Analytic-numerical method of determining the freezing front location

• Autorzy: Grzymkowski R. , Hetmaniok E. , Pleszczyński M.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

solidification process; information technology; foundry industry; one-phase Stefan problem; moving boundary problem

PL

proces krzepnięcia; technologia informacyjna; przemysł odlewniczy; jednofazowy problem Stefana; problem brzegowy

• Wydawca: Komisja Odlewnictwa Polskiej Akademii Nauk Oddział w Katowicach
• Czasopismo: Archives of Foundry Engineering
• Rocznik: 2011
• Tom: Vol. 11, iss. 3 spec.
• Strony: 75--80
• Opis fizyczny: Bibliogr. 5 poz., wykr.

Twórcy

autor

Grzymkowski R.

• Institute of Mathematics, Silesian University of Technology, Kaszubska 23, 44-100 Gliwice, Poland

autor

Hetmaniok E.

• Institute of Mathematics, Silesian University of Technology, Kaszubska 23, 44-100 Gliwice, Poland

autor

Pleszczyński M.

• Institute of Mathematics, Silesian University of Technology, Kaszubska 23, 44-100 Gliwice, Poland

Bibliografia

• [1] J.R. Ockendon, W.R. Hodgkins, Moving Boundary Problems in Heat Flow and Diffusion, Clarendon Press, Oxford, 1975.
• [2] D.G. Wilson, A.D. Solomon, P.T. Boggs, Moving Boundary Problems, Academic Press, New York, 1978.
• [3] J. Crank, Free and Moving Boundary Problems, Clarendon Press, Oxford, 1984.
• [4] E. Hetmaniok, D. Słota, R. Wituła, A. Zielonka, Comparison of the Adomian decomposition method and the variational iteration method in solving the moving boundary problem, Computers and Mathematics with Applications, vol.61 (2011), 1931-1934.
• [5] E. Hetmaniok, M. Pleszczyński, Analitycal method of determining the freezing front location, Research Bulletin of Silesian University of Technology 2011 (in Polish, in print).