Verification of a binary fluid solidification model using semi-analitycal solution of 1D heat diffusion equation

• Autorzy: Wacławczyk T. , Schäfer M.

Identyfikatory

DOI

10.24425/119101

• Języki publikacji: EN

Abstrakty

EN

The aim of the present work is to verify a numerical implementation of a binary fluid, heat conduction dominated solidification model with a novel semi-analytical solution to the heat diffusion equation. The semi-analytical solution put forward by Chakaraborty and Dutta (2002) is extended by taking into account variable in the mushy region solid/liquid mixture heat conduction coefficient. Subsequently, the range in which the extended semi-analytical solution can be used to verify numerical solutions is investigated and determined. It has been found that linearization introduced to analytically integrate the heat diffusion equation impairs its ability to predict solidus and liquidus line positions whenever the magnitude of latent heat of fusion exceeds a certain value.

Słowa kluczowe

EN

heat diffusion; semi-analytical solution; numerical methods; binary fluid solidification

PL

dyfuzja ciepła; metody numeryczne

• Wydawca: Komitet Inżynierii Chemicznej i Procesowej Polskiej Akademii Nauk
• Czasopismo: Chemical and Process Engineering
• Rocznik: 2018
• Tom: Vol. 39, nr 1
• Strony: 85–--102
• Opis fizyczny: Bibliogr. 16 poz., rys.

Twórcy

autor

Wacławczyk T.

• Institute of Aeronautics and Applied Mechanics,Warsaw University of Technology, Warszawa, ul. Nowowiejska 24, Poland

autor

Schäfer M.

• Institute of Numerical Methods in Mechanical Engineering, Technische Universität Darmstadt, Dolivostr. 15, Germany

Bibliografia

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• 3. BennonW.D., Incropera F.P., 1987. A continuum model for momentum, heat and species transport in binary solidliquid phase change systems – I. Model formulation. Int. J. Heat Mass Transf., 30, 2161–2170. DOI: 10.1016/ 0017-9310(87)90094-9.
• 4. BennonW.D., Incropera F.P., 1987. A continuum model for momentum, heat and species transport in binary solidliquid phase change systems – II. Application to solidification in rectangular cavity. Int. J. Heat Mass Transf., 30, 2161–2170. DOI: 10.1016/0017-9310(87)90095-0.
• 5. Braga S.L., Viskanta R., 1990. Solidification of a binary solution on a cold isothermal surface, Int. J. Heat Mass Transf., 33, 745–754. DOI: 10.1016/0017-9310(90)90172-Q.
• 6. Chakaraborty S., Dutta P., 2002. An analytical solution for conduction dominated unidirectional solidification of binary mixtures. Appl. Math. Model., 26, 545–561. DOI: 10.1016/S0307-904X(01)00073-7.
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• 12. Wacławczyk T., Sternel D., Schäfer M., 2011. Verification of binary fluid solidification model. In ICNAAM AIP Conference Proc., vol. 1389, Halkidiki, Greece. DOI: 10.1063/1.3636676.
• 13. Wacławczyk T., Schäfer M., 2016. Verification of binary fluid solidification model in the finite volume flow solver. arXiv preprint arXiv:1507.01131. Available at: https://arxiv.org/ftp/arxiv/papers/1507/1507.01131.pdf
• 14. Wang Chao-Yang, Beckermann C., 1993. A two-phase mixture model of liquid-gas flow and heat transfer in capillary porous media – I. Formulation. Int. J. Heat Mass Transf., 36, 2747–2758. DOI: 10.1016/0017-9310(93) 90094-M.
• 15. Wang Chao-Yang, Beckermann C., A two-phase mixture model of liquid-gas flow and heat transfer in capillary porous media – II. Application to pressure-driven boiling flow adjacent to a vertical heated plate. Int. J. Heat Mass Transf., 36, 2759–2768. DOI: 10.1016/0017-9310(93)90095-N.
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Uwagi

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).