Problem Of Nonstationary Heat Conduction Research Articles

Анализ живучести магистрального нефтепровода в зоне стыкового сварного соединения

The article describes the development of a technique for analyzing the survivability of the trunk pipeline in the zone of the transverse weld during operation, taking into account the residual welding stresses. The calculation of residual welding stresses was performed by solving the problem of thermoelasto-viscoplasticity for a material with a non-stationary structure by the finite element method. Solving the nonlinear nonstationary heat conduction problem was carried out by the finite difference method using boundary conditions of the third kind. Modeling the kinetics of transformation of austenite into ferrite-pearlite and bainite under non-isothermal conditions during welding was carried out on the basis of the theory of isokinetic reactions. The calculation of survivability is based on the Irwin criterion and the Paris formula.

Non-stationary heat conduction problems for thermosensitive plate with nonlinear boundary condition on one of the surfaces

Non-stationary heat conduction problems for thermosensitive plate with nonlinear boundary condition on one of the surfaces

Determination of heat exchange coefficient in heat conductivity problems with asymmetric boundary conditions

This paper depicts an approximate analytical solution of the non-stationary heat conduction problem for an infinite plate under asymmetric boundary conditions of the third kind according to the heat balance integral method. The solution is a simple, engineering-friendly product of exponential and coordinate functions. The coordinate functions are found by the method of undetermined coefficients so that the asymmetric boundary conditions of the third kind meet the main criteria primarily. Satisfactory accuracy of the obtained solution for engineering use is provided by residual orthogonality condition abidance of the differential equation to the coordinate function obtained in this research. This method allows for errors by no more than 1% in the second approximation, in the range 1.0 < Fo < ∞ for Bi = 0 and Bi2 = 0.1. The heat transfer coefficient was determined a plate surface using the named solution along with data on the temperature change at a fixed plate spot, thus solving the inverse heat conductivity problem.

Analytical and numerical solutions of two-dimensional problems of heat conduction and electronic optics

This work is devoted to a comparative analysis of the effectiveness of various methods for the numerical solution of a non-stationary two-dimensional problem of heat conduction in a cylindrical coordinate system in the absence of axial symmetry. The analysis is carried out on the basis of the obtained analytical solution of the two-dimensional problem of heat conduction in a steady state. The results of this work are of great applied importance in calculating the processes of gas transportation through offshore pipelines, as well as in calculating the electrostatic field of focusing systems during transportation of charged particle beams in problems of electronic optics.

THE USE OF THE METHOD OF SEPARATION OF VARIABLES (FOURIER) FOR SOLVING BOUNDARY PROBLEMS OF UNSTATIONARY HEAT CONDUCTIVITY IN A MULTILAYER MEDIUM

Anticorrosive coating of pipes, precipitation of hardness salts on the walls of pipes in hot water supply systems, heating, refrigeration systems, in coils for charging and discharging heat accumulators, coils of heat exchangers and a multilayer structure of metal-plastic pipes for the heating system and for the floor heating systems is an additional thermal resistance for the transfer of heat from the coolant to the environment. This resistance must be taken into account when calculating heat transfer from the pipe surface, both to increase the efficiency of heat exchangers and to calculate unproductive heat losses to the environment from main pipelines and risers of engineering systems. During the design process, the specialists are faced with the question of how to reduce or increase the heat transfer of 1 m of a steel pipe. To increase, you need to change the infrared radiation up. This is done with paint. Red color enhances heat dissipation. It is better if the paint is matte. Another approach is to install ribs. They are mounted externally. This will increase the heat transfer area. And for a "warm floor" system or a coil immersed in a solid medium (for example, a ground collector of a heat pump or a coil for charging / discharging a heat accumulator with a solid heat storage material), it is necessary to correctly calculate the heat transfer of 1 m of the pipe in order to ensure heating or cooling of this pipe to the required parameters. When do you need to decrease the parameter? The need arises when optimizing a section of the pipeline located outside the residential area, in an unheated volume. Then experts recommend insulating the site - isolating it from the external environment. According to M. Jacob's data, the formulas for heat transfer by thermal conductivity through flat walls can often be applied with sufficient accuracy for cylindrical walls, if the heat transfer surface is taken along the average thickness. Moreover, a large number of practical problems of calculating temperature fields in multilayer objects can be calculated as one-dimensional. Previously, an analytical solution to the homogeneous problem of non-stationary heat conduction in multilayer objects with stationary boundary conditions of the third kind was proposed. This article discusses the issues of unsteady heat conduction in multilayer objects. A solution to the homogeneous boundary problem with nonstationary boundary conditions of the third kind is proposed. The solution is based on the Fourier variable separation method by the eigenfunctions of the problem and the Duhamel integral. The proposed solution formula has an explicit form and, due to the recurrent form of writing the basic relations, can be useful in numerous calculations.

Nonstationary Heat-Conduction Problem for a Half-Space with a Multilayer Coating Upon Cyclic Change in the Ambient Temperature

Using the integral Laplace transformation and generalized boundary conditions, the authors have obtained the analytical solution to a one-dimensional nonstationary heat-conduction problem for a half-space with a multilayer coating on piecewise uniform change in the ambient temperature. A study has been made and regularities have been established of thermal processes occurring in the body and the coating in thermal cycling.

Modeling and investigation of temperature fields at phase boundaries in powder mixtures undergoing melting and chemical transformation

An important component of the process of hardening parts by induction surfacing is the heating of hard alloy and flux particles in the surfacing charge. The article describes complex studies on measuring and modeling temperatures at phase boundaries in complex melting and thermoreactive powder mixtures. To register the temperature in the process of induction surfacing, it is proposed to use the XA-microthermocouple method and the method of thermal indication using SHS compositions. The data of numerical modeling and solution of the non-stationary problem of heat conduction in the selected model of composite contact materials are presented. The developed methods of complex registration of temperature in the process of induction surfacing make it possible to determine the melting temperatures of the surfacing charge and its individual components, as well as the surface of the part.

Cylindrical body temperature field simulation which made in the transitional thermal process conditions out of polymer material

The advancing requirements for strength, relaxation, thermophysical, electrical, and other structural elements characteristics actualizes the polymer composite material use for the soft part and node point manufacture, which improves performance index. This paper reported the need to take into account relaxation phenomena in predicting the body’s thermal field development that is made of polymeric materials, and the thermal relaxation time and the thermal damping time proportional to the duration of transient thermal process certain periods. In this article three-period thermal process in a cylindrical body mathematical model is presented. cylindrical body made of a low-heat-conducting material by using a heat conduction hyperbolic equation that is reflecting the heat flow relaxation and thermal damping phenomenon. A numerical solution to the problem of unsteady heat conduction in a circular disk for a two-phase delay equation is presented, which is based on the grid method implementation by using a three-layer implicit difference scheme and the finite difference method use. Calculation formulas for the run-through coefficients as well as the temperature values at the outer boundaries are concluded using the boundary conditions approximation for the intermediate and upper time layers, taking into account the multi-period of the process. The implementation of the modified run-through method when solving the non-stationary heat conduction problem in a cylindrical body, taking into account the finite heat propagation speed and thermal damping is described. The calculation results for the cylindrical body temperature field are obtained by using the polymethyl methacrylate example upon sudden heating based on a model with a two-phase delay. The results presented in this paper aid in an increase in predicting temperature field accuracy in polymer composite materials in the transient thermal processes study.

Software for motion analysis of devices installed on polymer shock absorbers

A description of the method and program for solving the problem of analyzing the motion of the device installed on the polymer shock absorber is given. The equation of dynamics using a small parameter is used to describe the motion of the device. The values of displacement and rotation angle of the device is obtained by modeling the motion by solving integro-differential equations. The procedures of the Green’s functions building as well as grid methods are used. The influence of temperature on the properties of shock absorbers is taken into account by way of solving the three-dimensional problem of non-stationary thermal conductivity for a shock absorber in the form of a parallelepiped. The Fourier method of dividing variables is used as a method of solving this problem. Temperature distributions by shock absorber volume are set and analyzed. Than temperature values in nonlinear expression are used in the kernel structure in Boltzmann - Volterra equations. The critical mode of motion of the device, when external excitation has a fast growth mode, and temperature range exceeds one hundred Celsius degrees, is analyzed and the dependence of the motion of the center of mass of the device on time and temperature is obtained. The description of the software in which the presented methods of calculation for problems of nonstationary thermal conductivity and device dynamics are realized, is given. The program works in console mode, a window interface is developed for displaying graphs of functions. The examples of the program’s operation both the nonstationary heat conduction problem and for shock absorber’s dynamics are presented.

Simulation of Frictional Wear with Account of Temperature for Polymer Composites

The paper proposes a finite element approach with a mathematical model and an algorithm for simulating the wear of polymer composites in friction joints with account of temperature. The polymer interaction with a counterpart is modeled by solving a stress-strain contact problem with regard for the physical nonlinearity of deformation in polymer composites. The contact temperature is estimated by solving a nonstationary heat conduction problem with regard for mechanical-to-thermal energy conversion and for heat loss via convection without any additional heat exchange assumption. Reasoning from the temperature calculated, the state of finite elements associated with the properties of a polymer composite is changed (elastic modulus, heat capacity, yield strength, tensile strength), and those elements for which one of the fracture criteria holds are deleted as “worn”. The mesh is thus rearranged into a new one with the current stress-strain and temperature values interpolated to it. The approach is applied to analyze the effect of temperature and roughness on the friction and wear of homogeneous polymer composites and polymer coating–steel substrate systems. The results of simulation are compared with experimental data for ultrahigh molecular weight polyethylene in dry sliding friction with a steel counterpart.

Evaluating the Stress and Vibration Conditions of the Rotor of Steam Turbine with the Defect

Consideration was given to the vibrations of the two-bearing weighty rotor of the steam turbine with the acquired defect in the form of cross crack caused by the working fluid temperature field. Rotor vibration equations were derived during the three-D simulation using the method of finite elements taking thus into consideration the temperature field in the form of additional volume forces. The equations are supplemented by a special mass matrix whose introduction allows us to take into consideration a change in centrifugal forces in a linear statement caused by the offsets and retain their radial directionality. The alternating two-dimensional temperature field is defined by the solution of the nonstationary problem of heat conductivity. The stressed state, the coefficients of stress intensity along the crack front and the crack edge contact conditions were defined for different rotor rotation phases. The stress intensity coefficient values calculated using asymptotic formulas for the rotor with the 50 % cross-section crack depth are much lower than critical and present no danger for the quasistatic state. However, these values can increase significantly in the case of the resonance state. The rotor vibration state was studied for different rotation frequencies in the presence and absence of temperature field. A maximum effect of the influence of nonstationary temperature field in the rotor with the cross crack on its vibrations is manifested at a maximum radial temperature difference. The temperature field reduces considerably maximum inflection values and peak-to-peak values. The superresonance 2/1 that occurred in the rotor in the absence of temperature field disappears and the vibrations approach a monoharmonic type and it is explained by the constancy of the contact area of crack edges during the rotor rotation.

Laminated cross-ply cylindrical shell due to transient heating

The stress-deformed state of an antisymmetric cross-ply laminated circular closed cylindrical shell subjected to initial local heating in initially is investigated. For the study, the mathematical model of the shear theory of inhomogeneous shells of the Tymoshenko type is used. The two-dimensional heat equation is deduced under the linear distribution of temperature over the thickness. By methods of Fourier and Laplace integral transformations the solution of the non-stationary heat conduction problem and the quasi-static thermoelasticity problem for a finite simply supported circular cylindrical shell is obtained. Numerical results are presented for four-layer orthotropic composite. Cite as: U. V. Zhydyk, “Laminated cross-ply cylindrical shell due to transient heating,” Prykl. Probl. Mekh. Mat. , Issue 17, 113–120 (2019) (in Ukrainian), https://doi.org/10.15407/apmm2019.17.113-120

Non-stationary heat conduction problems for thermosensitive plates

Determination of the temperature fields in the plates, taking into account the non-uniform distribution of the initial temperature, thermal radiation, temperature dependence of thermophysical characteristics, densities of surface and volume heat sources is reduced to recurrent systems of nonlinear algebraic equations. The Kirchhoff transform, Green's functions of corresponding linear heat conduction problems and linear splines were used. An example of numerical studies is provided. Cite as: B. V. Protsyuk, “Non-stationary heat conduction problems for thermosensitive plates,” Prykl. Probl. Mekh. Mat. , Issue 17, 121–133 (2019) (in Ukrainian), https://doi.org/10.15407/apmm2019.17.121-133

Solution to Non-stationary Inverse Heat Conduction Problems for Multi-layer Bodies, Based on Effective Search for the Regularization Parameter

Solution to Non-stationary Inverse Heat Conduction Problems for Multi-layer Bodies, Based on Effective Search for the Regularization Parameter

SIMPLIFIED BOUNDARY CONDITIONS AT CERTAIN RESOURCE DURABILITY OF PISTONS AT DIFFERENT DESIGN STAGES

The analysis of the literature on obtaining the control functions boundary conditions non-stationary heat conduction problem piston, which allows us to estimate its resource. On the basis of the experimental study piston of the diesel 4CHN12/14 it was established that for the zones of the first and second piston rings it is necessary to have data on the control of the boundary conditions Ф t (τ) for a number of transients. Considering the complexity of obtaining these functions, it is proposed to allow the simplification boundary conditions, namely the control functions Ф t (τ), in determining the resource strength piston at the initial stages design. For this purpose, an instantaneous change in the boundary conditions was delayed in time relative to the real beginning transition process. The study was conducted for a piston of the diesel 4ЧН12/14 at power N е =75,3кВт. It is established that the estimated level of accumulated damage to the material in the zone edge combustion chamber, considering the high-frequency component, is an order of magnitude higher than without consideration. Also, a series of calculations for simplified boundary conditions Ф t (τ) for the zones of the first and second piston rings with a different delay time in relation to the moment of the start of the transient process of the diesel engine was performed. The authenticity of the proposed simplifications of the boundary conditions with the observance of the concept of guaranteed resource provision was determined using the indicator of the relative estimated increase of the resource ϕ. The values of the indicator ϕ are given with and without the high-frequency component. The results showed that for various types of simplifications boundary conditions the influence of the high-frequency component varies. So, at the initial stages of designing the application of a simplified type boundary conditions control function with a delay in time in the range of 17-22 sec, it is possible to conduct a comparative analysis of structures without considering the high-frequency component of their temperature state. Since these data have a weight of less than 1%. To ensure the reliability of the result, by observing the concept guaranteed assurance physical reliability structures in the process of their design and refinement, the consideration of the high-frequency component temperature in the surface layer piston rod is compulsory.

Production of three-layer steel bimetallic strips in the unit of continuous casting and deformation. Report 1

High technical and economic efficiency of the use of bimetals in chemical, oil, transport and energy engineering and other industries is described. The urgency of creating high-performance continuous processes for the production of bimetallic strips is substantiated. The authors have established the main technological tasks for development of the processes of obtaining bimetal of wide class. The paper describes resource-saving production technology of three-layer bimetals alloyed steel – constructional steel – alloyed steel at the unit of combined process of continuous casting and deformation. Possibilities of the proposed technology are outlined from the standpoint of improving the quality of bimetallic strips. The initial data are given to determine the temperature change over time of the main steel strip as it passes through the molten metal of the alloyed steel. The equations are given for non-stationary heat conduction, initial and boundary conditions for determining the temperature fields of main strip and cladding layer when obtaining a three-layer bimetallic strip on the unit of a combined process of continuous casting and deformation. The values of density, thermal conductivity and heat capacity for steel St3 were determined in a given temperature range. A procedure is described for calculating temperatures in the ANSYS package by solving a non-stationary heat conduction problem in a flat formulation by the finite element method. The authors have described the geometric model for calculating the temperature of strip and molten metal of the cladding layer. Values of the coefficient of heat transfer between the main strip and molten metal of the cladding layers of bimetallic strip are given adopted for calculation. Characteristic points are indicated in the model for calculating the temperatures of main strip and molten metal of the cladding layer. The graphs show temporal changes in these temperatures at production of a three-layer bimetallic strip on the unit of combined process of continuous casting and deformation. Calculated data on the time variation of temperature of main strip and molten metal of the cladding layer at characteristic points are given for different values of the contact heat transfer coefficient.

Stochastic transient analysis of thermal stresses in solids by explicit time-domain method

Stochastic heat conduction and thermal stress analysis of structures has received considerable attention in recent years. The propagation of uncertain thermal environments will lead to stochastic variations in temperature fields and thermal stresses. Therefore, it is reasonable to consider the variability of thermal environments while conducting thermal analysis. However, for ambient thermal excitations, only stationary random processes have been investigated thus far. In this study, the highly efficient explicit time-domain method (ETDM) is proposed for the analysis of non-stationary stochastic transient heat conduction and thermal stress problems. The explicit time-domain expressions of thermal responses are first constructed for a thermoelastic body. Then the statistical moments of thermal displacements and stresses can be directly obtained based on the explicit expressions of thermal responses. A numerical example involving non-stationary stochastic internal heat generation rate is investigated. The accuracy and efficiency of the proposed method are validated by comparison with the Monte-Carlo simulation.

THERMOELECTRIC DEVICE FOR TREATMENT PANARIATION

Objectives The aim of the study is to develop a thermoelectric device for the treatment of felon, its mathematical modeling, experimental tests of the laboratory model of the device, the study of thermal processes occurring in it. Method. A design of a thermoelectric device for the treatment of felon, providing the possibility of both uniform and contrasting therapeutic heat effects on the fingers is proposed. Result. A mathematical model of the device has been developed, implemented on the basis of solving a non-stationary two-dimensional heat conduction problem for a system of complex configuration with boundary conditions of the second and third kind. Experimental studies of the device were carried out on a specially designed test bench for checking the adequacy of the mathematical model. A two-dimensional non-stationary heat conduction problem was solved for a complex system with a rectangular geometry of fragments and heat sources. The temperature change of various points of the “device-object” system of exposure in space and in time at various values of the cooling and heating capacity of a thermoelectric battery (TEB) was studied. Comparison of calculated and experimental data. Conclusion. The results of research have shown the effectiveness of the use of the developed device for the implementation of thermal procedures in the treatment of felon in terms of efficiency, versatility, impact reliability, comfort and accuracy of maintaining temperature conditions. It is shown that it is possible to increase the efficiency of the device using a combination of thermopile operation modes (maximum cooling capacity and maximum coefficient of performance), as well as improving the intensity of heat removal from its reference junctions.

Інтегральні моделі нестаціонарних задач теплопровідності на основі методу теплових потенціалів

Інтегральні моделі нестаціонарних задач теплопровідності на основі методу теплових потенціалів

The problem of a periodically two-layered coating on a homogeneous half-space heated by moving heat fluxes

The paper deals with the nonstationary heat conduction problem of a homogeneous half-space with a multi-layered periodic coating subjected to the action of a moving heat source with constant velocity on its surface. The analysis is performed with the framework of two approaches: (1o) the first one is based on the exact description, (2o) the second one uses the homogenized model with microlocal parameters. Some special cases of the heat source and components of the stratified coating are investigated. The obtained results are compared for the determination of applicability of the homogenized model and the periodically layered coatings.