Stability analysis of soret effect on thermohaline convection in dusty ferrofluid saturating a Darcy porous medium

  • Authors

    • R. Sekar
    • K. Raju
    2015-02-17
    https://doi.org/10.14419/gjma.v3i1.3086
  • Darcy Model, Ferromagnetic Fluid, Linear Stability Analysis, Soret Parameter, Thermohaline Convection.
  • The Soret–driven ferro thermoconvective instability of multi–component fluid in a porous medium heated from below and salted from above in the presence of dust particles subjected to a transverse uniform magnetic field has been analyzed using Darcy model for various values of permeability of the porous medium. The salinity effect has been contained in magnetization and density of the ferrofluid. A small thermal perturbation imparted on the basic state and a linear stability analysis is used for this model for which normal mode technique is applied. An exact solution is obtained for the case of two free boundaries and both stationary and oscillatory instabilities have been investigated. It is found that the system destabilizes only through stationary mode. The non-buoyancy magnetization parameter, the dust particle parameter and the permeability of the porous medium are found to destabilize the system. The results are depicted graphically.

  • References

    1. [1] R.E. Rosensweig, Ferrohydrodynamics, Cambridge University Press, Cambridge, (1985).

      [2] S. Odenbach, Recent progress in magnetic fluid research, J. of Physics. Condensed Matter, 16 (32) (2004), R1135-R1150 (1).

      [3] N. Rudraiah, G.N. Shekar, Convection in magnetic fluid with internal heat generation, ASME, Journal of Heat Transfer, 113 (1991) 122-127. http://dx.doi.org/10.1115/1.2910514.

      [4] P.G. Siddheshwar, Rayleigh-Benard convection in a ferromagnetic fluid with second sound, Japan. Soc. Mag. Fluids, 25 (1993) 32-36.

      [5] N. Rudraiah, M.S. Malashetty, The influence of coupled molecular diffusion on double diffusive convection in a porous medium, ASME Journal of Heat Transfer, 108 (1986) 872 – 896. http://dx.doi.org/10.1115/1.3247026.

      [6] N. Rudraiah, P.G. Siddheshwar, A weak non-linear stability analysis of double diffusive convection with cross-diffusion in a fluid saturated porous medium, Heat and Transfer, 33 (1998) 287–293.

      [7] P.A. Lakshmi Narayana, P.V.S.N. Murthy, Rama Subba Reddy Gorla, Soret-driven thermosolutal convection induced by inclined thermal and solutal gradients in a shallow horizontal layer of a porous medium, Journal of Fluid Mechanics, 612 (2008) 1 – 19.

      [8] A. Bahloul, N. Boutana, P. Vasseur, Double diffusive and Soret induced convection in a shallow horizontal porous layer, Journal of Fluid Mechanics, 491 (2003) 325 – 352. http://dx.doi.org/10.1017/S0022112003005524.

      [9] B.A. Finlayson, Convective instability of ferromagnetic fluids, International Journal of Fluid Mechanics, 40 (1970) 753. http://dx.doi.org/10.1017/S0022112070000423.

      [10] G. Vaidyanathan, R. Sekar, R. Balasubramanian, Ferroconvective instability of fluids saturating a porous medium, International Journal of Engineering Sciences, 29 (1991) 1259. http://dx.doi.org/10.1016/0020-7225(91)90029-3.

      [11] R. Sekar, G. Vaidyanathan, A. Ramanathan, Ferroconvection in an anisotropic porous medium, International Journal of Engineering Sciences, 34 (1996) 399 – 405. http://dx.doi.org/10.1016/0020-7225(95)00113-1.

      [12] G. Vaidyanathan, R. Sekar, A. Ramanathan, Ferroconvection in an anisotropic densely packed porous medium, Indian Journal of Chemical Technology, 9 (2002) 446 – 449.

      [13] P.G. Baines, A.E. Gill, on thermohaline convection with linear gradients, Journal of Fluid Mechanics, 37 (1969) 289 – 306. http://dx.doi.org/10.1017/S0022112069000553.

      [14] G. Vaidyanathan, R. Sekar, A. Ramanathan, Ferro thermohaline convection, Journal of Magnetism and Magnetic Materials, 176 (1997) 321 – 330. http://dx.doi.org/10.1016/S0304-8853(97)00468-X.

      [15] G. Vaidyanathan, R. Sekar, A. Ramanathan, Ferro thermohaline convection in a porous medium, Journal of Magnetism and Magnetic Materials, 149 (1995) 137 – 142. http://dx.doi.org/10.1016/0304-8853(95)00356-8.

      [16] G. Vaidyanathan, R. Sekar, R. Hemalatha, R. Vasanthakumari, S. Senthilnathan, Soret-driven ferro thermohaline convection, Journal of Magnetism and Magnetic Materials, 288 (2005) 460 – 469. http://dx.doi.org/10.1016/j.jmmm.2004.09.137.

      [17] R. Sekar, G. Vaidyanathan, R. Hemalatha, S. Senthilnathan, Effect of sparse distribution pores in Soret-driven ferro thermohaline convection, Journal of Magnetism and Magnetic Materials, 302 (2006) 20 – 28. http://dx.doi.org/10.1016/j.jmmm.2005.08.008.

      [18] R. Sekar, D. Murugan, K. Raju, Stability analysis of thermohaline convection in ferrofluid in densely packed porous medium with Soret effect, World Journal of Engineering, 10 (2013) 439-447. http://dx.doi.org/10.1260/1708-5284.10.5.439.

      [19] R. Sekar, K. Raju, R. Vasanthakumari, A linear analytical study on Soret-driven ferrothermohaline convection in an anisotropic porous medium, Journal of Magnetism and Magnetic Materials, 331 (2013) 122–128. http://dx.doi.org/10.1016/j.jmmm.2012.10.028.

      [20] R. Sekar, K. Raju, R. Vasanthakumari, Linear stability analysis of coriolis force on ferrothermohaline convection saturating an anisotropic porous medium with Soret effect, Global Journal of Mathematical Analysis, Vol. 1, No. 2, (2013), 37–47. http://dx.doi.org/10.14419/gjma.v1i2.858.

      [21] R. Sekar, K. Raju, Effect of Soret and temperature dependent viscosity on thermohaline convection in a ferrofluid saturating a porous medium, International Journal of Applied Mechanics and Engineering, Vol. 19, No. 2, (2014) 321 – 336. http://dx.doi.org/10.2478/ijame-2014-0021.

      [22] R. Sekar, K. Raju, Effect of magnetic field dependent viscosity on Soret-driven thermoconvective instability of ferromagnetic fluid in the presence of rotating anisotropic porous medium of sparse particle suspension, International Journal of Mathematical Sciences, Vol.12, (2013), 13–31.

      [23] R. Sekar, K. Raju, Effect of magnetic field dependent viscosity on Soret-driven ferrothermohaline convection saturating an anisotropic porous medium of sparse particle suspension, World Journal of Engineering, Vol. 11, No.3, (2014), pp.213-228. http://dx.doi.org/10.1260/1708-5284.11.3.213.

      [24] R. Sekar, G. Vaidyanathan, R. Hemalatha, Soret driven thermohaline convection in dusty ferrofluids saturating a porous medium, International Journal of Applied Mechanics and Engineering, Vol. 13, No. (4), (2008), pp.1003-1018.

      [25] S. Chandrasekhar, Hydrodynamics and Hydromagnetic stability, Oxford Univ. Press, London, (1961).

      [26] Sunil, Anu Sharma, R.C. Sharma, Effect of dust particles on ferrofluid heated from below. International Journal of Thermal Sciences 45 (2006) 347-358. http://dx.doi.org/10.1016/j.ijthermalsci.2005.06.003.

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    Sekar, R., & Raju, K. (2015). Stability analysis of soret effect on thermohaline convection in dusty ferrofluid saturating a Darcy porous medium. Global Journal of Mathematical Analysis, 3(1), 37-48. https://doi.org/10.14419/gjma.v3i1.3086