scholarly journals DETERMINATION OF THE NON-STATIONARY TEMPERATURE FIELD IN THE SYSTEM OF TWO CYLINDRICAL SHELL UNDER THE FIRE CONDITIONS

Fire Safety ◽  
2019 ◽  
pp. 84-90
Author(s):  
R. M. Tatsii ◽  
O. Y. Pazen ◽  
L. S. Shypot
Keyword(s):  
Boundary Condition ◽  
Cylindrical Shell ◽  
Temperature Field ◽  
Original Problem ◽  
Auxiliary Problem ◽  
Technical Problem ◽  
Small Radius ◽  
Steel Shell ◽  
Solid Cylinder ◽  
Stationary Temperature Field

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determining the distribution of a non-stationary temperature field in a two-layer hollow cylindrical structure with a "withdrawn" cylinder of sufficiently small radius is raised in parallel.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To find the solution of the original problem, the idea of the boundary transition is used by passing the radius of the withdrawn cylinder to zero.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.

scholarly journals DETERMINATION OF NON-STATIONARY TEMPERATURE FIELD IN THE SYSTEM OF TWO SPHERICAL SHELL

2019 ◽  
Vol 19 ◽  
pp. 79-86
Author(s):  
R. Tatsii ◽  
O. Pazen
Keyword(s):  
Boundary Condition ◽  
Temperature Field ◽  
Temperature Change ◽  
Fire Resistance ◽  
Outer Surface ◽  
Original Problem ◽  
Auxiliary Problem ◽  
Technical Problem ◽  
Small Radius ◽  
Stationary Temperature Field

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.

MATHEMATICAL MODELING OF THE HEAT TRANSFER PROCESS IN THE SYSTEM OF MULTILAYER CYLINDRICAL SOLID BODIES CONSIDERING INTERNAL SOURCES OF HEAT

2020 ◽  
Vol 1 (1) ◽  
pp. 66-75
Author(s):  
O Pazen ◽  
R Tatsiy
Keyword(s):  
Heat Transfer ◽  
Original Problem ◽  
Direct Method ◽  
Auxiliary Problem ◽  
Heat Transfer Process ◽  
Small Radius ◽  
Shell System ◽  
Multilayer Cylindrical Shell ◽  
Internal Sources ◽  
Solid Bodies

The article is devoted to the application of the direct method to the study of heat transfer processes in the "continuous cylinder inside a multilayer cylindrical shell" system. To solve the initial problem, an auxiliary problem is posed with a “remote” cylinder of sufficiently small radius. The solution is based on the reduction method, the concept of quasiderivatives, the Fourier scheme using the modified eigenfunctions method. The solution to the original problem was obtained by following the radius of the remote cylinder to zero.

scholarly journals Calculation of nonlinear elastic three-layer cylindrical shell of finite length with taking into account the continuous inhomogeneity caused by the temperature field

2019 ◽  
Vol 91 ◽  
pp. 02018 ◽  
Author(s):  
Vladimir I. Andreev ◽  
Lyudmila S. Polyakova
Keyword(s):  
Cylindrical Shell ◽  
Temperature Field ◽  
Outer Layer ◽  
Temperature Effects ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Variable Parameters ◽  
Stationary Temperature Field ◽  
Nonlinear Elastic ◽  
Nonlinear Nature

The article deals with the problem of determining the stressstrain state of a thick-walled cylindrical shell hinged on the rim near the ends, which is exposed to temperature effects. The shell consists of three layers: two layers of heat-resistant concrete and a steel outer layer. The calculation takes into account the continuous inhomogeneity of materials caused by a stationary temperature field, as well as the nonlinear nature of concrete deformation. The nonlinear problem with variable parameters of elasticity E and ν was solved by the method of successive approximations.

scholarly journals RESEARCH OF THE TEMPERATURE FIELD IN THE SYSTEM OF MULTILAYER CYLINDRICAL SOLID BODIES UNDER FIRE CONDITIONS

Fire Safety ◽  
2021 ◽  
Vol 37 ◽  
pp. 64-71
Author(s):  
R. Tatsii ◽  
O. Pazen ◽  
L. Shypot
Keyword(s):  
Cylindrical Shell ◽  
Temperature Field ◽  
Field Distribution ◽  
Direct Method ◽  
Auxiliary Problem ◽  
Nonstationary Temperature ◽  
Temperature Field Distribution ◽  
Cylindrical Structures ◽  
Urgent Task ◽  
Multilayer Cylindrical Shell

Introduction. The current urgent task is to find the temperature field distribution in cylindrical structures such as "solid cylinder inside a multilayer cylindrical shell". A characteristic feature of such structures is different mechanical and thermophysical characteristics of the layers combination, which makes them more perfect. However, this approach causes significant difficulties in developing analytical methods for their study. Therefore, new research methods development for multilayer, in particular, cylindrical structures is an urgent task today.Purpose. Direct method is used to study the heat transfer processes in the system "one-piece cylinder inside a multilayer cylindrical shell".Methods. To solve the initial parallel, the auxiliary problem of determining the distribution of a nonstationary temperature field in a multilayer hollow cylindrical structure with a "removed" cylinder of a sufficiently small radius is set. The solution of the auxiliary problem is realized by applying the method of reduction using the concept of quasi-derivatives. The Fourier schemeis used by using a modified method of eigenfunctions.Results. To find the solution to the problem, we used the idea of a boundary transition by directing the radius of the removedcylinder to zero. It is established that in this approach, all eigenfunctions of the corresponding problem have no singularities atzero, which means that the solutions of the original problem are limited in the whole structure. To illustrate the proposed method,a model example of finding the temperature field distribution in a four-layer column of circular cross-section (tubular concretecolumn) under the influence of the standard temperature of the fire. The results of the calculations are presented in the form of athree-dimensional graph of temperature changes depending on time and spatial coordinates.Conclusions. A direct method was used to solve the initial problem, using the idea of a boundary transition for the first time.In the general formulation (the function of changing the temperature of the environment is considered arbitrary, no restrictionsare imposed on the thickness of the shell and the number of layers) such a problem is solved for the first time.The structure of the obtained explicit exact formulas allows creating an algorithm for calculating the temperature field inthe form of automated programs, where it is enough to enter the initial data. Note that such algorithms include: a) calculating theroots of the characteristic equation; b) multiplication of a finite number of known matrices; c) calculation of definite integrals; d)summation of the required number of members of the series to obtain a given accuracy of the calculation.

scholarly journals SOLUTION OF THE PROBLEM OF THERMOELASTICITY FOR NONLINEAR ELASTIC INHOMOGENEOUS THICK-WALL CYLINDRICAL SHELL

2019 ◽  
Vol 15 (4) ◽  
pp. 133-142
Author(s):  
Lyudmila Polyakova ◽  
Vladimir Andreev
Keyword(s):  
Cylindrical Shell ◽  
Temperature Field ◽  
Comparative Analysis ◽  
Piecewise Linear ◽  
Physical Nonlinearity ◽  
Thick Wall ◽  
Stationary Temperature Field ◽  
Comparison Of The Results ◽  
Nonlinear Elastic ◽  
Nonlinear Nature

The distinctive paper presents the calculation of a thick-walled cylindrical shell with hinged and free ends on the temperature effect. The shell consists of three layers: two layers of heat-resistant concrete and steel out­er layer. The calculation takes into account the piecewise linear inhomogeneity of the shell due to its three-layer construction and the continuous inhomogeneity caused by the action of a stationary temperature field. To take into account the nonlinear nature of concrete deformation, the problem was solved using the method of successive ap­proximations described in [1]. A comparative analysis of the results of the calculation of the shell with and without taking into account the continuous inhomogeneity and the nonlinear nature of the deformation of concrete is given. Comparison of the results showed a significant decrease in circumferential stresses in the most loaded concrete lay­ers when calculating the shell with regard to physical nonlinearity and heterogeneity of materials.

scholarly journals Analytical study of the non-stationary temperature field of a thermally thin plate

2021 ◽  
Vol 1155 (1) ◽  
pp. 012007
Author(s):  
I I Latypov ◽  
L A Bigaeva ◽  
G S Mukhametshina ◽  
N A Shaikhutdinova ◽  
A Y Gilev
Keyword(s):  
Temperature Field ◽  
Thin Plate ◽  
Analytical Study ◽  
Stationary Temperature Field

scholarly journals Three-Dimensional Electro-Thermal Analysis of a New Type Current Transformer Design for Power Distribution Networks

Energies ◽  
2021 ◽  
Vol 14 (6) ◽  
pp. 1792
Author(s):  
Bingbing Dong ◽  
Yu Gu ◽  
Changsheng Gao ◽  
Zhu Zhang ◽  
Tao Wen ◽  
...  
Keyword(s):  
Boundary Condition ◽  
Temperature Field ◽  
Temperature Gradient ◽  
Field Distribution ◽  
Distribution Network ◽  
Current Transformer ◽  
Internal Temperature ◽  
Temperature Field Distribution ◽  
Type Design ◽  
New Type

In recent years, the new type design of current transformer with bushing structure has been widely used in the distribution network system due to its advantages of miniaturization, high mechanical strength, maintenance-free, safety and environmental protection. The internal temperature field distribution is an important characteristic parameter to characterize the thermal insulation and aging performance of the transformer, and the internal temperature field distribution is mainly derived from the joule heat generated by the primary side guide rod after flowing through the current. Since the electric environment is a transient field and the thermal environment changes slowly with time as a steady field under the actual conditions, it is more complex and necessary to study the electrothermal coupling field of current transformer (CT). In this paper, a 3D simulation model of a new type design of current transformer for distribution network based on electric-thermal coupling is established by using finite element method (FEM) software. Considering that the actual thermal conduction process of CT is mainly by conduction, convection and radiation, three different kinds of boundary conditions such as solid heat transfer boundary condition, heat convection boundary condition and surface radiation boundary condition are applied to the CT. Through the model created above, the temperature rise process and the distribution characteristics of temperature gradient of the inner conductor under different current, different ambient temperatures and different core diameters conditions are studied. Meanwhile, the hottest temperature and the maximum temperature gradient difference are calculated. According to this, the position of weak insulation of the transformer is determined. The research results can provide a reference for the factory production of new type design of current transformer.

An analytical solution of a two-dimensional temperature field in a hollow cylinder under a time periodic boundary condition using Fourier series

2009 ◽  
Vol 223 (8) ◽  
pp. 1889-1901 ◽  
Author(s):  
G Atefi ◽  
M A Abdous ◽  
A Ganjehkaviri ◽  
N Moalemi
Keyword(s):  
Boundary Condition ◽  
Temperature Field ◽  
Fourier Series ◽  
Temperature Distribution ◽  
Analytical Solution ◽  
Hollow Cylinder ◽  
Periodic Boundary Condition ◽  
Periodic Boundary ◽  
Separation Of Variables ◽  
Two Dimensional

The objective of this article is to derive an analytical solution for a two-dimensional temperature field in a hollow cylinder, which is subjected to a periodic boundary condition at the outer surface, while the inner surface is insulated. The material is assumed to be homogeneous and isotropic with time-independent thermal properties. Because of the time-dependent term in the boundary condition, Duhamel's theorem is used to solve the problem for a periodic boundary condition. The periodic boundary condition is decomposed using the Fourier series. This condition is simulated with harmonic oscillation; however, there are some differences with the real situation. To solve this problem, first of all the boundary condition is assumed to be steady. By applying the method of separation of variables, the temperature distribution in a hollow cylinder can be obtained. Then, the boundary condition is assumed to be transient. In both these cases, the solutions are separately calculated. By using Duhamel's theorem, the temperature distribution field in a hollow cylinder is obtained. The final result is plotted with respect to the Biot and Fourier numbers. There is good agreement between the results of the proposed method and those reported by others for this geometry under a simple harmonic boundary condition.

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