A linear analytical study of Soret-driven ferrothermohaline convection in an anisotropic porous medium R. Sekar a,* , K. Raju a , R. Vasanthakumari b a Department of Mathematics, Pondicherry Engineering College, Puducherry 605014, India b Kasthurba College for Women, Villianur, Puducherry 605110, India article info Article history: Received 13 July 2012 Received in revised form 15 October 2012 Available online 7 November 2012 Keywords: Ferroconvection Soret-parameter Anisotropic porous medium Multi-component system Magnetic fluid Linear stability analysis Brinkman model abstract The Soret-driven ferrothermoconvective instability of multi- component fluid in an anisotropic porous medium heated from below and salted from above has been analyzed using Brinkman model for various values of anisotropic parameter. The salinity effect is contained in magnetization and density of the ferrofluid and the system is assumed to have anisotropy in the vertical direction and isotropy in the horizontal direction. A small perturbation imparted on the basic state and a linear stability analysis is used for this model for which the normal mode technique is applied. The present analysis has been carried out through both stationary as well as oscillatory modes. The vertical anisotropy tends to destabilize the system. & 2012 Elsevier B.V. All rights reserved. 1. Introduction Recent interest in the study of electromagnetic field theory has been motivated by its innumerable applications like satellite communication, microwave communication, TV communication, mobile communication and wireless communication. This theory is also used in analysis and designing of antenna, transmission, bio-medical system, lines and wave guides, reducing acidity in vegetables to improve taste, electric motors, weather forecast radars, plasmas, surface hardening, remote sensing radars, lasers, radiation therapy, soldering, dielectric heating, annealing and masers. Ferrofluids are such smart materials that are to be synthesized but not available in free state in nature. Such types of fluids have several applications in mechanical engineering, analytical instrumentation, heat transfer, electronic devices, aero- space, etc. and are widely used in rotating X-ray tubes and sealing of computer hard disk drives. These are used as lubricants in bearing and dumpers. In biomedicine field, there is an idea to use ferrofluids for cancer treatment by heating the tumor soaked in ferrofluids by means of an alternating magnetic field. Ferrofluids are single-magnetic-domain, two-phase three-compo- nent fluids [1], where the core stands for the single domain, core with carrier fluids stands for the two phases, and core with surfactant and carrier fluids stands for three components. In many investigations, porous medium is taken to be isotropic for geological and pedological process but it is rarely isotropic , as is usually assumed in transport studies. Processes such as frost action, sedimentation, compaction and reorientation of solid matrix are responsible for the creation of anisotropic natural porous media. In chemical engineering process, anisotropy can be characteristic of artificial porous like fiber materials. Epherre [2] first attempted to study the onset of convection in a horizontal porous layer with anisotropic thermal conductivity. The Soret-driven ferrothermohaline convection is a double- diffusive convective system. Rudraiah and Malashetty [3] have analyzed the effect of coupled molecular diffusion on double- diffusive convection in a horizontal porous layer by use of finite amplitude method. Later, the study is made for weakly non-linear analysis by Rudraiah and Siddheshwar [4]. Lakshmi Narayana et al. [5] investigated the linear stability analysis of a steady convective double-diffusive flow of Hadley type considering the Soret effect which is set up by the horizontal components of temperature and concentration gradient in a shallow horizontal layer of a fluid saturating a porous medium. Bahloul et al. [6] studied, numerically and analytically, natural convection in a horizontal Darcy porous layer filled by a binary fluid. In both cases double-diffusive and Soret induced convections were used. The critical Rayleigh numbers for the onset of supercritical, overstable and oscillatory convections were determined in terms of the govern- ing parameters. Benano-Melly et al. [7] studied Soret coefficient measurement experiments in a porous medium in the presence of thermal and solutal convective system. They have reproduced the Contents lists available at SciVerse ScienceDirect journal homepage: www.elsevier.com/locate/jmmm Journal of Magnetism and Magnetic Materials 0304-8853/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jmmm.2012.10.028 * Corresponding author. Tel.: þ914132655281; fax: þ914132655101. E-mail address: rsekar@pec.edu (R. Sekar). Journal of Magnetism and Magnetic Materials 331 (2013) 122–128