Wyniki wyszukiwania - Biblioteka Nauki

1

Wybrane metody modelowania procesów wymiany ciepła

100%

Białecki R. , Fic A. , Rudnicki Z. , Składzeń J. , Skorek J.

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tom nr 1

22-28

2

Zagadnienie Stefana dla żebra pracującego przy wrzeniu

75%

Orzechowski T.

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2006

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tom Nr 6s

179-180

EN

The Stefan problem dealing with the determination of a boundary shape has been presented. A numerical analysis with the use of heat polynomials has been conducted. On the example of a triangular fin a methodology and its effectiveness for boiling heat transfer were shown.

3

The Taylor transformation hybrid method applied for solving the Stefan problem

75%

Grzymkowski R. , Hetmaniok E. , Pleszczyński M.

Silesian Journal of Pure and Applied Mathematics

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2016

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tom Vol. 6, iss. 1

111--123

EN

The paper presents the analytic-numerical hybrid method using, among others, the Taylor transformation, thanks to which the solution of the Stefan problem is replaced by the solution of a nonlinear system of equations.

4

Application of the enthalpy approach in numerical modelling of solidification process

75%

Mochnacki B. , Lara S. , Pawlak E.

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2002

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tom Vol. 1, nr 1

163--176

EN

The numerical modelling of the Stefan problem using directly the typical description of the process is rather difficult. In this connection one can find in literature the models basing on the enthalpy convention and the artificial mushy zone introduction. This paper summarizes the state of the art of the enthalpy models of phase change problems. The part of the approaches discussed has been modified by the authors of the paper, we also present the new interpretations of some models.

5

Numerical scheme for one phase 1D fractional Stefan problem using the similarity variable technique

63%

Błasik M.

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tom Vol. 13, nr 1

13--21

EN

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.

6

Reconstruction of the heat transfer coefficient in the inverse Stefan problem

63%

Matlak J. , Słota D. , Zielonka A.

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tom Vol. 85, nr 1

6--9

EN

In the paper we will present the method of finding the heat transfer coefficient in the inverse problem of pure metal solidification. In the considered model the shrinkage of metal and the air-gap between material and mold will be taken into account. The method is based on the algorithm for solution of the direct problem and on the Artificial Bee Colony algorithm. In the algorithm for solving the direct problem we use the finite element method supplemented by the procedure allowing to define the position of the moving interface and the change of material size associated with the shrinkage. To solve the inverse problem, a functional defining the error of approximate solution must be minimized. To minimize this functional we use the Artificial Bee Colony algorithm. Then we present the computational example illustrating precision and stability of the presented method.

PL

W pracy zaprezentowana zostanie metoda wyznaczania współczynnika wnikania ciepła w zagadnieniu odwrotnym krzepnięciem czystego metalu. W rozważanym modelu uwzględniony będzie skurcz metalu oraz szczelina powietrzna pomiędzy odlewem i wlewkiem. Prezentowana metoda wykorzystuje algorytm rozwiązania zagadnienia bezpośredniego oraz algorytm pszczeli. W algorytmie rozwiązania zagadnienia bezpośredniego wykorzystano metodę elementów skończonych uzupełnioną o procedurę pozwalającą określić położenie granicy rozdziału faz oraz zmianę wymiarów wlewka spowodowaną skurczem metalu. W rozwiązaniu zagadnienia odwrotnego należy zminimalizować funkcjonał określający błąd rozwiązania przybliżonego. W tym celu wykorzystano algorytm pszczeli. Przedstawiono także przykład obliczeniowy ilustrujący dokładność i stabilność prezentowanej metody.

7

Application of generalized finite difference method in numerical modelling of moving boundary problems

51%

Mochnacki B. , Lara S.

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tom Vol. 2, nr 1

129--143

EN

The application of generalized finite difference method for numerical modelling of thermal processes proceeding in the solidifying casting domain is presented. The solidification of pure metals and eutectic alloys is considered. In such case the solidification process takes place at the constant temperature (the Stefan problem). From the numerical point of view the solution of this task is very complex; in particular, in the case of 2D or 3D domains; and in literature one can find the procedures enabling to avoid the difficulties with the direct modelling of the problem discussed. The part of them consist in the substitution of the solidification point T* by the certain interval [T* - ΔT, T* + ΔT]. In this way the subdomain of artificial mushy zone is introduced and the fixed domain approach [1] can be used. On the stage of numerical algorithm construction and numerical simulation the generalized finite difference method is used. In the final part of the paper the examples of computations are shown.