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In this paper, a non-isothermal flow of a micropolar fluid in a thin pipe with circular cross- -section is considered. The fluid in the pipe is cooled by the exterior medium and the heat exchange on the lateral part of the boundary is described by Newton’s cooling condition. Assuming that the hydrodynamic part of the system is provided, we seek for the micropolar effects on the heat flow using the standard perturbation technique. Different asymptotic models are deduced depending on the magnitude of the Reynolds number with respect to the pipe thickness. The critical case is identified and the explicit approximation for the fluid temperature is built improving the known result for the classical Newtonian flow as well. The obtained results are illustrated by some numerical simulations.
Słowa kluczowe
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Tom
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569--579
Opis fizyczny
Bibliogr. 15 poz., rys.
Twórcy
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- Czech Technical University, Faculty of Civil Engineering, Czech Republic
autor
- University of Zagreb, Faculty of Science, Zagreb, Croatia
autor
- Universidad de Sevilla, Facultad de Matem´aticas, Sevilla, Spain
Bibliografia
- 1. Ali K., Ashraf M., 2014, Numerical simulation of the micropolar fluid flow and heat transfer in a channel with a shrinking and a stationary wall, Journal of Theoretical and Applied Mechanics, 52, 557-569
- 2. Dupuy D., Panasenko G., Stavre R., 2004, Asymptotic methods for micropolar fluids in a tube structure, Mathematical Models and Methods in Applied Sciences, 14, 735-758
- 3. Dupuy D., Panasenko G., Stavre R., 2008, Asymptotic solution for a micropolar flow in a curvilinear channel, Zeitschrift für Angewandte Mathematik und Mechanik, 88, 793-807
- 4. Eringen A.C., 1966, Theory of micropolar fluids, Journal of Mathematics and Mechanics, 16, 1, 1-18
- 5. Ladyzhenskaya O.A., Solonnikov V.A., Uraltseva N.N., 1967, Linear and quasilinear equations of parabolic type, Translations of Mathematical Monographs, 23, American Mathematical Society, Providence, R.I.
- 6. Lukaszewicz G., 1999, Micropolar Fluids: Theory and Applications, Birkhäuser, Boston
- 7. Marušić S., Marušić-Paloka E., Pažanin I., 2008, Effects of strong convection on the cooling process for a long or thin pipe, C.R. Mécanique, 336, 493-499
- 8. Marušić-Paloka E., Pažanin I., 2009, Non-isothermal fluid flow through a thin pipe with cooling, Journal of Applied Analysis, 88, 495-515
- 9. Papautsky I., Brazzle J., Ameel T., Frazier A.B., 1999, Laminar fluid behaviour in microchannels using micropolar fluid theory, Sensors and Actuators A: Physical, 73, 101-108
- 10. Pažanin I., 2011a, Asymptotic behavior of micropolar fluid flow through a curved pipe, Acta Applicandae Mathematicae, 116, 1-25
- 11. Pažanin I., 2011b, Effective flow of micropolar fluid through a thin or long pipe, Mathematical Problems in Engineering, 2011, Article ID 127070, 18 pages
- 12. Pažanin I., 2013, Modeling of solute dispersion in a circular pipe filled with micropolar fluid, Mathematical and Computer Modelling, 57, 2366-2373
- 13. Prathap Kumar J., Umavathi J.C., Chamkha A.J., Pop I., 2010, Fully-developed freeconvective flow of micropolar and viscous fluids in a vertical channel, Applied Mathematical Modelling, 34, 1175-1186
- 14. Si X., Zheng L., Lin P., Zhang X., Zhang Y., 2013, Flow and heat transfer of a micropolar fluid in a porous channel with expanding or contracting walls, International Journal of Heat and Mass Transfer, 67, 885-895
- 15. Shu J.-J., Lee J.S., 2008, Fundamental solutions for micropolar fluids, Journal of Engineering Mathematics, 61, 69-78
Typ dokumentu
Bibliografia
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