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The spatiotemporal instability on mixed convection in porous media

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Abstract

The absolute and convective instability on mixed convection in porous media is examined, and the phase transition from the oscillatory wave motion to the stationary vortex one is observed. Based on linear and weakly nonlinear analyses, the critical conditions to mark the onset of traveling transverse rolls are analytically obtained for small Péclet numbers. The flow change from transverse wave to longitudinal vortex is reproduced by numerical simulation. These criteria made good agreement with the available experiment data.

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References

  1. C.W. Horton and F. T. Rogers, J. Appl. Phys., 16, 367 (1945).

    Article  Google Scholar 

  2. E. R. Lapwood, Proc. Camb. Phil. Soc., 44, 518 (1948).

    Article  Google Scholar 

  3. M. Prats, J. Geophys. Research, 71, 4835 (1966).

    Google Scholar 

  4. M. A. Combarnous and P. Bia, Soc. Pet. Eng. J., 251, 399 (1971).

    Google Scholar 

  5. C. T. Hsu and P. Cheng, Int. J. Heat Mass Transfer, 23, 798 (1980).

    Article  Google Scholar 

  6. M. C. Kim, J. S. Baik, I. G. Hwang, D.-Y. Yoon and C. K. Choi, Chem. Eng. Sci., 54, 619 (1999).

    Article  CAS  Google Scholar 

  7. J. H. Park, T. J. Chung, C. K. Choi and M. C. Kim, AIChE J., 52, 2677 (2006).

    Article  CAS  Google Scholar 

  8. C. K. Choi, T. J. Chung and M. C. Kim, Int. J. Heat Mass Transfer, 47, 2629 (2004).

    Article  CAS  Google Scholar 

  9. D. H. Lee, D.-Y. Yoon and C. K. Choi, Int. J. Heat Mass Transfer, 43, 2895 (2000).

    Article  CAS  Google Scholar 

  10. T. J. Chung, J.H. Park, C.K. Choi and D.-Y. Yoon, Int. J. Heat Mass Transfer, 45, 3061 (2002).

    Article  Google Scholar 

  11. M. Combarnous, Convection naturelle et convection mixte en milieu poreux, Ph.D. thesis, Faculté des sciences de l’univ. de Paris (1970).

  12. A. Delache, M. N. Ouarzazi and M. Combarnous, Int. J. Heat Mass Transfer, 50, 1485 (2007).

    Article  CAS  Google Scholar 

  13. F. Dufour and M.-C. Neel, Phys. Fluids, 10, 2198 (1998).

    Article  CAS  Google Scholar 

  14. H.W. Müller, M. Lücke and M. Kamps, Phys. Rev. A, 45, 3714 (1992).

    Article  Google Scholar 

  15. A. Recktenwald, M. Lücke and H.W. Müller, Phys. Rev. E, 48, 4444 (1993).

    Article  Google Scholar 

  16. S.V. Patankar, Numerical heat transfer and fluid flow, Taylor and Francis (1980).

  17. B. Blankenbach, F. Busse, U. Christensen, L. Cserepes, D. Gunkel, U. Hansen, H. Harder, G. Jarvis, M. Koch, G. Marquart, D. Moore, P. Olson, H. Schmeling and T. Schanubelt, Geophys. J. Int., 98, 23 (1989).

    Article  Google Scholar 

  18. K. L. Walker and G. M. Homsy, J. Fluid Mech., 87, 449 (1978).

    Article  Google Scholar 

  19. S. S. Chen and A. S. Lavine, Int. J. Heat Mass Transfer, 39, 1 (1996).

    Article  CAS  Google Scholar 

  20. C. K. Choi, J. H. Park, H.K. Park, H. J. Cho, T. J. Chung and M. C. Kim, Int. J. Thermal Sci., 43, 817 (2004).

    Article  Google Scholar 

  21. M. T. Ouazzani, J. P. Caltagirone, G. Meyer and A. Mojtabi, Int. J. Heat Mass Transfer, 32, 261 (1989).

    Article  CAS  Google Scholar 

  22. D. D. Joseph, Stability of fluid motions I and II, Springer-Verlag, New York (1976).

    Google Scholar 

  23. A. E. Gill, J. Fluid Mech., 35, 545 (1969).

    Article  Google Scholar 

  24. P. Huerre, Propagation in system far from equilibrium, edited by J. E. Wesfreid, H. R. Brand, P. Manneville, G. Albinet and N. Boccara, 340 (1988).

  25. A. C. Newell and J.A. Whitehead, J. Fluid Mech., 38, 279 (1969).

    Article  Google Scholar 

  26. L. Segel, J. Fluid Mech., 38, 203 (1969).

    Article  Google Scholar 

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Correspondence to Tae Joon Chung.

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This paper is dedicated to Professor Chang Kyun Choi to celebrate his retirement from the school of chemical and biological engineering of Seoul National University.

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Chung, T.J., Kim, M.C. & Choi, C.K. The spatiotemporal instability on mixed convection in porous media. Korean J. Chem. Eng. 26, 332–338 (2009). https://doi.org/10.1007/s11814-009-0056-3

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  • DOI: https://doi.org/10.1007/s11814-009-0056-3

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