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EN
The paper presents an investigation of the possibility for initiation of initial conditions in a road pavement model for thermal analysis incorporating non-stationary heat transfer. The procedure requires performance of computations for a sufficiently long initiation period to obtain the initial temperature distribution that may serve as the basis for further heat transfer analyses. The main part of the article is devoted to presentation of a numerical experiment performed for four configurations of parameters in the heat transfer model in a multilayer system, representing road pavement. Each parameter configuration corresponds to a different pavement structure (two models of flexible pavements and two models of pavements with foam concrete base course). Calculations were performed for three different amplitudes of the sinusoidal function describing the change of temperature in time, which was defined as boundary condition in the pavement model. The numerical experiment was supplemented by calculations performed on a single chosen model parameter configuration, but adopting a boundary condition based on values registered by a sensor installed in real pavement. Analysis of the obtained results confirmed that the presented method of non-stationary heat transfer analysis enables initiation of the initial conditions in the heat equation.
PL
W pracy rozpatrzono możliwość inicjacji warunków początkowych w modelu do analizy termicznej nawierzchni drogowej w warunkach niestacjonarnego przepływu ciepła. Procedura wymaga przeprowadzenia obliczeń dla odpowiednio długiego czasu inicjacji do uzyskania początkowego rozkładu temperatury, który jest podstawą dalszych analiz przepływu energii cieplnej. Główną część pracy stanowi prezentacja eksperymentu numerycznego przeprowadzonego dla czterech konfiguracji wartości parametrów modelu przepływu energii cieplnej w ośrodku wielowarstwowym, jakim jest nawierzchnia. Każda konfiguracja parametrów odpowiada innej konstrukcji (dwa modele nawierzchni podatnej i dwa modele z warstwą z pianobetonu). Obliczenia przeprowadzono kolejno dla trzech różnych wartości amplitud sinusoidalnej funkcji zmiany temperatury w czasie, którą zdefiniowano jako warunek brzegowy w modelu nawierzchni. Uzupełnieniem eksperymentu numerycznego były obliczenia przeprowadzone dla jednej wybranej konfiguracji wartości parametrów modelu, w którym warunek brzegowy stanowiły wartości temperatury zarejestrowane czujnikiem wbudowanym w nawierzchnię. Na podstawie analizy uzyskanych wyników potwierdzono, że inicjacja warunków początkowych w równaniu przewodzenia ciepła jest możliwa w oparciu o analizę niestacjonarnego przepływu ciepła przedstawioną metodą.
EN
The effective thermal conductivity and air permeability of a multifilament polyester yarn used in sports T-shirts was investigated by computer modeling using finite element analysis (COMSOL Multiphysics, ABAQUS/CAE). It has been shown that the number of fibers, the porosity of the yarn and the proportion of fibers in the volume fraction of the yarn have a direct effect on the effective thermal conductivity and air permeability of the multifilament yarn. It was found that with the increase in the number of fibers, the porosity of the yarn decreases linearly, while the volume fraction of the fibers increases, and thus the effective thermal conductivity increases. In addition, air permeability decreases exponentially.
PL
Zbadano efektywne przewodzenie ciepła i przepuszczalność powietrza wielowłókienkowej przędzy poliestrowej stosowanej w koszulce sportowej poprzez modelowanie obliczeniowe z użyciem analizy elementów skończonych (COMSOL Multiphysics, ABAQUS/CAE). Wykazano, że liczba włókien, porowatość przędzy oraz udział objętościowy włókien w przędzy mają bezpośredni wpływ na przewodzenie ciepła i przepuszczalność powietrza przędzy wielowłókienkowej. Wraz ze wzrostem liczby włókien porowatość przędzy maleje liniowo, natomiast zwiększa się udział objętościowy włókien, a tym samym efektywne przewodnictwo cieplne. Ponadto przepuszczalność powietrza maleje wykładniczo.
EN
It has been confirmed that structures with micro dimensions display size-dependent thermomechanical behaviors. Moreover, according to the findings of empirical and theoretical researches, thermoelastic damping (TED) has been recognized as one of inescapable causes of energy dissipation in microstructures. The current article is an effort to provide a novel size-dependent framework for approximating the amount of TED in microring resonators with rectangular cross section. To include size effect into structural and thermal constitutive relations, the modified couple stress theory (MCST) and the Moore–Gibson–Thompson (MGT) heat equation are utilized, respectively. By solving the coupled heat equation in the purview of MGT model, the fluctuation temperature throughout the ring is determined. By employing the obtained temperature distribution and constitutive relations of MCST, the peak values of strain and wasted thermal energies during one cycle of vibration are computed. Based on the description of TED in the energy dissipation (ED) method, a mathematical expression containing the scale parameters of MCST and MGT model is derived for estimating TED value. To ensure the correctness and veracity of the established solution, a comparative study is carried out on the basis of the data released by other researchers for more plain models. A section is also designated for an all-out study to ascertain the association between TED spectrum and some influential factors like scale parameters of MCST and MGT model, vibration mode number, one-dimensional (1D) and two-dimensional (2D) heat conduction, geometry and material. The extracted data enlighten that the impact of applying MCST and MGT model on TED has a close relationship with the vibration mode number of the ring.
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.
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.
6
Content available remote Jakość cieplna ścian zewnętrznych z pustaków niejednorodnych cieplnie
PL
Przedmiotem artykułu jest jakość cieplna zewnętrznych pustaków niejednorodnych cieplnie. Autor przedstawia metody określania przewodności cieplnej takich pustaków, a następnie opisuje sposoby określania współczynnika przewodzenia ciepła pustaków ściennych niejednorodnych cieplnie na podstawie obliczeń numerycznych.
EN
The subject of this article is thermal quality of external thermally heterogeneous hollow bricks. The author presents methods of determining the thermal conductivity of such hollow bricks, and then describes the methods of determining the thermal conductivity coefficient of thermally heterogeneous wall hollow bricks based on numerical calculations.
EN
This article intends to examine thermoelastic damping (TED) in circular cylindrical nanoshells by considering small-scale effect on both structural and thermal areas. To fulfill this aim, governing equations are extracted with the aid of nonlocal elasticity theory and dual-phase-lag (DPL) heat conduction model. Circular cylindrical shell is also modeled on the basis of Donnell–Mushtari–Vlasov (DMV) equations for thin shells. By inserting asymmetric simple harmonic oscillations of nanoshell into motion, compatibility and heat conduction equations, the size-dependent thermoelastic frequency equation is obtained. By solving this equation and deriving the frequency of nanoshell affected by thermoelastic coupling, the value of TED can be calculated through complex frequency approach. Results of this investigation are given in two sections. First, to appraise the validity of presented formulation, a comparison study is conducted between the results of this work in special cases and those reported in the literature. Next, by providing several numerical data, a detailed parametric study is performed to highlight the profound impact of nonlocality and dual-phase-lagging on TED value in simply supported cylindrical nanoshells. The influence of some determining factors such as mode number and type of material on TED is also evaluated.
EN
In the present study, we have applied the reduced differential transform method to solve the thermoelastic problem which reduces the computational efforts. In the study, the temperature distribution in a two-dimensional rectangular plate follows the hyperbolic law of heat conduction. We have obtained the generalized solution for thermoelastic field and temperature field by considering non-homogeneous boundary conditions in the x and y direction. Using this method one can obtain a solution in series form. The special case is considered to show the effectiveness of the present method. And also, the results are shown numerically and graphically. The study shows that this method provides an analytical approximate solution in very easy steps and requires little computational work.
EN
In this paper, the effect of the fractional order of the Caputo time-derivative occurring in heat conduction models on the temperature distribution in a finite cylinder consisting of an inner solid cylinder and an outer concentric layer is investigated. The inner cylinder (core) and the cylindrical layer are in perfect thermal contact. The Robin boundary condition on the outer surface and the Neumann conditions on the ends of the cylinder are assumed. An internal heat source is represented in the mathematical model by taking into account in the heat conduction equation of a function which depends on the space and time variable. An analytical solution of the problem is derived in the form of the double series of eigenfunctions. Numerical examples are presented.
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.
11
Content available remote Modelowanie procesów wymiany ciepła w dzianinach futerkowych
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.
EN
In the paper, a solution of the time-fractional single-phase-lagging heat conduction problem in finite regions is presented. The heat conduction equation with the Caputo time-derivative is complemented by the Robin boundary conditions. The Laplace transform with respect to the time variable and an expansion in the eigenfunctions series with respect to the space variable was applied. A method for the numerical inversion of the Laplace transforms was used. Formulation and solution of the problem cover the heat conduction in a finite slab, hollow cylinder and hollow sphere. The effect of the fractional order of the Caputo derivative and the phase-lag parameter on the temperature distribution in a slab has been numerically investigated.
EN
At this time, the solution to the problem of energy use, namely: energy conservation and energy efficiency is extremely important. Saving energy in buildings by solving the practical problems of reducing the total consumption of energy resources, is implemented through the use of effective thermal insulation materials, energy-efficient structures of external walls and a significant increase in thermal protection of the operated Fund. The actual solution to these problems is the development of new approaches to the calculation, design and manufacturing of insulation materials in wall constructions and how they are implemented. Therefore, it is necessary to improve the theoretical and scientific basis in order to make a more thorough study of the distribution of temperature within the material from which the design is made. Different methods of researching the thermal conductivity of multilayer structures and methods for calculating the temperature field of single- and multi-layered building structures have been proposed in studies of temperature distribution and energy efficiency improvements of building materials and products.
PL
Obecnie rozwiązanie problemu zużycia energii, a mianowicie: oszczędzanie energii i efektywność energetyczna, jest niezwykle ważne. Oszczędzanie energii w budynkach poprzez rozwiązywanie praktycznych problemów zmniejszenia całkowitego zużycia zasobów energetycznych realizowane jest poprzez zastosowanie efektywnych materiałów termoizolacyjnych, energooszczędnych konstrukcji ścian zewnętrznych oraz znaczny wzrost ochrony cieplnej. Rzeczywistym rozwiązaniem tych problemów jest opracowanie nowych podejść do obliczania, projektowania i produkcji materiałów izolacyjnych wykorzystywanych w konstrukcjach ścian oraz sposobu ich zastosowania. Dlatego konieczne jest ulepszenie podstaw teoretycznych i naukowych w celu dokładniejszego zbadania rozkładu temperatury w materiale, z którego wykonany jest dany element konstrukcji. Do analizy rozkładu temperatury i poprawy efektywności energetycznej materiałów i produktów budowlanych zaproponowano różne metody badania przewodności cieplnej konstrukcji wielowarstwowych oraz obliczania pola temperatur jedno- i wielowarstwowych konstrukcji budowlanych.
EN
In this paper, effects of non-Fourier thermal wave interactions in a thin film have been investigated. The non-Fourier, hyperbolic heat conduction equation is solved, using finite difference method with an implicit scheme. Calculations have been carried out for three geometrical configurations with various film thicknesses. The boundary condition of a symmetrical temperature step-change on both sides has been used. Time history for the temperature distribution for each investigated case is presented. Processes of thermal wave propagation, temperature peak build-up and reverse wave front creation have been described. It has been shown that (i) significant temperature overshoot can appear in the film subjected to symmetric thermal load (which can be potentially dangerous for reallife application), and (ii) effect of temperature amplification decreases with increased film thickness.
PL
Jedną z uniwersalnych a zarazem prostych metod dla numerycznego rozwiązywania zadań nieustalonego przewodzenia ciepła w obudowie budynku jest metoda objętości skończonych. Jednak, przy sformułowaniu jawnym konieczne jest dobranie kroku czasowego, gwarantującego stabilność rozwiązania. W tym artykule wartość takiego kroku czasowego została określona z warunku zerowej różnicy pomiędzy teoretycznym a numerycznym rozwiązaniem dla danej geometrii ściany. Rozpatrzono wpływ współczynnika przewodzenia ciepła ściany na długość kroku. Warunki brzegowe przyjęte w artykule odpowiadały obciążeniom ogniowym ściany schronu.
EN
One of the most simple and versatile method for numeric solving of the problems of transient heat conduction in the building envelope is the finite volume method. In explicit scheme however there is a problem of assuming correct time step for solution stability. In this article stable step value was determined from the condition of zero difference between the theoretical and numerical solution for the particular geometry of the wall. The influence of the thermal conductivity on the step length has been evaluated. Condition for the correctness of solutions obtained from the analysis in this article is sharper than the condition of equations stability according to the literature. For the boundary conditions adopted solution can be applied to the study of resistance of buildings shelters to long fire.
EN
In the paper the authors present the effectiveness of the generalized thermal conductivity method for polymer foams, including modelling their geometrical structure. Calculations of the effective thermal conductivity coefficient λ are based on the generally accepted assumption of the additivity of different thermal exchange mechanisms in porous media and this coefficient is presented as a sum the coefficients of conductive λq, radiative λp, and convective λk thermal conductivity. However, in literature not enough attention is given to relations determined by means of the theory of generalized conductivity, including modelling the geometrical structure. This paper presents an analysis of these relations and verifies their ability to predict experimental data in comparison with the best formulae included in the paper [2].
PL
W artykule opisano metody obliczeniowe wykorzystywane do badania zjawiska przepływu ciepła. Do analizy użyte zostały wybrane kształty prętów i żeber wykonanych z materiałów o różnych właściwościach cieplnych. Stworzono model numeryczny przewodzenia ciepła analizowanych obiektów. Zbudowano stanowisko laboratoryjne do wizualizacji rozkładu temperaturyw prętach prostych oraz stożkowych z wykorzystaniem kamery termowizyjnej. Głównym celem prezentowanej pracy było sprawdzenie poprawności stosowania modelu analitycznego.Zbadano również strumienie ciepła przekazywane przez wybrane żebra. Przedstawiono wyniki różnych metod obliczeniowych oraz wyciągnięto z nich wnioski. Porównano wpływ kształtu oraz materiału prętów na wymianę ciepła i rozkłady temperatury.
EN
The article describes the calculation methods used to study the heat transfer. Selected shapes of pin fins and materials with different thermal properties were used for the analysis. Anumerical model of heat conduction of the analyzed objects was created. A laboratory set up was built to visualize the temperature distribution of the straight pin fins and pin fins of cone profile with blunt tip using the infrared camera. The main purpose of the presented chapter of the monograph was to check the right of using the analytical model. The results and conclusions of different calculation methods were presented. The shapes and materials of fins were also compared.
EN
The time-fractional heat conduction equation with heat absorption proportional to temperature is considered in the case of central symmetry. The fundamental solutions to the Cauchy problem and to the source problem are obtained using the integral transform technique. The numerical results are presented graphically.
EN
In this paper, the results of analytical and numerical solution of the problem of heat transport in the rod of finite length are presented. The analytical solution is obtained with the use of the Fourier series. The numerical model of the problem is based on the Finite Element Method (FEM). In addition, to check the compatibility of both solutions, distributions of the temperature for selected time moments are compared and discussed.
20
Content available remote Izolacje techniczne w obiektach rewitalizowanych
PL
W artykule omówiono kwestie prawne i przesłanki techniczne doboru i montażu izolacji technicznych w obiektach rewitalizowanych.
EN
The article further presents the legal aspects and technical criteria for selection and installation of engineering insulation at revitalized buildings.
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