Effect of soret and temperature dependent viscosity on thermohaline convection in a ferrofluid saturating a porous medium

• Autorzy: Sekar R. , Raju K.

Identyfikatory

DOI

10.2478/ijame-2014-0021

• Języki publikacji: EN

Abstrakty

EN

Soret driven ferrothermoconvective instability in multi-component fluids has a wide range of applications in heat and mass transfer. This paper deals with the theoretical investigation of the effect of temperature dependent viscosity on a Soret driven ferrothermohaline convection heated from below and salted from above subjected to a transverse uniform magnetic field in the presence of a porous medium. The Brinkman model is used in the study. It is found that the stationary mode of instability is preferred. For a horizontal fluid layer contained between two free boundaries an exact solution is examined using the normal mode technique for a linear stability analysis. The effect of salinity has been included in magnetization and density of the fluid. The critical thermal magnetic Rayleigh number for the onset of instability is obtained numerically for sufficiently large values of the buoyancy magnetization parameter M1 using the method of numerical Galerkin technique. It is found that magnetization and permeability of the porous medium destabilize the system. The effect of temperature dependent viscosity stabilizes the system on the onset of convection.

Słowa kluczowe

EN

ferroconvection; porous medium; Soret effect; multi-component system; Brinkman model; temperature dependent viscosity; Galerkin technique

PL

porowatość; ciecz wieloskładnikowa; wymiana ciepła i masy

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mechanics and Engineering
• Rocznik: 2014
• Tom: Vol. 19, no. 2
• Strony: 321--336
• Opis fizyczny: Bibliogr. 24 poz., wykr.

Twórcy

autor

Sekar R.

• Department of Mathematics Pondicherry Engineering College Puducherry – 605 014, INDIA

autor

Raju K.

• Department of Mathematics Pondicherry Engineering College Puducherry – 605 014, INDIA

Bibliografia

• [1] Baines P.G. and Gill S.E. (1969): On thermohaline convection with linear gradients. - Journal of Fluid Mechanics, vol.37, pp.289-306.
• [2] Berkovsky B. and Bastovoy V. (1996): Magnetic Fluids and Application Handbook. - New York: Begell House Publishers.
• [3] Chandrasekhar S. (1981): Hydrodynamics and Hydromagnetic Stability. - New York: Dover Publication.
• [4] Finlayson B.A. (1970): Convective instability of ferromagnetic fluids. - International Journal of Fluid Mechanics, vol.40, pp.753-767.
• [5] Gazeau F., Baravian C, Bacri J.C., Perzynski P. and Shiomis M.I. (1997): Physics Reviews - E 56, pp.614.
• [6] Nanjundappa C.E., Shivakumara I.S. and Arunkumar R. (2010): Bénard-Marangoni ferroconvection magnetic field ependent viscosity. - Journal of Magnetism and Magnetic Materials, vol.322, pp.2256-2263.
• [7] Nanjundappa C.E., Shivakumara I.S. and Arunkumar R. (2012): Onset of Marangoni-Bénard ferroconvection with temperature dependent viscosity. - Microgravity Sci. Technol. DOI 10.1007/s 12217-012-9330-9.
• [8] Odenbach S. and Thurm S. (2012): Magnetoviscous Effects in Ferrofluids. - edited by Stefan Odenbach (Springer-Verlag, Berlin, Heidelberg).
• [9] Ramanathan A. and Muchikel N. (2006): Effect of temperature dependent viscosity on ferroconvection in a porous medium. - International Journal of Applied Mechanics and Engineering, vol.11, pp.93-104.
• [10] Rosensweig R.E. (1985): Ferrohydrodynamics. - Cambridge: Cambridge University Press.
• [11] Schwab L., Hildebrandt U. and Stierstadt K. (1983): Magnetic Bénard Convection. - Journal of Magnetism and Magnetic Materials, vol.39, pp.113-114.
• [12] Sekar R., Vaidyanathan G., Hemalatha R. and Senthilnathan S. (2006): Effect of sparse distribution pores in a Soretdriven ferro thermohaline convection. - Journal of Magnetism and Magnetic Materials, vol.302, pp.20-28.
• [13] Sekar R., Raju K. and Vasanthakumari R. (2013): A linear analytical study on Soret-driven ferrothermohaline convection in an anisotropic porous medium. - Journal of Magnetism and Magnetic Materials, vol.331, pp. 122-128.
• [14] Sekar R., Raju K. and Vasanthakumari R. (2013a): Linear stability analysis of Coriolis force on ferrothermohaline convection saturating an anisotropic porous medium with Soret effect. - Global Journal of Mathematical Analysis, vol.1(2), pp.37-47.
• [15] Sekar R. and Raju K. (2013): 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, pp.13-31.
• [16] Shivakumara I.S., Nanjundappa C.E. and Ravisha M. (2010): The onset of buoyancy-driven convection in a ferromagnetic fluid saturated porous medium. - Meccanica, vol.45, pp.213-223.
• [17] Siddheshwar P.G. (2004): Thermorheological effect on magneto convection in weak electrically conducting fluids and 1g or μg. - Pramana J. Phys., vol.62, pp.61-68.
• [18] Stiles P.J. and Kagan M. (1990): Thermoconvective instability of a horizontal layer of ferrofluid in a strong vertical magnetic field. - Journal of Magnetism and Magnetic Materials, vol.85, pp.196-198.
• [19] Sunil, Chand P., Mahajan A. and Sharma P. (2011): Effect of rotation on double-diffusive convection in a magnetized ferrofluid with internal angular momentum. - Journal of Applied Fluid Mechanics, vol.4, pp.43-52.
• [20] Suresh Govindan., Vasanthakumari R. and Radja Sacravarthy P. (2012): Numerical study on the effect of temperature dependent viscosity on ferroconvection in an anisotropic porous medium. - International Journal of Engineering Technology and Advanced Engineering, vol.2, pp.51-55.
• [21] Vaidyanathan G., Sekar R. and Balasubramanian R. (1991): Ferroconvective instability of fluids saturating a porous medium. - International Journal of Engineering Sciences, vol.29, pp.1259-1267.
• [22] Vaidyanathan G., Sekar R. and Ramanathan A. (1995): Ferrothermohaline convection in a porous medium. - Journal of Magnetism and Magnetic Materials, vol.149, pp.137-142.
• [23] Vaidyanathan G., Sekar R. and Ramanathan A. (1997): Ferrothermohaline convection. - Journal of Magnetism and Magnetic Materials, vol.176, pp.321-330.
• [24] Vaidyanathan G., Sekar R., Hemalatha R., Vasanthakumari R. and Senthilnathan S. (2005): Soret-driven ferrothermohaline convection. - Journal of Magnetism and Magnetic Materials, vol.288, pp.460-469.