОПРОВОДКИ ПАССАЖИРСКОГО ВАГОНА ПО ТЕПЛОВОМУ ИЗЛУЧЕНИЮ

Emergency states that arise at influence of free fire on an oil and gasoline tank shell lead to thermal stress that can cause shell damage, a decrease of hardness and material strength. The paper considers a method for determination of a non-steady thermal field of the shell in a fire centre. Besides, the authors have got a thermal conductivity equation in partial derivatives and suggest a new approximation of the thermal field in the form of polynomials. The method is realized in the MathCad program complex and can be used at design of railway tanks for transportation of dangerous freights and at development of systems for protection from emergency thermal influences.

МОДЕЛИРОВАНИЕ НЕСТАЦИОНАРНОГО ТЕМПЕРАТУРНОГО ПОЛЯ ОБОЛОЧКИ КОТЛА НЕФТЕБЕНЗИНОВОЙ ЦИСТЕРНЫ ПРИ ПОЖАРЕ

Emergency states that arise at influence of free fire on an oil and gasoline tank shell lead to thermal stress that can cause shell damage, a decrease of hardness and material strength. The paper considers a method for determination of a non-steady thermal field of the shell in a fire centre. Besides, the authors have got a thermal conductivity equation in partial derivatives and suggest a new approximation of the thermal field in the form of polynomials. The method is realized in the MathCad program complex and can be used at design of railway tanks for transportation of dangerous freights and at development of systems for protection from emergency thermal influences.

RESEARCH OF THE VALUE OF CONTACT MELTING DEPENDING ON THE COMPONENTS OF THE CONTACT MATERIAL DURING CURRENT SWITCHING

The amount of melting of PML-type starter contacts with current load 4 is investigated; 6.3; 10A. The contact material of the starters used for the production of silver-based serial contacts (СрН-90 and СрМ-0.2+М1) and experimental copper-based contacts is used in the research. The formula for determining the amount (depth) of penetration during a single current switching is given. The electric arc (its burning time) is directly related to electroerosion phenomena (depth of contact penetration). The formula for determining the depth of penetration is obtained by solving the equation of thermal conductivity taking into account the boundary conditions of the II kind and relates the value of the depth of penetration to the energy and thermophysical parameters of the contact material, which is determined by the constituent components of the material. Difficult operating conditions in agriculture and numerous influencing factors complicate the choice of contact material for starters. In order to ensure the operation of devices with specified reliability indicators, their contact details must resist the influence of an electric arc, a chemically and biologically aggressive atmosphere, and mechanical loads. In general, contacts should be characterized by the following physical parameters: stability of contact transient resistance, high specific electrical conductivity, high erosion resistance and corrosion resistance, high arc resistance and resistance to welding, a combination of mechanical strength and high plasticity. It is practically impossible to choose a universal material that would meet all the mentioned requirements, therefore, depending on the functional purpose of the contact node, a compromise decision has to be made. Contacts of starters operating in the area of small and medium currents (and infrequent switching on and off of short-circuit currents) must, first of all, ensure the stability of the transient resistance under the influence of aggressive atmospheric impurities in combination with high arc resistance and resistance to welding. Therefore, in recent years, attempts have been made to replace the contact material Ag-Ni and Ag-CdO (used in PML starters from 25 A and above) with other materials. Transient resistance depends on the actual contact area of the contacts and on the specific resistance of the contact material. The effective area of contact depends on the magnitude of the contact pressure and increases exponentially with its growth until the compressive stress is higher than the yield point of the material. On the other hand, the transient resistance depends on the resistance of the boundary layer, which is determined by its composition (the presence of oxide, sulfide and other films, dust, etc.) and specific electrical resistance. Taking into account the requirements for switching devices of starters suitable for work in the agricultural sector and in order to save precious metals, it is appropriate to develop contact materials in the direction of improving the properties of multi-component composite materials based on copper and refractory compounds. Copper is the closest material to silver in terms of physical and mechanical properties. But its main drawback is that it oxidizes in the air and the oxidation process intensifies as the temperature rises. As a result, insulating films appear on the surface of the copper, which disrupt the operation of the contacts and lead to failures. It is known that copper oxide films are formed even at room temperature and their thickness reaches no more than 5 μm. Such a film protects copper from further oxidation by oxygen. The specific resistance of Cu2O is 10 μΩˑm, but it does not significantly affect the contact resistance of the electrodes, since the film is very thin, so electrons pass through it due to the tunnel effect.

Stressed and strained state of layered cylindrical shell under local convective heating

The stress-strain state of a layered composite cylindrical shell under local heating by the environment due to convective heat exchange has been studied. The equation of the six-modal theory of thermoelasticity and the two-dimensional equation of thermal conductivity of inhomogeneous anisotropic shells are used for this purpose. The solution of the nonstationary heat transfer problem and the quasi-static thermoelasticity problem for a finite hinged orthogonally reinforced shell of symmetric structure is found by the methods of integral Fourier and Laplace transforms. Numerical results are given for the three-layer shell.

THE USE OF INFRARED HEATING IN SOIL DISINFECTION IN PROTECTED GROUND AND THE MECHANISM OF HEAT PROPAGATION

To disinfect the soil in protected ground, installations operating on various methods of energy supply are used. The article proposes using infrared heating as an energy carrier. When infrared radiation interacts with the surface of the medium, it is partially reflected, and partially penetrates into the material, is absorbed in it and turns into heat. The transfer of thermal energy (kinetic energy of microparticles) in a substance (in a solid layer of soil) is determined by the processes of thermal conductivity. The phenomenon of thermal conductivity is manifested by direct contact of individual particles in the soil layer having different temperatures, through the propagation of elastic waves. Infrared radiation has a small penetrating power. The question arises whether infrared heating can provide the required depth of soil disinfection. Therefore, a theoretical and experimental justification of the heat propagation in the soil is necessary. (Research purpose) The research purpose is studying the possibility of using infrared heating during soil disinfection in protected ground and the mechanism of heat propagation. (Materials and methods) The following assumptions were used for the analytical analysis of soil heating: the soil is isotropic and homogeneous, that is, its properties are the same in all directions, and the temperature dependences of the physical coefficients are weak; the source of heat is the soil surface and it does not depend on temperature. The article presents the solution of the equation of thermal conductivity. (Results and discussion) In order to verify the adequacy of the mathematical model and evaluate the empirical coefficients, full-scale studies of the temperature field in protected ground conditions were carried out. A numerical study of the solution of the equation in the range of its approximations from 100 to 200 terms gives the value of the heating time τ = 15-16 minutes. (Conclusions) It is recommended to use infrared heating when disinfecting only thin layers, for example, a layer of soil on a conveyor belt or any surface in protected soil.

Choosing the thermal conduction equation solution method in SPH

The set of explicit iterative schemes for parabolic problems (heat conduction as example) is reviewed. The iterative process is constructed based on algebraic polynomials (Chebyshev, Lanczos, or Legendre) properties. They combine the simplicity of explicit time-integration with the increased allowed timestep. This approach may be applied at smoothed particle hydrodynamics (SPH) simulations as a replacement for the popular implicit time-integration schemes, whose drawbacks might get stronger especially on SPH-like contrary to mesh-style space description.

MATHEMATICAL MODELING OF THERMAL EFFICIENCY OF BUILDING EN-VELOPE OF MULTI-STOREY BUILDINGS WITH ACCOUNT OF INDIVIDUAL INSULATION

At present, the problem of general thermal modernization of building envelopes is given much attention both at the level of scientists and consumers. This is one of the effective ways to reduce natural gas consumption, reduce the negative impact on the environment, maintain and improve comfortable indoor conditions. Over the last decade, the population has rapidly begun to insulate their homes in order to raise the indoor air temperature to a comfortable level in the multi-storey residential sector. Due to insufficient attention of the authorities in the housing and communal sector, the lack of scientific research and widespread public awareness, there is a massive thermal insulation of building by residents of multi-store buildings within their own apartments. But the study of thermal processes that occur in individual thermal insulation of enclosing structures is currently not fully completed. Therefore, in the context of significant increases in gas and electricity prices, this problem is relevant.
 In the study was carried out mathematical modeling of a fragment of a partially insulated wall of an enclosing structure with determination of heat flux by solving a three-dimensional differential equation of thermal conductivity with boundary conditions of II, III and IV kind and distribution of characteristics of building structures and insulation. These results can be used in the analysis of the efficiency of insulation of the building taking into account the fragmentary insulation and of comparison with systemic thermal modernization.
 As a result of modeling, the three-dimensional temperature fields of wall surfaces, are determined, there are additional heat fluxes (thermal bridges), which are not considered in the simplified one-dimensional calculation. In one-dimensional calculation, the heat flux from the wall is reduced by 2.43 times during insulation. Taking into account the total heat flow from the side surfaces near the window (thermal bridges) and system insulation - by 1.75 times. With fragmentary insulation and considering the total heat flux from the side surfaces near the window - by 1.6 times.
 The next stage of calculations is the determination of the actual air temperatures in the premises of a multi-storey building considering the actual condition of enclosing structures and heating systems, heaters, mode parameters of the coolant and outdoor air parameters. The methods and means of this analysis can take into account the final data of heat loss adjustment after the mathematical modeling presented in this paper. In consequence, the results will be taken into account in the projects of thermal modernization of buildings, reconstruction of heating systems, rational placement of sources, selection of equipment and regulation of devices.

Нeat and mass transfer models at boundary lubrication to determine the transition temperatures

At present, kinetic and thermodynamic methods for assessing the lubricating effect of oils are being increasingly developed. At the limit friction, the reduction of friction and wear of surfaces is due to the ability of the lubricant to form layers of adsorption or chemical origin on the surface. Analytical models of transition temperatures and wear in the limit lubrication mode must be used to mathematically describe the processes in the subsystems and the transition between them. The Fourier equation of thermal conductivity is accepted as the basic calculated dependence. It is assumed that the process of heat propagation under the conditions of formation of lubricating films is not Markovian, i.e. the magnitude of the heat flux is determined by the entire "history" of heat transfer in a certain elementary volume. The equation of motion of a lubricating film over the surface of a body that is being lubricated is obtained from the equation of motion for a Newtonian continuous medium. As a result, nonlinear heat and mass transfer models are obtained to determine the transition temperatures in the formation of boundary lubricating films in the concept of structural-thermodynamic approaches to describe the processes of boundary lubrication of surfaces

Modeling of thermal stresses during hardening the product surface by thermal pulse

A particular solution of a linear variant of the dynamic thermal elasticity problem is considered in application to modeling the conditions of surface hardening of metal products by an energy pulse. The authors determined the equation of medium motion with the model of temperature pulse tested earlier for compatibility with special cases of the equations of parabolic and hyperbolic thermal conductivity. The problem of loading a flat plane of a short circular cylinder (disk) with a temperature pulse is presented. Pulse is a consequence of adopted structure of the volumetric power density of the heat flux, the time multiplier of which has the form of a single wave of the Heaviside function. Classical thermoelastic displacement potential and the method of its division into the product of independent variables functions were used to construct the thermal stress tensor. Differential equations for multiplier functions and their general solutions were found. Natural boundary conditions were set for the components of thermal stress tensor, and their tasks were solved. The obtained solutions are in the form of segments of functional series (the Bessel function in radial coordinate and the exponential function in axial coordinate). The article considers a numerical example of loading a disk made of 40KhN steel which has the mechanical properties sensitive to temperature treatment. Maple computer mathematics package was used in the calculations. Approximate solutions take into account the first 24 terms of the functional series. Estimation of the example makes it possible to explain the presence of stress peaks and stress intensity as a consequence of mutually inverse processes of temperature stress growth and reduction of elasticity coefficients with temperature rise. The numerical example warns against relying only on estimates of solutions to thermoelasticity problems without taking into account the plastic and viscous properties of the material.

Monitor and control test room for investigating thermal performance of panels incorporating phase-change material

Abstract. This article aims to present equipment designed and developed to study the effective thermal conductivity of composite panels. The composite panel used is a rigid polyurethane foam covered with a layer of aluminum on both sides. The panel is mounted in the test chamber equipped with several sensors and actuators connected via an Arduino platform. Tests have been carried out by applying heat to impose various interior temperatures. Sensors at different locations are used to monitor and record temperatures in and around the composite panel during heating and natural cooling. A model, based on the Fourier equations of thermal conduction and natural convection heat transfer for the steady state, was developed to assess the effective thermal conductivity. The performance of the system was confirmed using temperature signals through the panels for thermal characterization of composite materials. The determined effective thermal conductivity obtained was in agreement with the experimental values reported in the technical data sheets with relative deviations of less than 10 %.

Математичні моделі температурного поля в термочутливих елементах електронних пристроїв

Nonlinear mathematical models for the analysis of temperature regimes in a thermosensitive isotropic plate heated by locally concentrated heat sources have been developed. For this purpose, the heat-active zones of the plate are described using the theory of generalized functions. Given this equation of thermal conductivity and boundary conditions contain discontinuous and singular right parts. The original nonlinear equations of thermal conductivity and nonlinear boundary conditions are linearized by Kirchhoff transformation. To solve the obtained boundary value problems, the integral Fourier transform was used and, as a result, their analytical solutions in the images were determined. The inverse integral Fourier transform was applied to these solutions, which made it possible to obtain analytical expressions for determining the Kirchhoff variable. As an example, the linear dependence of the thermal conductivity on temperature is chosen, which is often used in many practical problems. As a result, analytical relations were obtained to determine the temperature in the heat-sensitive plate. The given analytical solutions are presented in the form of improper convergent integrals. According to Newton’s method (three eighths), numerical values of these integrals are obtained with a certain accuracy for given values of plate thickness, spatial coordinates, specific power of heat sources, thermal conductivity of structural materials of the plate and geometric parameters of the heat-active zone. The material of the plate is silicon and germanium. To determine the numerical values of temperature in the structure, as well as the analysis of heat transfer processes in the middle of the plate due to local heating, developed software, using which geometric mapping of temperature distribution depending on spatial coordinates, thermal conductivity, specific heat flux density. The obtained numerical values of temperature testify to the correspondence of the developed mathematical models of the analysis of heat exchange processes in the thermosensitive plate with local heating to the real physical process.

The comparison of a discrete-continuous approach and a method of finite differences in solving the problem of unsteady-state heat and moisture transfer in the building envelope

This article is devoted to the development of methods for calculating heat and humidity regime in the building envelope. The equation of steady-state thermal conductivity with boundary conditions of the third kind and the formula for calculating heat losses of a building based on the heat transfer equation have been considered. The equation of unsteady-state thermal conductivity as well as its solution using the discrete-continual approach has also been studied. The solution of the unsteady-state heat conductivity problem with invariable over time boundary conditions using the discrete-continuous approach was proposed by A.B. Zolotov and P.A. Akimov. The subsequent modernization of the solution was conducted by V.N. Sidorov and S.M. Matskevich. The unsteady-state equation of moisture transfer based on Fick’s second law using the theory of moisture potential is derived. The solution of the unsteady-state moisture transfer equation using the finite difference method according to an explicit difference scheme as well as the solution of the unsteady-state moisture transfer equation using the discrete-continuous approach is demonstrated. To prove the effectiveness of using the discrete-continuous approach in the area of the unsteady-state humidity conditions we compared the calculation results of the distribution of moisture in a single-layer enclosing structure made of aerated concrete using two methods of moisture potential theory. It was found that the difference in the results of calculation by the discrete-continual formula and by the method of finite differences does not exceed 3.2%.

Experimental study of R-32/R-125 (75/25 wt.%) thermal conductivity in the vapor phase

The article presents the investigation of the thermal conductivity of binary mixture R-32/R-125 (75/25) in the gas state. Measurements were taken with a coaxial cylinders method in the temperature range of 305-426 K and the pressure range of 0.1-1.8 MPa. The dependence of thermal conductivity on pressure and temperature was discussed. The equations for thermal conductivity on the dew line and in the ideal gas state were obtained.