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    Wyświetlanie 1-9 z 9
    Tytuł:
    Heat flux formulation for 1D dual-phase lag equation
    Autorzy:
    Majchrzak, E.
    Kałuża, G.
    Powiązania:
    https://bibliotekanauki.pl/articles/122784.pdf
    Data publikacji:
    2015
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    dual phase lag equation
    finite difference method
    thin metal film
    Opis:
    The thin metal film subjected to the ultra-short laser pulse is analyzed. Heat transfer processes occurring in the domain considered are described by the dual-phase lag model in which the unknown is the heat flux, not, as usual, temperature. This approach is especially convenient in the case of Neumann boundary conditions, which are taken into account here. The mathematical model supplemented by initial conditions is solved using the explicit scheme of finite difference method. In the final part of the paper the examples of computations are shown and the conclusions are formulated.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2015, 14, 1; 71-78
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Solution of dual phase lag equation by means of the boundary element method using discretization in time
    Autorzy:
    Majchrzak, E.
    Turchan, Ł.
    Powiązania:
    https://bibliotekanauki.pl/articles/122850.pdf
    Data publikacji:
    2013
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    dual phase lag equation
    boundary element method
    discretization in time
    Opis:
    The dual phase lag equation describing the temperature field in a 3D domain is considered. This equation supplemented by boundary and initial conditions is solved by means of the boundary element method using discretization in time, while at the same time the Dirichlet and Neumann boundary conditions are taken into account. Numerical realization of the BEM for the constant boundary elements and constant internal cells is presented. The example of computations concerns the temperature field distribution in a heated domain. The conclusions connected with the proper choice of time step and discretization of the domain considered are formulated.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2013, 12, 4; 89-95
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Implicit scheme of the finite difference method for the second-order dual phase lag equation
    Autorzy:
    Majchrzak, E.
    Mochnacki, B.
    Powiązania:
    https://bibliotekanauki.pl/articles/280549.pdf
    Data publikacji:
    2018
    Wydawca:
    Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
    Tematy:
    microscale heat transfer
    dual phase lag model
    implicit scheme of finite difference method
    Opis:
    The second-order dual phase lag equation (DPLE) as a mathematical model of the microscale heat transfer is considered. It is known that the starting point determining the final form of this equation is the generalized Fourier law in which two positive constants (the relaxation and thermalization times) appear. Depending on the order of the generalized Fourier law expansion into the Taylor series, different forms of the DPLE can be obtained. As an example of the problem described by the second-order DPLE equation, thermal processes proceeding in the domain of a thin metal film subjected to a laser pulse are considered. The numerical algorithm is based on an implicit scheme of the finite difference method. At the stage of numerical modeling, the first, second and mixed order of the dual phase lag equation are considered. In the final part of the paper, examples of different solutions are presented and conclusions are formulated.
    Źródło:
    Journal of Theoretical and Applied Mechanics; 2018, 56, 2; 393-402
    1429-2955
    Pojawia się w:
    Journal of Theoretical and Applied Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Integro-differential form of the first-order dual phase lag heat transfer equation and its numerical solution using the Control Volume Method
    Autorzy:
    Ciesielski, M.
    Mochnacki, B.
    Majchrzak, E.
    Powiązania:
    https://bibliotekanauki.pl/articles/38606551.pdf
    Data publikacji:
    2020
    Wydawca:
    Instytut Podstawowych Problemów Techniki PAN
    Tematy:
    micro-scale heat transfer
    dual phase lag model
    integro-differential equation
    Control Volume Method
    Opis:
    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.
    Źródło:
    Archives of Mechanics; 2020, 72, 5; 415-444
    0373-2029
    Pojawia się w:
    Archives of Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    1D generalized dual-phase lag equation. Sensitivity analysis with respect to the porosity
    Autorzy:
    Kałuża, G.
    Majchrzak, E.
    Turchan, Ł.
    Powiązania:
    https://bibliotekanauki.pl/articles/123000.pdf
    Data publikacji:
    2016
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    bioheat transfer
    generalized dual-phase lag model
    sensitivity analysis
    finite difference method
    przepływ biociepła
    metoda różnic skończonych
    analiza wrażliwości
    Opis:
    Thermal processes occurring in the heated tissue are described by the 1D generalized dual-phase lag equation supplemented by appropriate boundary and initial conditions. Using the sensitivity analysis method, the additional problem connected with the porosity is formulated. Both problems are solved by means of the explicit scheme of the finite difference method. In this way it is possible to estimate the temperature changes due to the perturbation of porosity. In the final part of the paper, the example of computation is shown and the conclusions are formulated.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2016, 15, 1; 49-58
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Dual-phase lag equation. Stability conditions of a numerical algorithm based on the explicit scheme of the finite difference method
    Autorzy:
    Majchrzak, E.
    Mochnacki, B.
    Powiązania:
    https://bibliotekanauki.pl/articles/122742.pdf
    Data publikacji:
    2016
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    heat conduction
    dual-phase lag equation
    finite difference method
    stability conditions of FDM explicit scheme
    przewodzenie ciepła
    metoda różnic skończonych
    Opis:
    The dual-phase lag equation (DPLE) is considered. This equation belongs to the group of hyperbolic PDE, contains a second order time derivative and higher order mixed derivative in both time and space. From the engineer’s point of view, the DPLE results from the generalized form of the Fourier law. It is applied as a mathematical model of thermal processes proceeding in the micro-scale and also in the case of bio-heat transfer problem analysis. At the stage of numerical computations the different approximate methods of the PDE solving can be used. In this paper, the authors present the considerations concerning the stability conditions of the explicit scheme of finite difference method (FDM). The appropriate conditions have been found using the von Neumann analysis. In the final part of the paper, the results of testing computations are shown.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2016, 15, 3; 89-96
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Numerical analysis of artificial hyperthermia treatment
    Analiza numeryczna zabiegu sztucznej hipertermii
    Autorzy:
    Turchan, Ł.
    Majchrzak, E.
    Powiązania:
    https://bibliotekanauki.pl/articles/408458.pdf
    Data publikacji:
    2014
    Wydawca:
    Politechnika Lubelska. Wydawnictwo Politechniki Lubelskiej
    Tematy:
    artificial hyperthermia
    finite difference method
    parallelized calculations
    dual phase lag model
    sztuczna hipertermia
    metoda różnic skończonych
    obliczenia równoległe
    uogólnione równanie z dwoma czasami opóźnień
    Opis:
    This paper presents numerical modelling of artificial hyperthermia treatment. Presented model takes into account not only the temperature distributions but also the thermal dose parameter. Obtaining of temperature distributions takes advantage of the generalized dual phase lag equation. For computer calculations the parallelized algorithm was prepared.
    Artykuł dotyczy numerycznego modelowania zabiegu sztucznej hipertermii. Analiza skuteczności zabiegu jest rozpatrywana nie tylko na podstawie czasoprzestrzennych rozkładów temperatury, ale także w oparciu o parametr dawki termicznej. Do modelowania przepływu ciepła w rozpatrywanym obszarze wykorzystano uogólnione równanie z dwoma czasami opóźnień. Na potrzeby obliczeń numerycznych napisano autorski program oparty o obliczenia równoległe.
    Źródło:
    Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska; 2014, 1; 48-53
    2083-0157
    2391-6761
    Pojawia się w:
    Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Modeling of Melting and Resolidification in Domain of Metal Film Subjected to a Laser Pulse
    Autorzy:
    Majchrzak, E.
    Mochnacki, B.
    Powiązania:
    https://bibliotekanauki.pl/articles/379913.pdf
    Data publikacji:
    2016
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    foundry process
    heat transfer
    melting
    solidification
    dual phase lag model
    numerical methods
    theoretical basis
    proces odlewniczy
    przenikanie ciepła
    topienie
    krzepnięcie
    model dwufazowy
    metody numeryczne
    podstawy teoretyczne
    Opis:
    Thermal processes in domain of thin metal film subjected to a strong laser pulse are discussed. The heating of domain considered causes the melting and next (after the end of beam impact) the resolidification of metal superficial layer. The laser action (a time dependent bell-type function) is taken into account by the introduction of internal heat source in the energy equation describing the heat transfer in domain of metal film. Taking into account the extremely short duration, extreme temperature gradients and very small geometrical dimensions of the domain considered, the mathematical model of the process is based on the dual phase lag equation supplemented by the suitable boundary-initial conditions. To model the phase transitions the artificial mushy zone is introduced. At the stage of numerical modeling the Control Volume Method is used. The examples of computations are also presented.
    Źródło:
    Archives of Foundry Engineering; 2016, 16, 1; 41-44
    1897-3310
    2299-2944
    Pojawia się w:
    Archives of Foundry Engineering
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Implicit scheme of the finite difference method for 1D dual-phase lag equation
    Autorzy:
    Majchrzak, E.
    Mochnacki, B.
    Powiązania:
    https://bibliotekanauki.pl/articles/973620.pdf
    Data publikacji:
    2017
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    micro-scale heat conduction
    dual-phase lag equation
    finite difference method
    stability of FDM implicit scheme
    równanie z dwoma czasami opóźnień
    metoda różnic skończonych
    DPLE
    schemat FDM
    Opis:
    The 1D dual-phase lag equation (DPLE) is solved using the implicit FDM scheme. The dual phase lag equation is the hyperbolic PDE and contains a second order time derivative and higher order mixed derivative in both time and space. The DPLE results from the generalization of the well known Fourier law in which the delay times are taken into account. So, in the equation discussed, two positive parameters appear. They correspond to the relaxation time τq and the thermalization time τ T. The DPLE finds, among others, the application as the mathematical description of the thermal processes proceeding in the micro-scale. In the paper, the numerical solution of DPLE based on the implicit scheme of the FDM is presented. The authors show that a such an approach in the case of DPLE leads to the unconditionally stable differential scheme.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2017, 16, 3; 37-46
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-9 z 9

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