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    Wyświetlanie 1-8 z 8
    Tytuł:
    Stefan problems in non-cylindrical domains arising in Czochralski process of crystal growth
    Autorzy:
    Fukao, T.
    Kenmochi, N.
    Pawłow, I.
    Powiązania:
    https://bibliotekanauki.pl/articles/206232.pdf
    Data publikacji:
    2003
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    problem Stefana
    domena niecylinryczna
    Stefan problem
    non-cylindrical domain
    prescribed convection
    Opis:
    In this paper we discuss a two-phase Stefan problem with convection in a non-cylindrical (time-dependent) domain. This work is motivated by phase change phenomenon arising in the Czochralski process of crystal growth. The time-dependence of domain is a mathematical description of the situation in which the material domain changes its shape with time by crystal growth. We consider the so-called enthalpy formulation for it and give its solvability, assuming that the time-dependence of the material domain is prescribed and smooth enough in time, and the convective vector is prescribed, too. Our main idea is to apply the theory of quasi-linear equations of parabolic type.
    Źródło:
    Control and Cybernetics; 2003, 32, 2; 201-221
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Solution of the Pure Metals Solidification Problem by Involving the Material Shrinkage and the Air-Gap Between Material and Mold
    Autorzy:
    Matlak, J.
    Słota, D.
    Powiązania:
    https://bibliotekanauki.pl/articles/381022.pdf
    Data publikacji:
    2015
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    solidification process
    air-gap
    Stefan problem
    metal shrinkage
    proces krzepnięcia
    szczelina powietrzna
    problem Stefana
    skurcz stopu
    Opis:
    In this paper we describe an algorithm for solving the pure metals solidification problem by involving the metal shrinkage and air-gap between material and mold. In this algorithm we use the finite element method supplemented by the procedures allowing to define the position of the moving interface and the change of the material size associated with the shrinkage. We present also an example illustrating the precision of presented method.
    Źródło:
    Archives of Foundry Engineering; 2015, 15, 3 spec.; 47-52
    1897-3310
    2299-2944
    Pojawia się w:
    Archives of Foundry Engineering
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Numerical modeling of pure metal solidification using the one domain approach
    Autorzy:
    Szopa, R.
    Powiązania:
    https://bibliotekanauki.pl/articles/973637.pdf
    Data publikacji:
    2015
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    solidification of metal
    Stefan problem
    artificial mushy zone
    numerical methods
    krzepnięcie metalu
    problem Stefana
    sztuczna strefa dwufazowa
    metody numeryczne
    Opis:
    Numerical modeling of pure metal solidification on the basis of the well-known Stefan model is rather difficult. The knowledge of temporary solidification front position and the local values of the solidification rate in the normal direction for time t are necessary in order to determine the new position of moving boundary for time t + ∆t. The problem is especially complicated for 2D and 3D tasks. The concept greatly simplifying the modeling of solidification process boils down to the introduction of the artificial region corresponding to the mushy zone sub-domain. For this region the substitute thermal capacity is defined and the mathematical model corresponds to the one domain approach. The artificial mushy zone appears owing to conventional enlargement of solidification point on a certain interval of temperature ∆T. The basic goal of the paper is the numerical analysis of the influence of the interval ∆T on the numerical solution simulating the thermal processes in the domain of the solidifying metal.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2015, 14, 3; 121-126
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Analytic-numerical method of determining the freezing front location
    Autorzy:
    Grzymkowski, R.
    Hetmaniok, E.
    Pleszczyński, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/381964.pdf
    Data publikacji:
    2011
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    solidification process
    information technology
    foundry industry
    one-phase Stefan problem
    moving boundary problem
    proces krzepnięcia
    technologia informacyjna
    przemysł odlewniczy
    jednofazowy problem Stefana
    problem brzegowy
    Opis:
    Mathematical modeling of thermal processes combined with the reversible phase transitions of type: solid phase – liquid phase leads to formulation of the parabolic boundary problems with the moving boundary. Solution of such defined problem requires, most often, to use sophisticated numerical techniques and far advanced mathematical tools. Excellent illustration of the complexity of considered problems, as well as of the variety of approaches used for finding their solutions, gives the papers [1-4]. In the current paper, the authors present the, especially attractive from the engineer point of view, analytic-numerical method for finding the approximate solution of selected class of problems which can be reduced to the one-phase solidification problem of a plate with the unknown a priori, varying in time boundary of the region in which the solution is sought. Proposed method is based on the known formalism of initial expansion of the sought function describing the temperature field into the power series, some coefficients of which are determined with the aid of boundary conditions, and on the approximation of the function defining the location of freezing front with the broken line, parameters of which are numerically determined.
    Źródło:
    Archives of Foundry Engineering; 2011, 11, 3 spec.; 75-80
    1897-3310
    2299-2944
    Pojawia się w:
    Archives of Foundry Engineering
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Identification of the Heat Transfer Coefficient in the Inverse Stefan Problem by Using the ABC Algorithm
    Autorzy:
    Hetmaniok, E.
    Słota, D.
    Zielonka, A.
    Powiązania:
    https://bibliotekanauki.pl/articles/382882.pdf
    Data publikacji:
    2012
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    solidification process
    foundry industry
    application of information technology
    Stefan problem
    swarm intelligence
    ABC algorithm
    proces krzepnięcia
    przemysł odlewniczy
    zastosowanie technologii informatycznych
    Problem Stefana
    inteligencja roju
    algorytm ABC
    Opis:
    A procedure based on the Artificial Bee Colony algorithm for solving the two-phase axisymmetric one-dimensional inverse Stefan problem with the third kind boundary condition is presented in this paper. Solving of the considered problem consists in reconstruction of the function describing the heat transfer coefficient appearing in boundary condition of the third kind in such a way that the reconstructed values of temperature would be as closed as possible to the measurements of temperature given in selected points of the solid. A crucial part of the solution method consists in minimizing some functional which will be executed with the aid of one of the swarm intelligence algorithms - the ABC algorithm.
    Źródło:
    Archives of Foundry Engineering; 2012, 12, 2s; 27-32
    1897-3310
    2299-2944
    Pojawia się w:
    Archives of Foundry Engineering
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Identification of the heat transfer coefficient in phase change problems
    Autorzy:
    Słota, D.
    Powiązania:
    https://bibliotekanauki.pl/articles/240218.pdf
    Data publikacji:
    2010
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    krzepnięcie
    odwrotne zagadnienie Stefana
    Inverse Stefan problem
    solidification
    Opis:
    In this paper, an algorithm will be presented that enables solving the two-phase inverse Stefan problem, where the additional information consists of temperature measurements in selected points of the solid phase. The problem consists in the reconstruction of the function describing the heat transfer coefficient, so that the temperature in the given points of the solid phase would differ as little as possible from the predefined values. The featured examples of calculations show a very good approximation of the exact solution and stability of the algorithm.
    Źródło:
    Archives of Thermodynamics; 2010, 31, 1; 61-78
    1231-0956
    2083-6023
    Pojawia się w:
    Archives of Thermodynamics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Numerical scheme for one phase 1D fractional Stefan problem using the similarity variable technique
    Autorzy:
    Błasik, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/122307.pdf
    Data publikacji:
    2014
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    Stefan problem
    anomalous diffusion
    fractional derivative
    finite difference method
    zagadnienie Stefana
    dyfuzja anomalna
    pochodna ułamkowa
    metoda różnic skończonych
    Opis:
    In this paper we present a numerical method to solve a one-dimensional, one-phase extended Stefan problem with fractional time derivative described in the Caputo sense. The proposed method is based on applying a similarity variable for the anomalous-diffusion equation and the finite difference method. In the final part, examples of numerical results are discussed.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2014, 13, 1; 13-21
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Effect of Mesh Quality on the Numerical Solution of the Solidification of Pure Metal
    Autorzy:
    Skrzypczak, T.
    Węgrzyn-Skrzypczak, E.
    Powiązania:
    https://bibliotekanauki.pl/articles/381672.pdf
    Data publikacji:
    2013
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    solidification process
    information technology
    foundry industry
    pure metal
    Stefan problem
    finite element method
    krzepnięcie stopu
    technologia informatyczna
    przemysł odlewniczy
    metal czysty
    zagadnienie Stefana
    metoda elementów skończonych
    Opis:
    The paper presents a method of mathematical and numerical modelling of directional solidification process of pure metal in the two-dimensional region. In this case, the thermal conditions associated with the process favours the occurrence of sharp solidification front. The mathematical description of the process is based on the Stefan formulation with appropriate continuity conditions on the solid-liquid interface. The numerical model is based on the finite element method (FEM). The calculations were made on a fixed mesh with diffused solidification front to avoid the difficulties associated with the discontinuity. Temporary position of the interface was calculated with the use of the level set method (LSM). Effect of the quality of the spatial discretization on the accuracy of numerical solution was investigated. Obtained results of the temporary front position were compared with the analytical solution. The correlation between the quality of the spatial discretization and the accuracy of the results was observed. Methods used in the work had significant impact on the computation time and helped avoid the explicit consideration of discontinuity of heat flux on the front.
    Źródło:
    Archives of Foundry Engineering; 2013, 13, 2 spec.; 89-92
    1897-3310
    2299-2944
    Pojawia się w:
    Archives of Foundry Engineering
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-8 z 8

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