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    Wyświetlanie 1-9 z 9
    Tytuł:
    Laplace transform solution of the problem of time-fractional heat conduction in a two-layered slab
    Autorzy:
    Kukla, S.
    Siedlecka, U.
    Powiązania:
    https://bibliotekanauki.pl/articles/122281.pdf
    Data publikacji:
    2015
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    fractional heat conduction
    two-layered slab
    Laplace transformation
    Opis:
    In this paper the Laplace transformation for solving the problem of fractional heat conduction in a two-layered slab has been applied. The different orders of Caputo derivative in the time-fractional equation governed the heat transfer in the layers are assumed. The inverse Laplace transform by using a numerical method is determined. The numerical results obtained by using of the eigenfunctions method and by numerically inverting the Laplace transform are compared.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2015, 14, 4; 105-113
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Heat conduction in a finite medium using the fractional single-phase-lag model
    Autorzy:
    Siedlecka, Urszula
    Powiązania:
    https://bibliotekanauki.pl/articles/200748.pdf
    Data publikacji:
    2019
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    single-phase-lagging heat conduction
    Caputo derivative
    fractional heat conduction
    przewodzenie ciepła
    Pochodna Caputo
    Opis:
    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.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2019, 67, 2; 401-407
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Fractional heat conduction in a sphere under mathematical and physical Robin conditions
    Autorzy:
    Kukla, S.
    Siedlecka, U.
    Powiązania:
    https://bibliotekanauki.pl/articles/280336.pdf
    Data publikacji:
    2018
    Wydawca:
    Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
    Tematy:
    heat conduction
    fractional heat equation
    Robin boundary condition
    Opis:
    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.
    Źródło:
    Journal of Theoretical and Applied Mechanics; 2018, 56, 2; 339-349
    1429-2955
    Pojawia się w:
    Journal of Theoretical and Applied Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A solution to the problem of time-fractional heat conduction in a multi-layer slab
    Autorzy:
    Siedlecka, U.
    Kukla, S.
    Powiązania:
    https://bibliotekanauki.pl/articles/122925.pdf
    Data publikacji:
    2015
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    heat conduction
    fractional derivative
    multi-layer slab
    przewodnictwo ciepła
    pochodna ułamkowa
    Opis:
    In this paper a solution of the time-fractional heat conduction problem in a multilayer slab is presented. The boundary conditions of the third kind and the perfect contact at the interfaces are assumed. A space-time dependent volumetric heat source in the slab and time dependent surroundings temperatures are taken into account in the formulation of the problem. The solution is obtained in the form of a series expansion with respect to eigenfunctions of an auxiliary problem. A numerical example shows temperature distribution in the slab for various values of the order of the Caputo fractional derivative in the heat conduction equation.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2015, 14, 3; 95-102
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    An analytical solution to the problem of time-fractional heat conduction in a composite sphere
    Autorzy:
    Kukla, S.
    Siedlecka, U.
    Powiązania:
    https://bibliotekanauki.pl/articles/202020.pdf
    Data publikacji:
    2017
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    heat conduction
    multilayered sphere
    Caputo fractional derivative
    przewodzenie ciepła
    powłoka wielowarstwowa
    pochodna ułamkowego rzędu Caputo
    Opis:
    An analytical solution to the problem of time-fractional heat conduction in a sphere consisting of an inner solid sphere and concentric spherical layers is presented. In the heat conduction equation, the Caputo time-derivative of fractional order and the Robin boundary condition at the outer surface of the sphere are assumed. The spherical layers are characterized by different material properties and perfect thermal contact is assumed between the layers. The analytical solution to the problem of heat conduction in the sphere for time-dependent surrounding temperature and for time-space-dependent volumetric heat source is derived. Numerical examples are presented to show the effect of the harmonically varying intensity of the heat source and the harmonically varying surrounding temperature on the temperature in the sphere for different orders of the Caputo time-derivative.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2017, 65, 2; 179-186
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Different kinds of boundary conditions for time-fractional heat conduction equation
    Autorzy:
    Povstenko, Y.
    Powiązania:
    https://bibliotekanauki.pl/articles/121936.pdf
    Data publikacji:
    2011
    Wydawca:
    Uniwersytet Humanistyczno-Przyrodniczy im. Jana Długosza w Częstochowie. Wydawnictwo Uczelniane
    Tematy:
    boundary conditions
    heat conduction
    time-fractional equation
    Caputo derivative
    przewodzenie ciepła
    warunki brzegowe
    pochodna Caputo
    Opis:
    The time-fractional heat conduction equation with the Caputo derivative of the order 0 ˂ α ˂ 2 is considered in a bounded domain. For this equation different types of boundary conditions can be given. The Dirichlet boundary condition prescribes the temperature over the surface of the body. In the case of mathematical Neumann boundary condition the boundary values of the normal derivative are set, the physical Neumann boundary condition specifies the boundary values of the heat flux. In the case of the classical heat conduction equation (α = 1), these two types of boundary conditions are identical, but for fractional heat conduction they are essentially different. The mathematical Robin boundary condition is a specification of a linear combination of the values of temperature and the values of its normal derivative at the boundary of the domain, while the physical Robin boundary condition prescribes a linear combination of the values of temperature and the values of the heat flux at the surface of a body.
    Źródło:
    Scientific Issues of Jan Długosz University in Częstochowa. Mathematics; 2011, 16; 61-66
    2450-9302
    Pojawia się w:
    Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Axisymmetric thermal stresses in a half-space in the framework of fractional thermoelasticity
    Autorzy:
    Povstenko, Y.
    Powiązania:
    https://bibliotekanauki.pl/articles/121806.pdf
    Data publikacji:
    2014
    Wydawca:
    Uniwersytet Humanistyczno-Przyrodniczy im. Jana Długosza w Częstochowie. Wydawnictwo Uczelniane
    Tematy:
    teoria naprężeń cieplnych
    naprężenia cieplne
    termosprężystość
    przewodnictwo cieplne
    pochodne ułamkowe
    theory of thermal stresses
    thermal stresses
    thermoelasticity
    heat conduction
    fractional derivatives
    Opis:
    A theory of thermal stresses based on the time-fractional heat conduction equation is considered. The Caputo fractional derivative is used. The fundamental solution to the axisymmetric heat conduction equation in a half-space under the Dirichlet boundary condition and the associated thermal stresses are investigated.
    Źródło:
    Scientific Issues of Jan Długosz University in Częstochowa. Mathematics; 2014, 19; 207-216
    2450-9302
    Pojawia się w:
    Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Identification of the Thermal Conductivity Coefficient in the Heat Conduction Model with Fractional Derivative
    Autorzy:
    Brociek, R.
    Słota, D.
    Powiązania:
    https://bibliotekanauki.pl/articles/382791.pdf
    Data publikacji:
    2019
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    heat conduction equation
    thermal conductivity coefficient
    inverse problem
    fractional derivative
    thermal conductivity
    model przewodzenia ciepła
    współczynnik przewodzenia ciepła
    problem odwrotny
    pochodna ułamkowa
    przewodność termiczna
    Opis:
    Main goal of the paper is to present the algorithm serving to solve the heat conduction inverse problem. Authors consider the heat conduction equation with the Riemann-Liouville fractional derivative and with the second and third kind boundary conditions. This type of model with fractional derivative can be used for modelling the heat conduction in porous media. Authors deal with the heat conduction inverse problem, which, in this case, consists in identifying an unknown thermal conductivity coefficient. Measurements of temperature, in selected point of the region, are the input data for investigated inverse problem. Basing on this information, a functional describing the error of approximate solution is created. Minimizing of this functional is necessary to solve the inverse problem. In the presented approach the Ant Colony Optimization (ACO) algorithm is used for minimization.
    Źródło:
    Archives of Foundry Engineering; 2019, 3; 38-42
    1897-3310
    2299-2944
    Pojawia się w:
    Archives of Foundry Engineering
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The fundamental solutions to the central symmetric time-fractional heat conduction equation with heat absorption
    Autorzy:
    Povstenko, Y.
    Klekot, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/122778.pdf
    Data publikacji:
    2017
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    non-Fourier heat conduction
    Caputo fractional derivative
    heat absorption
    Laplace integral transform
    Fourier transform
    Mittag-Leffler function
    przewodzenie ciepła
    pochodna ułamkowa Caputo
    absorpcja ciepła
    transformata Laplace'a
    transformata Fouriera
    funkcja Mittag-Lefflera
    Opis:
    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.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2017, 16, 2; 101-112
    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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