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1

Thermal stresses associated with a thermosensitive multilayered disc analysed due to point heating

Srinivas V. B., Manthena V. R., Warbhe S. D., Kedar G. D., Lamba Navneet Kumar

International Journal of Applied Mechanics and Engineering

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2024

|

Vol. 29, no. 2

118--137

EN

In this paper, analytical solutions are presented for temperature and thermal behavior of a thermosensitive multilayered annular disc due to point heat source. Convective heating is applied to both the innermost and outermost layers. The nonlinearity of the thermal diffusivity equation is dealt using Kirchhoff’s transformation technique. A finite integral transform in the form of Bessel’s function is used to deal with the radial variable r. Fourier transform and angular eigen functions are also used to solve the thermal diffusivity equation. Deflection, resultant forces, shearing forces, resultant moments and thermal stresses are obtained. A mathematical representation is formulated for a 3-layered disc, with the inner, middle and outer layers composed of copper, zinc and aluminum respectively. The results are depicted graphically.

2

Study on Preparation Technology and Heat Conduction Mechanism of High-Purity & Ultra-Fine Alumina Powder from Scrap Aluminum Cans

Wang Chengmin, Politov Anatoly, Wang Xiuhui, Yang Jinlong

Archives of Foundry Engineering

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2024

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Vol. 24, iss. 1

158--164

EN

In view of the increasing scarcity of bauxite resources in China, the high energy consumption and high pollution of electrolytic aluminum, and the requirements for energy conservation and environmental protection, aluminum recycling and high-value utilization of its derivatives have evolved into a crucial development requirement for the aluminum industry in the future. As an important part of the development of recycled aluminum resources, the high-value application of scrap aluminum cans has always been a hot research topic in various recycled aluminum processing enterprises and scientific research units. The traditional regeneration system of waste cans includes a series of complex technological processes such as pretreatment, paint removal, smelting system and casting system, which is difficult to control in the middle of the process. Most of the recycled scrap aluminum cans are cast and downgraded for later use, except for a part of them used as alloy materials for new cans. In this paper, combined with the research on the preparation of metal aluminum alkoxide, combined with recrystallization heat conduction to further study the effective dissolution or adsorption how to remove impurity elements to obtain high-purity aluminum alcohol salt mechanism research, and thermal effect of alcohols with different carbon chains on the synthesis of high-purity aluminum alkoxide was further investigated. Moreover, the changes in morphology and pore size distribution of hydrolyzed alumina precursor materials under different hydrothermal temperature conditions were discussed by means of the alkoxide hydrolysis-sol-gel process. Eventually, the aluminum alkoxide was obtained by the reaction of waste cans with isopropanol and heavy crystal thermal conductivity, and the high-purity aluminum alkoxide was purified by vacuum distillation. Under the hydrothermal condition of 160°C, the high-purity alumina material with a purity of 99.99% and an original crystal size of 200nm was prepared.

3

Analyzing the Impact of Population Size in AI-Based Reconstruction of the Thermal Parameter in Heat Conduction Modeling

Gawrońska Elżbieta, Zych Maria, Dyja Robert, Kowalkowski Michał

Advances in Science and Technology. Research Journal

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2024

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Vol. 18, no 2

349--364

EN

The research shows how to use swarming algorithms to rebuild the heat transfer coefficient, especially in regard to the continuous border condition. The authors utilized their application software to do numerical computations, employing classical variants of swarm algorithms. The numerical calculations employed a functional determining error to assess the accuracy of the estimated result. The functional minimization was conducted with the swarm algorithms (especially ABC and ACO). The geometry analyzed in this study consisted of a square shape referred to as the cast, enclosed within another square shape known as the casting mold. These two squares were separated by a layer facilitating heat conduction, characterized by the coefficient κ. The coefficient of the thermally conductive layer was recalibrated utilizing swarm methods within the range of 900 - 1500 [W/m^2K] and subsequently compared to a predetermined reference value. A finite element mesh consisting of 576 nodes was used for the calculations. The study involved simulations with populations of 5, 10, 15, and 20 individuals. Furthermore, each scenario also took into account noise of 0%, 2%, and 5% of the reference values. Results make evident the reconstructed value of the κ coefficient, cooling curves, and temperatures for the ABC and ACO algorithms are physically correct. The consequences indicate a notable level of satisfaction and strong concurrence with the anticipated of the κ parameter values. The results from the numerical simulations demonstrate considerable promise for applying artificial intelligence algorithms in optimizing production processes, analyzing data, and facilitating data-driven decision-making.

4

Application of generalized boundary conditions for homogenization of thermal and filtration properties of soils

Wojciechowski Marek

Studia Geotechnica et Mechanica

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2023

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Vol. 45, nr s1

362--369

EN

In the paper, generalized boundary conditions were used for the homogenization of coefficients of the Laplace partial differential equation in the context of Darcy flow and heat diffusion phenomena. The mesoscopic boundary value problem was defined and analyzed from the variational perspective and the finite element formulation of the homogenization problem was provided. The matrix equation for the apparent macroscopic properties, resulting from FEM discretization, was derived and utilized in two illustrative examples: homogenization of the filtration coefficient of clay amended with expanded shale and thermal conductivity of the soil with multiple fractions. It is shown, that generalized boundary conditions can provide very good homogenization results without the assumption of the periodicity of the material. For best results, the microscopic length parameter has to be properly estimated.

5

Modelling of the solar heating of a multi-layered spherical cone

Siedlecka Urszula

Journal of Applied Mathematics and Computational Mechanics

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2023

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Vol. 22, nr 4

53-63

EN

In this paper, the solar heating of a multi-layered spherical body with azimuthal symmetry is considered. The mathematical model is related to the determination of the steady state of the temperature distribution in the spherical cone consisting of concentric spherical layers. The solar heating is composed of two parts of the heat flux: direct and diffusion. Also, the simultaneous cooling of the cone by its outer surface (as convective heat flow to the environment) is taken into account. The proposed system of the partial differential equations supplemented by the adequate boundary conditions is solved in the analytical way by using, among others, the Legendre functions of the first kind. The sample results of temperature distribution in the cross-section of the cone with different polar angles are also presented.

6

On spatial vs referential isotropic fourier’s law in finite deformation thermomechanics

Wcisło Balbina, Pamin Jerzy, Rose Lars, Menzel Andreas

Engineering Transactions

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2023

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Vol. 71, iss. 1

111--140

EN

This paper deals with the issue of isotropic heat conduction in thermomechanical largestrain problems. The aim of the paper is a comparison of different variants of Fourier’s law used in the literature for a large strain problem. In particular, Fourier’s law is specified either in the reference or in the deformed configuration by using different options of heat flux density vectors which are presented and discussed. The paper includes working examples to illustrate the presented theory. Moreover, different formulations of Fourier’s law are tested by using the finite element method to investigate the influence of the applied variant on simulation results. The analysis reveals that in a strongly deformed area the temperature distribution varies.

7

Chosen possibilities of ɛ-fuzzy boundary elements method application in the analysis of conductivity problems with uncertainties

Witek Halina, Witek Bernard

Computer Assisted Methods in Engineering and Science

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2023

|

Vol. 30, no. 4

407--426

EN

The paper presents a methodology of solving boundary problems with uncertainty parameters based on the use of interval perturbation numbers. This methodology allows for the analysis of very complex problems with different uncertain parameters. Fuzzy Boundary Element Method (FBEM) using ɛ-number will be called ɛ-Fuzzy Boundary Element Method (ɛ-FBEM). Detailed discussion of the problems of computing and applications will be presented on the example of the fuzzy boundary integral equation arising from the boundary problem for the potential problems with heterogeneous, fuzzy boundary conditions of Dirichlet and Neumann type, fuzzy internal sources, fuzzy boundary and fuzzy fundamental solution. The presented methodology can be used to solve various engineering problems (e.g. in civil engineering, power engineering and others) – e.g. to analyze the temperature distribution in structural elements or elements located in the vicinity of objects or devices. In the latter case the increased temperature may be a symptom of a severe failure (e.g. power transformer overload, overexcitation or a fault) which cannot be tolerated due to the threat to the object and to the entire power system. Proposed method maybe used for electrical equipment diagnosis and in consequence as a power system failure prevention. In this paper calculation methodology is illustrated on the example of an area bounded by a square, on the left boundary of which a certain temperature is set, while on the rest of the boundaries the conditions are equal to zero. A dedicated computer program allows for the calculation of both temperature and temperature derivative for any number of boundary elements using ɛ-FBEM.

8

Impact of input parameters on numerical calculations optimized by swarming algorithms during computer simulations of the heat conduction phenomenon

Zych Maria, Gawrońska Elżbieta, Dyja Robert, Krawiec Piotr

Journal of Applied Mathematics and Computational Mechanics

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2022

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Vol. 21, nr 4

107--118

EN

The article presents the application of swarming algorithms in heat conduction, taking into account the continuity of the boundary condition (type IV). The influence of the input parameters of the bee and ant algorithm and tessellation on the selection of the heat conduction coefficient between the casting mold and the casting in computer simulations was presented. The results were compared for two different finite element grids, a different number of individuals, and a different number of iterations. The study also considered the magnitude of the reference temperature disturbance as the input temperature for numerical calculations. The analysis showed that the relative error of reproducing the value of the thermal conductivity coefficient in the continuity condition did not exceed 1.5% of the reference value of this coefficient.

9

Approximate analytical solution to the Cattaneo heat conduction model with various laser sources

Nuruddeen Rahmatullah Ibrahim

Journal of Applied Mathematics and Computational Mechanics

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2022

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Vol. 21, nr 1

67--78

EN

The present manuscript investigates the role being played by various laser short heating sources in a conduction process of a metallic substrate. The Cattaneo heat conduction model is considered in favour of its finiteness of conduction speed. The analytical solutions for the temperature fields are determined via the application of the Laplace integral transform. Finally, we sought a numerical Laplace inversion scheme where the analytical inversion failed and graphically examined the significance of the heating parameters on the temperature fields.

10

Time-Reversible Thermodynamic Irreversibility : One-Dimensional Heat-Conducting Oscillators and Two-Dimensional Newtonian Shockwaves

Hoover William Graham, Hoover Carol Griswold

Computational Methods in Science and Technology

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2022

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Vol. 28, No. 4

133--141

EN

We analyze the time-reversible mechanics of two irreversible simulation types. The first is a dissipative onedimensional heat-conducting oscillator exposed to a temperature gradient in a three-dimensional phase space with coordinate q, momentum p, and thermostat control variable ζ. The second type simulates a conservative two-dimensional N-body fluid with 4N phase variables {q, p} undergoing shock compression. Despite the time-reversibility of each of the three oscillator equations and all of the 4N manybody motion equations both types of simulation are irreversible, obeying the Second Law of Thermodynamics. But for different reasons. The irreversible oscillator seeks out an attractive dissipative limit cycle. The likewise irreversible, but thoroughly conservative, Newtonian shockwave eventually generates a reversible near-equilibrium pair of rarefaction fans. Both problem types illustrate interesting features of Lyapunov instability. This instability results in the exponential growth of small perturbations, ∝ e λt where λ is a “Lyapunov exponent”.

11

n-sided polygonal hybrid finite elements involving element boundary integrals only for anisotropic thermal analysis

Cao R. F., Zhao X. J., Lin W. Q., Wang H.

Archives of Mechanics

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2020

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Vol. 72, nr 2

109--137

EN

As a combination of the traditional finite element method and boundary element method, the n-sided polygonal hybrid finite element method with fundamental solution kernels, named as HFS-FEM, is thoroughly studied in this work for two-dimensional heat conduction in fully anisotropic media. In this approach, the unknown temperature field within the polygon is represented by the linear combination of anisotropic fundamental solutions of problem to achieve the local satisfaction of the related governing equations, but not the specific boundary conditions and the continuity conditions across the element boundary. To tackle such a shortcoming, the frame temperature field is independently defined on the entire boundary of the polygonal element by means of the conventional one-dimensional shape function interpolation. Subsequently, by the hybrid functional with the assumed intra- and inter-element temperature fields, the stiffness equation can be obtained including the line integrals along the element boundary only, whose dimension is reduced by one compared to the domain integrals in the traditional finite elements. This means that the higher computing efficiency is expected. Moreover, any shaped polygonal elements can be constructed in a unified form with the same fundamental solution kernels, including convex and non-convex polygonal elements, to provide greater flexibility in meshing effort for complex geometries. Besides, the element boundary integrals endow the method higher versatility with a non-conforming mesh in the pre-processing stage of the analysis over the traditional FEM. No modification to the HFS-FEM formulation is needed for the non-conforming mesh and the element containing hanging nodes is treated normally as the one with more nodes. Finally, the accuracy, convergence, computing efficiency, stability of non-convex element, and straightforward treatment of non-conforming discretization are discussed for the present n-sided polygonal hybrid finite elements by a few applications in the context of anisotropic heat conduction.

12

Thermal defect characterization and heat conduction modeling during fiber laser cutting carbon fiber reinforced polymer laminates

Chen Limei, Li Maojun, Yang Xujing, Li Bin

Archives of Civil and Mechanical Engineering

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2020

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Vol. 20, no. 2

453--466

EN

High-power fiber laser has been proven to be feasible for cutting carbon fiber reinforced polymers with several advantages including noncontact force, high efficiency and flexibility, while the characteristics of thermal damage and heat conduction in materials are not yet fully understood. Continuous-wave fiber laser was applied in this work to cut 2.0-mm-thick carbon fiber reinforced polymer laminates with different layup configurations. The influence of processing parameters including laser power and cutting speed on thermal damage was investigated. The characteristics of various thermal defects on different positions of machined surface were analyzed using high-resolution SEM and mathematical models. Interestingly, swollen fibers were observed and they connected together to form irregular swollen masses. According to further analysis on the initial heat distribution, it showed that cutting speed was the main factor affecting heat accumulation. In addition, modified heat conduction model was developed to analyze heat transfer within unidirectional carbon fiber reinforced polymer laminates in comparison with experimental results, which can be applied to predict heat affect zone during high-power fiber laser cutting composite materials.

13

Modelowanie procesów wymiany ciepła w dzianinach futerkowych

Więzowska Anna

Zeszyty Naukowe. Włókiennictwo / Politechnika Łódzka

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2019

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z. 75

39--75

PL

Ciepłochronność jest podstawowym parametrem determinującym praktyczne zastosowanie dzianin futerkowych. Analiza wymiany ciepła oraz metodyka określenia podstawowych parametrów struktury do optymalizacji konstrukcji z uwagi na wymagany poziom izolacyjności cieplnej nie zostały jeszcze dotychczas opisane dla dzianin futerkowych. Brak rozwiązań problemów ciepłochronności dla tego typu dzianin wskazuje na celowość podjęcia rozważanej tematyki. Celem prac prowadzonych w ramach dysertacji doktorskiej było opracowanie modelu przepływu ciepła, który może być wykorzystany do projektowania dzianin futerkowych o wymaganych właściwościach termofizycznych. Zaprezentowany model opisu zjawiska przepływu ciepła ma uzasadnienie praktyczne w odniesieniu do dzianin futerkowych. Przyjęta metoda pozwala uniknąć badań wielu parametrów, ograniczając je do minimum: udział objętościowy poszczególnych składników w stosunku do każdej warstwy oraz stosunek grubości poszczególnych warstw do grubości całego wyrobu. Do badań wykorzystuje się powszechnie dostępne urządzenia pomiarowe. Uzyskuje się ponadto możliwość symulacji eksperymentu, bez konieczności wytwarzania dzianiny futerkowej. Metoda ta pozwala na dowolne modelowanie warunków brzegowych i początkowych, co nie zawsze jest możliwe dla metod empirycznych ze względu na ograniczenia sprzętowe. Opracowany model obliczeniowy przepływu ciepła przez dzianiny futerkowe umożliwia uzyskanie rozkładu temperatury w tej konstrukcji oraz może stanowić punkt wyjścia doboru optymalnego struktury dla osiągnięcia 40 Anna Więzowska wymaganych właściwości wyrobów. Projektowanie dzianiny futerkowej o wymaganym poziomie izolacyjności cieplnej, z zastosowaniem przedstawionego modelu, może posłużyć do powstania rzeczywistego materiału o określonych właściwościach ciepłochronnych.

EN

The fundamental function of the knitted fur fabrics, which are commonly used to manufacture the clothes and shoes, is to protect the human body against heat loss in low environmental temperature. Thus, the heat-insulating properties of fur fabrics are the basic criterion for their functional characteristics. The aim of this work is to determine the heat transfer model, which can be applied to design the knitted fur fabrics of the required thermophysical properties. The mathematical model of heat transport within knitted fur fabrics allows to obtain the temperature distribution in the structure and can be a starting point to optimize the structural shape in respect of the requested properties. The available literature does not introduce the heat transport problems in the knitted fur fabrics. A few works describe in general form some parameters of the structure whereas the corresponding standards are inaccessible. To explain the nature of heat transfer inside the knitted fur fabrics, the dissertation describes the basic phenomena of heat transfer. The heat conduction is defined more precisely as the dominant heat transport mechanism in textiles. The material properties influencing the heat flux density transferred in textile product are also described. The particular cases of heat conduction mechanisms in the single layer and the multi-layer structure have been analysed and next applied to determine the heat transfer in the homogenized fur fabric. The solution methodology of simple and complex heat transfer problems has been explained. The literature pertaining to the measurements of heat isolation in textiles has been reviewed in respect of the measurement methods, character of processes, measured parameters and field of their application vs. both structure of examined material as well as the layers arrangement. Assuming the complex structure of knitted fur fabrics (i.e. the multilayer arrangement, participation of glue in bottom layer, air inside the void spaces under inclined fibers), we have rejected the measurements methods influencing the material structure during the test. Heat transport within knitted fur fabrics is described by means of the heat conduction coefficient tested in steady conditions. The measured conduction coefficient is often of substitute nature and can additionally include the convective and radiative heat transport. The thermal properties of knitted fur fabrics are determined by means of the test device Tilmet 75. The preliminary investigations were conducted using the device Tilmet 75 for different knitted fabrics made of homogenous materials with the diversified thickness and surface mass. The fur fabrics were characterized using the same standard indexes which are tested for the knitted fabrics i.e. the thickness and surface mass. There are tested the heat conduction and heat permeability as well as determined the structure of knitted fabrics samples vs. the characteristics of thermal properties. The empirically determined heat conduction coefficient and heat resistances vs. basic structural parameters do not describe the influence of raw material in the knitted fur fabrics on the material heat characteristics. Both growing surface mass and growing fabric thickness does not determine unequivocally the gradation of these features in respect of thermal properties. According to the preliminary test results, it is necessary to change the factors determining the complex knitted fur fabrics in respect of the structure and raw material composition. The description of the knitted fur fabric can cause difficulties in heat transport correlations. Parameters of fur fabrics of the complex, space and multilayer structure are hard to determine and investigate using the standard test methods. The structure consists of the bottom layer and the fleece layer which are made of different raw materials: the yarn, band and glue as well as considerable volume fraction of air inside. Thus, the description of physical model is troublesome. Let us introduce the following assumptions concerning the fur fabric: (i) the same height of fleece layer; (ii) the uniform distribution of fibres density in cover layer; (iii) the uniform distribution of yarn, fibres and air in bottom layer; (iv) the void spaces between the yarn in bottom layer are filled by both air and glue; (v) the glue does not penetrate the cover layer. Under the above assumptions, the space 3D description can be simplified to the plane 2D problem introducing the homogenized particular layer of fabric. The structure is defined by the volume fraction and heat conduction coefficient of each layer. The heat conduction coefficient is determined using the rule of mixture which limits the domain of study of corresponding parameters to the volume fractions of particular component in every layer. The principal investigations were conducted for the knitted fur fabrics of the diversified both length of fleece and basis weight, subjected to the different finishing processes. The test methods applicable for the different textile materials were analysed in respect of the measurement characteristics i.e. applicable for thickness, density, mass related to materials / textile products and their particular layers. The complex structure of knitted fur fabrics can be characterized by the innovative, non-standard test methods as well as the standard methods, which are not usually applied for those materials. The thickness of knitted fur fabric tested for the various pressures strongly depends on the load applied. The presented model of heat transfer description is practically motivated for the knitted fur fabric. The adopted method can avoid the large number of tests of required parameters and restricts the analysis to the following cases: the volume fraction of particular component within each layer and thickness fraction of particular layer to the complete thickness of product. The commonly available test equipment is used during the tests. Additionally, the experiments are simulated which substitute the manufactured knitted fur fabric. This method allows to model 75 optionally the boundary and initial conditions which is not always applicable for empirical methods due to equipment limitations. Design of knitted fur fabric of the requested thermal isolation level, based on the model presented in this work, can help to create the real material of the prescribed heat-insulating properties. The next stage of the current investigations can be focused on determination of indexes characterizing the knitted fur fabrics in presented model vs. technological parameters necessary to manufacture the designed product.

14

Simulations of the influence of the heat flux at the shaft surface of the conical slide bearing on its hydrodynamic lubrication and operating parameters

Czaban Adam, Miszczak Andrzej

Journal of KONES

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2019

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Vol. 26, No. 4

29--37

EN

The aim of this work is to investigate, how in the adopted model of hydrodynamic lubrication of a conical slide bearing, the change of the heat flux value at the bearing shaft, affects bearing operating parameters. In this research, the authors use, the known from the literature, Reynolds type equation, describing the stationary hydrodynamic lubrication process of a conical slide bearing. The analytical, solutions, that determine the components of the lubricating oil velocity vector and the equation (analytical solution of energy equation) determining the threedimensional temperature distribution in the lubrication gap, was also adopted from previous works. In order to obtain numerical solutions, the Newton’s method was used, and the derivatives in the Reynolds type equation were approximated by the finite differences. An application of the method of subsequent approximations allowed considering the influence of temperature, pressure and shearing rate on the viscosity of lubricating oil. The considerations were performed by adopting the Reynolds condition of the hydrodynamic oil film. It was tested, how the assumed value of the heat flux on the bearing shaft surface affects the values of the obtained operating parameters, i.e. the transverse and longitudinal component of the load carrying capacity, friction force and coefficient of friction.

15

Mathematical modelling of stationary thermoelastic state for a plate with periodic system of inclusions and cracks

Zelenyak Volodymyr

Acta Mechanica et Automatica

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2019

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Vol. 13, no. 1

11--15

EN

Two-dimensional stationary problem of heat conduction and thermoelasticity for infinite elastic body containing periodic system of inclusions and cracks is considered. Solution of the problem is constructed using the method of singular integral equations (SIEs). The numerical solution of the system integral equations are obtained by the method of mechanical quadrature for a plate heated by a heat flow, containing periodic system elliptic inclusions and thermally insulated cracks. There are obtained graphic dependences of stress intensity factors (SIFs), which characterise the distribution of intensity of stresses at the tops of a crack, depending on the length of crack, elastic and thermoelastic characteristics inclusion, relative position of crack and inclusion.

16

Fractional heat conduction in a sphere under mathematical and physical Robin conditions

Kukla S., Siedlecka U.

Journal of Theoretical and Applied Mechanics

|

2018

|

Vol. 56 nr 2

339--349

EN

In this paper, the effect of a fractional order of time-derivatives occurring in fractional heat conduction models on the temperature distribution in a composite sphere is investigated. The research concerns heat conduction in a sphere consisting of a solid sphere and a spherical layer which are in perfect thermal contact. The solution of the problem with a classical Robin boundary condition and continuity conditions at the interface in an analytical form has been derived. The fractional heat conduction is governed by the heat conduction equation with the Caputo time-derivative, a Robin boundary condition and a heat flux continuity condition with the Riemann-Liouville derivative. The solution of the problem of non-local heat conduction by using the Laplace transform technique has been determined, and the temperature distribution in the sphere by using a method of numerical inversion of the Laplace transforms has been obtained.

17

An efficient analysis of steady-state heat conduction involving curved line/surface heat sources in two/three-dimensional isotropic media

Mohammadi M., Hematiyan M. R., Shiah Y. C.

Journal of Theoretical and Applied Mechanics

|

2018

|

Vol. 56 nr 4

1123--1137

EN

In this paper, a new formulation based on the method of fundamental solutions for two/three- -dimensional steady-state heat conduction problems involving internal curved line/surface heat sources is presented. Arbitrary shapes and non-uniform intensities of the curved heat sources can be modeled by an assemblage of several parts with quadratic variations. The presented mesh-free modeling does not require any internal points as in domain methods. Four numerical examples are studied to verify the validity and efficiency of the proposed method. Our analyses have shown that the presented mesh-free formulation is very efficient in comparison with conventional boundary or domain solution techniques.

18

Numerical analysis of influence of bearing material thermal conductivity coefficient on hydrodynamic lubrication of a conical slide bearing

Czaban A.

Journal of KONES

|

2018

|

Vol. 25, No. 2

89--96

EN

One of the main parameters affecting the hydrodynamic lubrication of slide bearings is the viscosity of lubricating oil. Many studies show, that significant changes in the viscosity of oil occur along with changes in its temperature. The influence on the temperature distribution in the lubrication gap of the slide bearing have a variety of factors, and one of them is the amount of heat exchanged between the lubricant and the environment. The temperature of the lubricating oil of operating bearing is usually higher than the ambient temperature. In addition to the convection, which occurs during the flow (heat exchange related to the oil supply and discharge system) some amount of heat is transferred to the bearing sleeve material (and also to the bearing shaft), and then it is conducted to sleeve outer surface. The amount of heat transferred through the bearing sleeve is mainly dependent on the difference of temperatures between inner and outer sleeve surfaces and also depend on the heat conduction coefficient of sleeve material. This article presents the results of modelling of the influence of amount of heat conducted through the bearing material, on the hydrodynamic lubrication of a conical slide bearing. The study concerned various values of the heat conduction coefficient of the bearing material to investigate its influence on the temperature values of lubricating oil, and thus, on its viscosity, on the distribution of hydrodynamic pressure and on the calculated values of bearing load carrying capacities and friction forces.

19

Numerical analysis of heat conduction influence on SCR aftertreatment systems EFF

Bachanek J., Rogóż R., Teodorczyk A.

Journal of KONES

|

2018

|

Vol. 25, No. 3

51--58

EN

Selective Catalytic Reduction (SCR) is well known method for reducing NOx emission in diesel engine exhaust gas. Urea-water solution (UWS) injected into hot stream decomposes due to thermolysis into ammonia and isocyanic acid which hydrolyses further into more ammonia and carbon dioxide. Resultant ammonia is the NOx reductor, producing water vapour and carbon dioxide from the reduction reaction. To provide sufficient NOx reduction efficiency, UWS needs to be properly atomized and mixed with exhaust gas. However, due to more and more restrictive emissions regulations provided by European Union and Close Coupled trend of aftertreatment systems in vehicles the design process is very complex and demanding. Computational Fluid Dynamics (CFD) simulations are integral part of product development, allowing save time and reduce costs of preparing prototypes for further tests. However, it is necessary to understand all the processes and problems connected with NOx reduction in SCR system. Strong turbulent flow of hot stream gas, urea-water solution spray injection, droplets interaction with wall, wallfilm generation are included. The objective of this work is to investigate the impact of heat transfer modelling inside mixing elements of SCR system on urea mixing uniformity and wallfilm deposit on the walls of the system. Simplified and more complex approach is compared with no heat transfer cases. All the simulations were conducted using AVL FIRETM software. Results showed that wall heat transfer might have an impact on mixing efficiency and wallfilm formulation. It is necessary to take into account the effect of mixing elements heat conduction in CFD simulations during the aftertreatment design process.

20

Optimal heat distributions by a gradient-based shape optimization method

Belhachmi Z., Meftahi B., Meftahi H.

Control and Cybernetics

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2018

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Vol. 47, no. 1

33--53

EN

In this paper, we consider the problem of locating coated inclusions in a 2D dimensional conductor material in order to obtain a suitable thermal environment. The mathematical model is described by elliptic partial diﬀerential equation with linear boundary condition, including heat transfer coeﬃcient. A shape optimization problem is formulated by introducing a cost functional to solve the problem under consideration. The shape sensitivity analysis is rigorously performed for the problem by means of a Lagrangian formulation. The optimization problem is solved by means of gradient-based strategy and numerical experiments are carried out to demonstrate the feasibility of the approach.