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    Wyświetlanie 1-8 z 8
    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:
    Numerical approaches to the heat transfer problem in modern electronic structures
    Autorzy:
    Raszkowski, T.
    Samson, A.
    Powiązania:
    https://bibliotekanauki.pl/articles/952934.pdf
    Data publikacji:
    2017
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    nanoscale heat transfer
    Fourier-Kirchhoff equation
    dual-phase-lag equation
    finite difference method
    Runge-Kutta method
    gear’s method
    thermal analyses
    Opis:
    The main aim of this paper is to present a detailed description of the research related to the modeling of heat conduction in modern electronic structures, including special consideration for numerical aspects of analyzed algorithms. The motivation to undertake the research as well as some of the most-important results of the experiments and simulations are also included. Moreover, a numerical approximation of the problem as well as the methodology used and a sample solution of the mentioned problem are presented. In the main part, the discretization techniques, Ordinary Differential Equation algorithms, and simulation results for Runge-Kutta’s and Gear’s algorithms are analyzed and discussed. Additionally, a new effective approach to the modeling of heat transfer in electronic nanostructures is demonstrated.
    Źródło:
    Computer Science; 2017, 18 (1); 71-93
    1508-2806
    2300-7036
    Pojawia się w:
    Computer Science
    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:
    Mathematical modeling of short pulsed laser irradiation in the cornea: a dual phase lag model
    Autorzy:
    Autar, Ram
    Kumar, Anuj
    Powiązania:
    https://bibliotekanauki.pl/articles/1839838.pdf
    Data publikacji:
    2021
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    temperature
    laser
    cornea
    refractive error
    Laser Thermo Keratoplasty
    LTK
    Laplace transformation technique
    dual phase lag equation
    temperatura
    rogówka
    termokeratoplastyka
    refrakcja oka
    Opis:
    A simple mathematical model for the temperature evolution in the cornea exposed to short-pulsed Ho: YAG laser under Laser Thermo Keratoplasty (LTK) treatment is developed by incorporating both the heat flux phase-lag and temperature gradient phase-lag in Fourier’s heat transfer model. An analytical solution to the mathematical model is obtained using the Laplace transformation technique. The computational results for the temperature profile and the temperature variation with time are presented through the graphs. The effect of some typical parameters: the heat flux phase-lag and the temperature gradient phase-lag on the temperature distribution and temperature variations are illustrated and discussed.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2021, 20, 3; 5-16
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Analytical solution of the dual phase lag equation describing the laser heating of thin metal film
    Autorzy:
    Ciesielski, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/122626.pdf
    Data publikacji:
    2017
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    dual phase lag equation
    laser heating process
    analytical solution
    Green's function method
    transfer ciepła
    laserowy proces ogrzewania
    równanie z dwoma czasami opóźnień
    metoda funkcji Greena
    Opis:
    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.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2017, 16, 1; 33-40
    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 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
    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
      Wyświetlanie 1-8 z 8

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