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Vertical heat transport at infinite Prandtl number for micropolar fluid

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We investigate the upper bound on the vertical heat transport in the fully 3D Rayleigh–Bénard convection problem at the infinite Prandtl number for a micropolar fluid. We obtain a bound, given by the cube root of the Rayleigh number, with a logarithmic correction. The derived bound is compared with the optimal known one for the Newtonian fluid. It follows that the (optimal) upper bound for the micropolar fluid is less than the corresponding bound for the Newtonian fluid at the same Rayleigh number. Moreover, strong microrotational diffusion effects can entirely suppress the heat transfer. In the Newtonian limit our purely analytical findings fully agree with estimates and scaling laws obtained from previous theories significantly relying on phenomenology.
Rocznik
Strony
525--553
Opis fizyczny
Bibliogr. 25 poz.
Twórcy
autor
  • Department of Information Engineering, Computer Science and Mathematics, University of L’Aquila, Via Vetoio, Coppito, 67100 L’Aquila, Italy
autor
  • Faculty of Mathematics and Computer Science, Jagiellonian University, Łojasiewicza 6, 30-348 Kraków, Poland
  • Institute of Applied Mathematics and Mechanics, University of Warsaw, Banacha 2, 02-097 Warsaw, Poland
  • Department of Magnetism, Institute of Geophysics, Polish Academy of Sciences, Księcia Janusza 64, 01-452 Warsaw, Poland
Bibliografia
  • 1. N.A.M. Al-Juma, A.J. Chamkha, Coupled heat and mass transfer by natural convection of a micropolar fluid flow about a sphere in porous media with Soret and Dufour effects, in: M.K. Jha, M. Lazard, A. Zaharim, K. Sopian [eds.], Recent Advances in Fluid Mechanics, Heat & Mass Transfer and Biology, pp. 204–209, WSEAS Press, Harvard, Cambridge, 2012.
  • 2. T. Ariman, M.A. Turk, N.D. Sylvester, On steady and pulsatile flow of blood, Journal of Applied Mechanics, 41, 1–7, 1974.
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  • 4. O. Aydin, I. Pop, Natural convection in a differentially heated enclosure filled with a micropolar fluid, International Journal of Thermal Sciences, 46, 963–969, 2007.
  • 5. A.Y. Bakier, Natural convection heat and mass transfer in a micropolar fluid-saturated non-Darcy porous regime with radiation and thermophoresis effects, Thermal Sciience, 15, S317–S326, 2011.
  • 6. G. Bourantas, V. Loukopoulos, Modeling the natural convective flow of micropolar nanofluids, International Journal of Heat and Mass Transfer, 68, 35–41, 2014.
  • 7. P. Constantin, C. Doering, Heat transfer in convective turbulence, Nonlinearity, 9, 1049–1060, 1996.
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  • 9. C.R. Doering, P. Constantin, On upper bounds for infinite Prandtl number convection with or without rotation, Journal of Mathematical Physics, 42, 784–795, 2001.
  • 10. C.R. Doering, F. Otto, M.G. Reznikoff, Bounds on vertical heat transport for infinite-Prandtl-number Rayleigh–Bénard convection, Journal od Fluid Mechanics, 560, 229–241, 2006.
  • 11. A. Eringen, Theory of micropolar fluids, Journal of Mathematics and Mechanics, 16, 1–16, 1966.
  • 12. A. Grossmann, D. Lohse, Scaling in thermal convection: a unifying theory, Journal of Fluid Mechanics, 407, 27–56, 2000.
  • 13. A. Grossmann, D. Lohse, Thermal convection for large Prandtl numbers, Physical Review Letters, 86, 3316–3319, 2001.
  • 14. Capd library., http://capd.ii.uj.edu.pl.
  • 15. P. Kalita, J.A. Langa, G. Łukaszewicz, Micropolar meets Newtonian. The Rayleigh–Bénard problem, Physica D: Nonlinear Phenomena, 392, 57–80, 2019, DOI: 10.1016/j.physd.2018.12.004.
  • 16. S. Kurgin, J.M. Dasch, D.L. Simon, G.C. Barber, Q. Zou, Evaluation of the convective heat transfer coefficient for minimum quantity lubrication (MQL), Industrial Lu- brication and Tribology, 64, 376–386, 2012.
  • 17. G. Łukaszewicz, Micropolar Fluids – Theory and Applications, Birkhäuser Basel, 1999.
  • 18. W.V.R. Malkus, Discrete transitions in turbulent convection, Proceedings of the Royal Society of London A, 225, 185–195, 1954.
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  • 20. M.A.M. Neto, R.M. Franca, J.R. Barbarosa, Jr., Convection-driven absorption of R-1234yf in lubricating oil, International Journal of Refrigeration, 44, 151–160, 2014.
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Typ dokumentu
Bibliografia
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