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1

Integro-differential form of the first-order dual phase lag heat transfer equation and its numerical solution using the Control Volume Method

Ciesielski M., Mochnacki B., Majchrzak E.

Archives of Mechanics

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2020

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Vol. 72, nr 5

415--444

EN

The start point of the dual phase lag equation (DPLE) formulation is the generalized Fourier law in which two positive constants (the relaxation and thermalization times) appear. This type of equation can be used (among others) to describe the heat conduction processes proceeding in micro-scale. Depending on the number of components in the development of the generalized Fourier law into a power series, one can obtain both the first-order DPLE and the second-order one. In this paper the first-order dual phase lag equation is considered. The primary objective of this research is the transformation of DPLE differential form to the integro-differential one supplemented by the appropriate boundary-initial conditions. The obtained form of the differential equation is much simpler and more convenient at the stage of numerical computations – the numerical algorithm based on the three-time-level scheme reduces to the two-time-level one. To find the numerical solution, the Control Volume Method is used (the heating of thin metal film subjected to a laser beam is considered). The choice of the numerical method was not accidental. The method has a simple physical interpretation ensuring the preservation of the local and global energy balances. To our knowledge, it has not been used so far in this type of tasks. In the final part of the paper the examples of numerical simulations are presented and the conclusions are formulated.

2

Zniekształcenia koncepcji CSR w łańcuchu dostaw

Ciesielski M.

Problemy Transportu i Logistyki

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2017

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nr 2 (38)

7--13

PL

Zagadnienia związane z CSR wymagają głębszej analizy, szczególnie gdy przyjmie się perspektywę łańcucha dostaw. Widać duże rozbieżności w ocenie CSR – od altruizmu do cynicznego działania marketingowego. Ich analiza wymaga wcześniejszego sformułowania hipotetycznego modelu funkcjonowania łańcuchów dostaw, w których występuje zjawisko dominacji. Model ten może zostać skonfirmowany lub odrzucony.

EN

CSR issues require further reflection, especially if one accepts the perspective of the supply chain. The great discrepancies in the assessment of CSR can be perceived from altruism to a cynical marketing activity. Their analysis requires the prior formulation of a hypothetical model of supply chains in which the phenomenon of domination occurs. This model can be confirmed or rejected. This would mean, of course, change in the CSR treatment.

3

Application of the Alternating Direction Implicit Method for numerical solution of the dual phase lag equation

Ciesielski M.

Journal of Theoretical and Applied Mechanics

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2017

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Vol. 55 nr 3

839—852

EN

The problem discussed in the paper concerns the numerical modeling of thermal processes proceeding in micro-scale described using the Dual Phase Lag Model (DPLM) in which the relaxation and thermalization time appear. The cylindrical domain of a thin metal film subjected to a strong laser pulse beam is considered. The laser action is taken into account by the introduction of an internal heat source in the energy equation. At the stage of numerical modeling, the Control Volume Method is used and adapted to resolve the hyperbolic partial differential equation. In particular, the Alternating Direction Implicit (ADI) method for DPLM is presented and discussed. The examples of computations are also presented.

4

Analytical solution of the dual phase lag equation describing the laser heating of thin metal film

Ciesielski M.

Journal of Applied Mathematics and Computational Mechanics

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2017

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Vol. 16, nr 1

33--40

EN

Heat transfer processes occurring in the micro-domains can be described using the dual-phase lag equation (DPLE). This equation can be applied as a model of heating of the thin metal film subjected to the femtosecond laser pulse. In the paper, the 1D dual phase lag equation containing the additional internal heat source resulting from the laser pulse irradiation and supplemented by the appropriate boundary and initial conditions is considered. Appearing in this equation two lag times τq the phase lag of the heat flux) and τT (the phase lag of the temperature gradient) are taken into account. An analytical solution of this equation under the assumption that τT > τq is presented. The separation of the variables technique and the Green’s function method are used in order to find this solution. In the final part of the paper, the example of computations is presented.

5

Czynniki kształtujące łańcuchy dostaw w skali globalnej

Ciesielski M., Kopeć M.

Gospodarka Materiałowa i Logistyka

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2017

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nr 4

20--26

PL

W ostatnich kilkunastu latach można było zaobserwować wzrost znaczenia niektórych czynników kształtujących łańcuchy dostaw. Stąd celem artykułu jest sformułowanie opisowego modelu hipotetycznego współczesnych łańcuchów dostaw w branżach konsumpcyjnych. Trzy najważniejsze czynniki to: oligopolistyczny charakter rynku, presja cenowa i zjawisko dominacji w łańcuchach dostaw. Duże znaczenie ma także to, iż obok deindustrializacji pojawiła się reindustrializacja, która może zmienić współczesne łańcuchy dostaw. W wyjaśnianiu omawianych zjawisk warto posługiwać się schematem eksplanacyjnym, a przede wszystkim rozumowaniem abdukcyjnym. Taką próbę podjęto w artykule. Duża liczba czynników i ich zmienność nie pozwalają bowiem na użycie w badaniach nad łańcuchami dostaw bardziej precyzyjnych sposobów wyjaśniania. Opisane rozważania doprowadziły do hipotezy o wzrostowej tendencji poziomu konkurencji, zarówno wewnątrz, jak i między łańcuchami dostaw jutra.

EN

In the last few years we have seen the growing importance of certain factors shaping the supply chains. Hence, the purpose of this article is to formulate a descriptive model of a hypothetical contemporary supply chains in the consumer industries. The three most important factors are: oligopolistic nature of the market, price pressure and the phenomenon of dominance in the supply chains. Great importance is also the fact that next to the deindustrialization appeared reindustrialization that could change the modern supply chains. In explaining the discussed phenomena, it is worth to use the explanation scheme and above all abduction. Such an attempt was made in the article. A large number of factors and their variability does not allow for the use in research on supply chains more accurate ways of explanation. Described considerations have led to the hypothesis of the upward trend in the level of competition between supply chains and within supply chains in the future.

6

The Sturm-Liouville eigenvalue problem - a numerical solution using the control volume method

Siedlecki J., Ciesielski M, Błaszczyk T.

Journal of Applied Mathematics and Computational Mechanics

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2016

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Vol. 15, nr 2

127--136

EN

The solution of the 1D Sturm-Liouville problem using the Control Volume Method is discussed. The second order linear differential equation with homogeneous boundary conditions is discretized and converted to the system of linear algebraic equations. The matrix associated with this system is tridiagonal and eigenvalues of this system are an approximation of the real eigenvalues of the boundary value problem. The numerical results of the eigenvalues for various cases and the experimental rate of convergence are presented.

7

Comparison of bio-heat transfer numerical models based on the Pennes and Cattaneo-Vernotte equations

Ciesielski M., Duda M., Mochnacki B.

Journal of Applied Mathematics and Computational Mechanics

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2016

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Vol. 15, nr 4

33--38

EN

The homogeneous soft tissue domain subjected to an external heat source is considered. Thermal processes in this domain are described using the well known Pennes equation and next the Cattaneo-Vernotte one. Within recent years the prevailing view is that the Cattaneo-Vernotte equation better describes the thermal processes proceeding in the biological tissue (it results from the specific internal tissue structure). Appearing in this equation the delay time of heat flux with respect to the temperature gradient (τq) is of the order of several seconds and the different values of τq are taken into account. At the stage of numerical modeling the finite difference method is used. In the final part of the paper, the examples of computations are shown.

8

Sensitivity of transient temperature field in domain of forearm insulated by protective clothing with respect to perturbations of external boundary heat flux

Mochnacki B., Ciesielski M.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2016

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Vol. 64, nr 3

591--598

EN

The problem discussed in the paper is numerical modeling of thermal processes in the domain of biological tissue secured by a layer of protective clothing being in thermal contact with the environment. The cross-section of the forearm (2D problem) is treated as non-homogeneous domain in which the sub-domains of skin tissue, fat, muscle and bone are distinguished. The air gap between skin tissue and protective clothing is taken into account. The process of external heating is determined by Robin boundary condition and sensitivity analysis with respect to the perturbations of heat transfer coefficient and ambient temperature is also discussed. Both the basic boundary-initial problem and the sensitivity problems are solved by means of control volume method using Voronoi polygons.

9

Dual Phase Lag Model of Melting Process in Domain of Metal Film Subjected to an External Heat Flux

Mochnacki B., Ciesielski M.

Archives of Foundry Engineering

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2016

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Vol. 16, iss. 4

85--90

EN

Heating process in the domain of thin metal film subjected to a strong laser pulse are discussed. The mathematical model of the process considered is based on the dual-phase-lag equation (DPLE) which results from the generalized form of the Fourier law. This approach is, first of all, used in the case of micro-scale heat transfer problems (the extremely short duration, extreme temperature gradients and very small geometrical dimensions of the domain considered). The external heating (a laser action) is substituted by the introduction of internal heat source to the DPLE. To model the melting process in domain of pure metal (chromium) the approach basing on the artificial mushy zone introduction is used and the main goal of investigation is the verification of influence of the artificial mushy zone ‘width’ on the results of melting modeling. At the stage of numerical modeling the author’s version of the Control Volume Method is used. In the final part of the paper the examples of computations and conclusions are presented.

10

Simulations of thermal processes in tooth proceeding during cold pulp vitality testing

Ciesielski M., Mochnacki B., Siedlecki J.

Acta of Bioengineering and Biomechanics

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2016

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Vol. 18, nr 3

33--41

EN

Purpose: This paper deals with the mathematical modeling of the thermal processes occurring in the tooth, during a very brief contact (a few seconds) with a very cold liquid on a part of the tooth crown. In this way one can simulate a heat transfer in tooth proceeding during a dental diagnostic test - pulp vitality testing. The impact of rapid ambient thermal changes acting on the tooth can cause toothache. Methods: The mathematical model: a system of partial differential equations with initialboundary conditions (the axially-symmetrical problem) and their numerical solutions using the control volume method is discussed. Results: Simulation results of the kinetics of the temperature changes inside the tooth are presented. The example of the control volume mesh (using the Voronoi polygons) well describing the shape of a molar tooth is given. Conclusions: The simulation results (the temperature distribution in the tooth at any moment of the simulation time and the kinetics of temperature variation at the points of the considered tooth domain) can help dentists in the selection of an appropriate method of treatment.

11

Wykorzystanie chmur punktów z lotniczego skanowania laserowego do weryfikacji stanu aktualności wybranych obiektów w bazie geometrycznej leśnej mapy numerycznej

Ciesielski M., Bałazy R., Mitelsztedt K., Zawiła-Niedźwiecki T.

Roczniki Geomatyki

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2015

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T. 13, z. 3(69)

217--225

PL

Celem pracy było sprawdzenie możliwości wykorzystania danych z lotniczego skanowania laserowego do detekcji budynków na terenach leśnych. Ponadto sprawdzono możliwość wykorzystania tych danych do aktualizacji wybranych warstw z leśnej mapy numerycznej. W pracy przeanalizowano obszar leśny wraz z buforem 100 m wokół wydzieleń na terenie dwunastu nadleśnictw górskich, położonych na obszarach badawczych w Sudetach i Beskidach. Przy wykorzystaniu danych z lotniczego skanowania laserowego wykryto 515 budynków co stanowiło 89,2% wszystkich budynków znajdujących się w wektorowej warstwie wydzieleń leśnych. Na poszczególnych obszarach badawczych osiągnięto dokładność odpowiednio 80,5%, 94,2% i 91,2%. Podsumowując, lotnicze skanowanie laserowe może być wykorzystywane do aktualizacji wybranych warstw w leśnej mapie numerycznej, zawierających informacje o budynkach oraz obiektach budowlanych. Istniejące algorytmy detekcji budynków nie są bezbłędne, więc przyszłe prace powinny skupić się na poprawie dokładność analiz.

EN

The aim of the presented studies was to determine the ability to detect buildings in forest areas on the basis of airborne laser scanning data. Moreover, the usefulness of this data for updating selected items of the FDM has been evaluated. In this study forest areas with a 100 m buffer zone have been analyzed, including twelve mountain forest districts, grouped in three research areas located in the Sudety and the Beskidy Mountains. Using LiDAR data 515 buildings have been detected which represents 89.2% of all buildings in the vector layer of the digital forest map. In particular research areas the detection accuracy reached to 80.5%, 92.4%, 91.2%. As a result of the study it can be concluded that the airborne laser scanning data may be helpful in updating the selected layers of the digital maps of forest, containing information of forest engineering. Existing building detection algorithms are not error-free, so further research should be conducted to improve the accuracy of analyzes.

12

Numerical solution of non-homogenous fractional oscillator equation in integral form

Ciesielski M., Błaszczyk T.

Journal of Theoretical and Applied Mechanics

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2015

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Vol. 53 nr 4

959--968

EN

In this paper, a non-homogenous fractional oscillator equation in finite time interval is considered. The fractional equation with derivatives of order α ∈ (0, 1] is transformed into its corresponding integral form. Next, a numerical solution of the integral form of the considered equation is presented. In the final part of this paper, some examples of numerical solutions of the considered equation are shown.

13

Transformation of the second order boundary value problem into integral form : different approaches and a numerical solution

Siedlecki J., Ciesielski M., Błaszczyk T.

Journal of Applied Mathematics and Computational Mechanics

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2015

|

Vol. 14, nr 3

103--108

EN

In this paper we present different approaches to the transformation of the second order ordinary differential equation, with respect to adequate boundary conditions, into integral equations. The obtained equations are Fredholm integral equations of the second kind. Next, a numerical method based on quadrature methods has been proposed to get an approximate solution of these equations.

14

Modele zdominowanych łańcuchów dostaw – podejście abdukcyjne

Ciesielski M.

Gospodarka Materiałowa i Logistyka

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2015

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nr 3

2--5

PL

Wiele uwagi poświęca się dziś negatywnym zjawiskom, które towarzyszą offshoringowi. Wskazuje się na presję cenową wobec dostawców i nieuczciwe praktyki wielkich odbiorców. Poszukuje się sposobów zmniejszania tych zjawisk, jako że prowadzą one oczywiście do nieefektywnego rynku. Wpierw jednak trzeba odpowiednio opisać i przeanalizować procesy dominacji w łańcuchach dostaw. Dobrym rozwiązaniem wydaje się zastosowanie rozumowania abdukcyjnego. Powodzenie takiego podejścia każe zwrócić większą uwagę na przydatność abdukcji.

EN

Nowadays much attention is paid to the negative phenomena, which are referred to offshoring. The price pressure on suppliers and unfair practices of large consumers are pointed. The methods for reduce these phenomena are searching because of the fact that they really lead to an inefficient market. However in the first place the processes of domination in the supply chains should be described and analysed. The abductional approach seems to be a good solution. The success of this approach makes the usefulness of abduction more distinct and leads to pay more attention to the phenomenon.

15

Micro-scale heat transfer : algorithm basing on the Control Volume Method and the identification of relaxation and thermalization times using the search method

Mochnacki B., Ciesielski M.

Computer Methods in Materials Science

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2015

|

Vol. 15, No.2

353--361

EN

The thermal processes proceeding in micro-domains can be described, among others, using the dual phase lag model (DPLM). According to the newest opinions the DPLM constitutes a very good description of the real heat transfer processes proceeding in the micro-scale, in particular on account of extremely short duration, extreme temperature gradients and the very small geometrical dimensions of domain considered. The base of DPLM formulation is a generalized form of Fourier law in which two times τq, τγ appear (the relaxation time and thermalization one, respectively). The numerical solution of the problem discussed bases on the author’s version of the Control Volume Method adapted to resolve the hyperbolic partial differential equations. The example illustrating the method application concerns the estimation of τq and τγusing the algorithm basing on the search method and the thin metal film subjected to the laser pulse is considered.

PL

Procesy cieplne zachodzące w mikro-obszarach mogą być opisane między innymi za pomocą modelu matematycznego z dwoma czasami opóźnień (DPLM). Według najnowszych opinii, model DPLM stanowi bardzo dobry opis rzeczywistych procesów przepływu ciepła w mikroskali, w szczególności ze względu na ekstremalnie krótki czas ich trwania, ekstremalne gradienty temperatury i bardzo małe wymiary geometryczne rozważanego obszaru . Podstawą formułowania DPLM jest uogólnienie prawa Fouriera, w którym występują dwa czasy opóźnień τq i τγ (odpowiednio-czas relaksacji i termalizacji). Numeryczne rozwiązanie omówionego zagadnienia opiera się na autorskiej wersji Metody Bilansów Elementarnych dostosowanej do rozwiązywania hiperbolicznych równań różniczkowych cząstkowych. Przykład ilustrujący zastosowanie metody dotyczy oszacowania czasów τq i τγ za pomocą algorytmu opartego na metodzie przeszukiwania, oraz rozpatrywana jest cienka folia metalowa poddawana działaniu impulsu laserowego.

16

Application of the Control Volume Method using the Voronoi polygons for numerical modeling of bio-heat transfer processes

Ciesielski M., Mochnacki B.

Journal of Theoretical and Applied Mechanics

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2014

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Vol. 52 nr 4

927--935

EN

In the paper, the problem concerning the numerical modeling of thermal processes in the domain of a biological tissue being in thermal contact with the environment is discussed. The changing ambient temperature causes that the non-steady heat transfer process is con- sidered. The cross-section of the forearm (2D problem) is treated as a non-homogeneous domain in which the sub-domains of skin tissue, fat, muscle and bone are distinguished. From the mathematical point of view, the boundary-initial problem described by the system of energy equations (the Pennes equations), boundary conditions on the external surface of the system, boundary conditions on the surfaces limiting the successive sub-domains and the initial condition is analyzed. At the stage of numerical computations, the Control Volume Method using the Voronoi polygons is applied. In the final part of the paper, examples of computations are shown.

17

Numerical simulation of the heating process in the domain of tissue insulated by protective clothing

Ciesielski M., Mochnacki B.

Journal of Applied Mathematics and Computational Mechanics

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2014

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Vol. 13, nr 2

13--20

EN

In this paper the 2D heterogeneous tissue domain (forearm cross-section) insulated by a layer of protective clothing is considered. The aim of considerations is to develop an algorithm simulating the tissue heating process resulting from the sudden change of external boundary conditions. Here, the authors exploit a certain version of the control volume method (CVM) using the Voronoi tessellation. The mathematical model of heat exchange in the domain analyzed is formulated in the form of a boundary-initial problem based on the system of partial differential equations (energy equations) supplemented by the adequate boundary and initial conditions. In the final part of the paper, the examples of numerical simulations are shown.

18

Model łańcucha dostaw zdominowanego przez sieci detaliczne

Ciesielski M

Gospodarka Materiałowa i Logistyka

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2014

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nr 3

2--5

PL

Coraz częściej wskazuje się na znaczenie zjawiska dominacji w łańcuchach dostaw. Trzeba szukać podstaw teoretycznych do badania tego problemu. Dla analizy europejskich żywnościowych łańcuchów dostaw zdominowanych przez sieci detaliczne można wykorzystać dorobek industrial economics. Analiza wskazuje, iż zdominowanie dostawców w tych łańcuchach umożliwia budowę cenowych barier wejścia. Tworzony jest więc rynek kontestowany. Rozpoznanie rodzaju rynku może być podstawą do działań ograniczających dominację.

EN

There is a tendency to emphasize the importance of the phenomenon of domination in supply chains. The problem need to be discussed and there is also a need for us to look for the theoretical basis of the problem. The output of industrial economics may be helpful for the analysis of the European food supply chains, which are dominated by retail networks. The analysis indicates, that the fact, that the suppliers in this chains are dominated enables to build the prices barriers to entry. So there is created a contestable market. The identification of the type of market may be the basis for actions to limit the domination.

19

Simulations of thermal processes in a restored tooth

Siedlecki J., Ciesielski M.

Journal of Applied Mathematics and Computational Mechanics

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2013

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Vol. 12, nr 4

103--108

EN

In this paper the analysis of the temperature distribution in restored tooth is considered. The aim of the research is to evaluate the impact of temperature changes in the pulp layer of tooth under the influence of rapid temperature changes in the ambient fluid. The axially-symmetrical model of the molar tooth (in vitro) without filling and with fillings (amalgam and composite resin) is analyzed. The equations of mathematical model are solved numerically using the control volume method. Finally, some examples of simulations are presented.

20

An approximation of the analytical solution of the fractional Euler-Lagrange equation

Ciesielski M., Błaszczyk T.

Journal of Applied Mathematics and Computational Mechanics

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2013

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Vol. 12, nr 4

23--30

EN

In this paper the fractional Euler-Lagrange equation of order α ∈ (0, 1] in the finite time interval is considered. This equation is transformed to the integral form by the use of the fractional integral operators. Next, the numerical approximation of the analytical solution is presented. Finally, some examples of numerical solutions are presented.