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Differential Equations and Nonlinear Mechanics
Volume 2009 (2009), Article ID 748794, 11 pages
http://dx.doi.org/10.1155/2009/748794
Research Article

Effects of Magnetic Field and Nonlinear Temperature Profile on Marangoni Convection in Micropolar Fluid

1Malaysian Institute of Chemical & Bioengineering Technology, Universiti Kuala Lumpur, 78000 Alor Gajah Melaka, Malaysia
2Department of Mathematics, Faculty of Science & Technology, Universiti Malaysia Terengganu, 21030 Kuala Terengganu, Malaysia
3Centre for Modelling & Data Analysis, School of Mathematical Sciences, Universiti Kebangsaan Malaysia, 43600 UKM Bangi Selangor, Malaysia

Received 20 May 2009; Accepted 8 December 2009

Academic Editor: Tasawar K. Hayat

Copyright © 2009 M. N. Mahmud et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. H. Bénard, “Les tourbillons cellulaires dans une nappe liquide,” Revue Générale des Sciences Pures et Appliquées, vol. 11, pp. 1261–1271, 1900. View at Google Scholar
  2. L. Rayleigh, “On convection currents in a horizontal layer of fluid when the higher temperature is on the other side,” Philosophical Magazine, vol. 32, pp. 529–546, 1916. View at Google Scholar
  3. J. R. A. Pearson, “On convection cells induced by surface tension,” Journal of Fluid Mechanics, vol. 4, pp. 489–500, 1958. View at Google Scholar
  4. S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability, The International Series of Monographs on Physics, Clarendon Press, Oxford, UK, 1961. View at Zentralblatt MATH · View at MathSciNet
  5. D. A. Nield, “Surface tension and buoyancy effects in the cellular convection of an electrically conducting liquid in a magnetic field,” Zeitschrift für Angewandte Mathematik und Physik, vol. 17, no. 1, pp. 131–139, 1966. View at Publisher · View at Google Scholar · View at Scopus
  6. M. Takashima, “Nature of the neutral state in convective instability induced by surface tension and buoyancy,” Journal of the Physical Society of Japan, vol. 28, p. 810, 1970. View at Google Scholar
  7. S. H. Davis and G. M. Homsy, “Energy stability theory for free-surface problems: buoyancy-thermocapillary layers,” Journal of Fluid Mechanics, vol. 98, no. 3, pp. 527–553, 1980. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. M.-I. Char and K.-T. Chiang, “Boundary effects on the Bénard-Marangoni instability under an electric field,” Applied Scientific Research, vol. 52, no. 4, pp. 331–354, 1994. View at Publisher · View at Google Scholar · View at Scopus
  9. I. Hashim and S. K. Wilson, “The effect of a uniform vertical magnetic field on the onset of oscillatory Marangoni convection in a horizontal layer of conducting fluid,” Acta Mechanica, vol. 132, no. 1–4, pp. 129–146, 1999. View at Google Scholar · View at Scopus
  10. I. Hashim, “On competition between modes at the onset of Bénard-Marangoni convection in a layer of fluid,” The Australian & New Zealand Industrial and Applied Mathematics Journal, vol. 43, no. 3, pp. 387–395, 2002. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. I. Hashim and N. Md Arifin, “The effect of a magnetic field on the linear growth rates of Bénard-Marangoni convection,” Microgravity Science and Technology, vol. 17, no. 2, pp. 5–8, 2005. View at Google Scholar · View at Scopus
  12. I. Hashim and Z. Siri, “Stabilization of steady and oscillatory marangoni instability in rotating fluid layer by feedback control strategy,” Numerical Heat Transfer A, vol. 54, no. 6, pp. 647–663, 2008. View at Publisher · View at Google Scholar · View at Scopus
  13. S. Awang Kechil and I. Hashim, “Control of Marangoni instability in a layer of variable-viscosity fluid,” International Communications in Heat and Mass Transfer, vol. 35, no. 10, pp. 1368–1374, 2008. View at Publisher · View at Google Scholar · View at Scopus
  14. Z. Siri and I. Hashim, “Control of oscillatory Marangoni convection in a rotating fluid layer,” International Communications in Heat and Mass Transfer, vol. 35, no. 9, pp. 1130–1133, 2008. View at Publisher · View at Google Scholar · View at Scopus
  15. S. Awang Kechil and I. Hashim, “Oscillatory Marangoni convection in variable-viscosity fluid layer: the effect of thermal feedback control,” International Journal of Thermal Sciences, vol. 48, no. 6, pp. 1102–1107, 2009. View at Publisher · View at Google Scholar · View at Scopus
  16. W.-M. Yang, “Thermal instability of a fluid layer induced by radiation,” Numerical Heat Transfer A, vol. 17, no. 3, pp. 365–376, 1990. View at Google Scholar · View at Scopus
  17. A. Y. Gelfgat and I. Tanasawa, “Numerical analysis of oscillatory instability of buoyancy convection with the Galerkin spectral method,” Numerical Heat Transfer A, vol. 25, no. 6, pp. 627–648, 1994. View at Google Scholar · View at Scopus
  18. E. Evren-Selamet, V. S. Arpaci, and A. T. Chai, “Thermocapillary-driven flow past the Marangoni instability,” Numerical Heat Transfer A, vol. 26, no. 5, pp. 521–535, 1994. View at Google Scholar · View at Scopus
  19. A. C. Eringen, “Micropolar theory of liquid crystals,” in Liquid Crystals and Ordered Fluids, J. F. Johnson and R. S. Porter, Eds., vol. 3, Plenum, New York, NY, USA, 1978. View at Google Scholar
  20. K. V. Rama Rao, “Thermal instability in a micropolar fluid layer subject to a magnetic field,” International Journal of Engineering Science, vol. 18, no. 5, pp. 741–750, 1980. View at Google Scholar · View at Scopus
  21. C. Pérez-García and J. M. Rubí, “On the possibility of overstable motions of micropolar fluids heated from below,” International Journal of Engineering Science, vol. 20, no. 7, pp. 873–878, 1982. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  22. R. C. Sharma and U. Gupta, “Thermal convection in micropolar fluids in porous medium,” International Journal of Engineering Science, vol. 33, no. 13, pp. 1887–1892, 1995. View at Google Scholar · View at Scopus
  23. G. Ramdath, “Bénard-Marangoni instability in a layer of micropolar fluid,” Journal of Non-Equilibrium Thermodynamics, vol. 22, no. 4, pp. 299–310, 1997. View at Google Scholar · View at Scopus
  24. Y. N. Murty and V. V. Ramana Rao, “Effect of throughflow on Marangoni convection in micropolar fluids,” Acta Mechanica, vol. 138, no. 3, pp. 211–217, 1999. View at Google Scholar · View at Scopus
  25. P. G. Siddheshwar and C. V. Sri Krishna, “Linear and non-linear analyses of convection in a micropolar fluid occupying a porous medium,” International Journal of Non-Linear Mechanics, vol. 38, no. 10, pp. 1561–1579, 2003. View at Publisher · View at Google Scholar · View at Scopus
  26. Sunil, P. Chand, P. K. Bharti, and A. Mahajan, “Thermal convection in micropolar ferrofluid in the presence of rotation,” Journal of Magnetism and Magnetic Materials, vol. 320, no. 3-4, pp. 316–324, 2008. View at Publisher · View at Google Scholar · View at Scopus
  27. R. Friedrich and N. Rudraiah, “Marangoni convection in a rotating fluid layer with non-uniform temperature gradient,” International Journal of Heat and Mass Transfer, vol. 27, no. 3, pp. 443–449, 1984. View at Google Scholar · View at Scopus
  28. N. Rudraiah, V. Ramachandramurthy, and O. P. Chandna, “Effects of magnetic field and non-uniform temperature gradient on Marangoni convection,” International Journal of Heat and Mass Transfer, vol. 28, no. 8, pp. 1621–1624, 1985. View at Google Scholar · View at Scopus
  29. N. Rudraiah and V. Ramachandramurthy, “Effects of non-uniform temperature gradient and Coriolis force on Bénard-Marangoni's instability,” Acta Mechanica, vol. 61, no. 1–4, pp. 37–50, 1986. View at Publisher · View at Google Scholar · View at Scopus
  30. O. Dupont, M. Hennenberg, and J. C. Legros, “Marangoni-Bénard instabilities under non-steady conditions. Experimental and theoretical results,” International Journal of Heat and Mass Transfer, vol. 35, no. 12, pp. 3237–3244, 1992. View at Google Scholar · View at Scopus
  31. M.-I. Char and C.-C. Chen, “Effects of nonuniform temperature gradients on the onset of oscillatory Marangoni convection in a magnetic field,” Acta Mechanica, vol. 161, no. 1-2, pp. 17–30, 2003. View at Publisher · View at Google Scholar · View at Scopus
  32. M.-I. Char and C.-C. Chen, “Effect of a non-uniform temperature gradient on the onset of oscillatory Bénard-Marangoni convection of an electrically conducting liquid in a magnetic field,” International Journal of Engineering Science, vol. 41, no. 15, pp. 1711–1727, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  33. K.-T. Chiang, “Effect of a non-uniform basic temperature gradient on the onset of Bénard-Marangoni convection: stationary and oscillatory analyses,” International Communications in Heat and Mass Transfer, vol. 32, no. 1-2, pp. 192–203, 2005. View at Publisher · View at Google Scholar · View at Scopus
  34. N. Rudraiah and P. G. Siddheshwar, “Effect of non-uniform basic temperature gradient on the onset of Marangoni convection in a fluid with suspended particles,” Aerospace Science and Technology, vol. 4, no. 8, pp. 517–523, 2000. View at Google Scholar · View at Scopus
  35. P. G. Siddheshwar and S. Pranesh, “Magnetoconvection in fluids with suspended particles under 1 g and μ g,” Aerospace Science and Technology, vol. 6, no. 2, pp. 105–114, 2002. View at Publisher · View at Google Scholar · View at Scopus
  36. R. Idris, H. Othman, and I. Hashim, “On effect of non-uniform basic temperature gradient on Bénard-Marangoni convection in micropolar fluid,” International Communications in Heat and Mass Transfer, vol. 36, no. 3, pp. 255–258, 2009. View at Publisher · View at Google Scholar · View at Scopus
  37. B. A. Finlayson, The Method of Weighted Residuals and Variational Principles, Academic Press, New York, NY, USA, 1972.