Effect of MFD Viscosity and Coriolis Force on Soret-Driven Ferrothermohaline Convection in An Anisotropic Darcy Porous Medium with LTNE: Linear Stability Analysis

Effect of MFD Viscosity and Coriolis Force on Soret-Driven Ferrothermohaline Convection in An Anisotropic Darcy Porous Medium with LTNE: Linear Stability Analysis

Anu Sharma¹, Neeti Goel²

¹Department of Mathematics, Rajdhani College, University of Delhi, Raja Garden, Ring Road, New Delhi, 110015, India.

²Department of Mathematics, Acharya Narendra Dev College, University of Delhi,

Govindpuri, Kalka Ji, New Delhi, 110019, India.

ABSTRACT:

In the present work, we have investigated theoretically the effect of magnetic field dependent viscosity and coriolis force on soret driven ferrothermohaline convection in an anisotropic Darcy porous medium with local thermal non-equilibrium (LTNE) model. The effect of anisotropy parameter of permeability of porous medium, soret parameter, Taylor number, MFD viscosity, salinity Rayleigh number, heat transfer coefficient, porosity modified conductivity ratio are examined using linear stability theory and results are shown graphically.

1 INTRODUCTION:

Ferrofluids are stable colloidal suspensions consisting of single-domain magnetic particles coated with surfactant immersed in a carrier fluid. Ferrofluid are of great interest due to application in medicine, sensors, flow control, printing and other fields [Rosenweig (1985)]. Chandrasekhar (1961) studied thermoconvective instability in fluid layer heated from below due to buoyancy force and also investigated the effect of uniform vertical magnetic field on such instability. Finlayson (1970) gave modification of Rayleigh-Benard convection for ferrofluid and later many authors [Lalas and Carmi (1971), Siddheshwar (1995), Vaidyanathan et al. (2002), Sunil and Mahajan (2008)] have studied ferroconvection problems. Hurle and Jakeman (1971) examined thermosolutal convection with soret effect. Stability analysis of soret driven ferrothermohaline convection problems have been studied by Vaidyanathan et al. (2005), Sekar et al. (2006), Hemalatha et al. (2011), Sekar and Raju (2014) and many others.

Increasing importance of ferrofluid flow in porous media because of their extensive utility in environmental science and engineering, several investigations on ferroconvection problems in porous media have been undertaken. In literature majority of the studies on ferro convection in porous medium have been dealt with LTE model. The assumption of LTE is found to be inadequate in many situations [Nield and Bejan (2013)]. In such cases local thermal nonequilibrium (LTNE) effects are to be considered by two field model energy equation representing fluid and solid phases separately. An excellent review of research on local thermal non-equilibrium (LTNE) phenomenon in porous medium convection, primarily free and forced convection boundary layers and free convection within cavities is given by Rees and Pop (2005). Lee et al. (2011) have examined LTNE effects on convection in ferromagnetic fluid layer saturating porous medium in the presence of uniform vertical magnetic field using Darcy model. Shivakumara et al. (2012) have analyzed the effects of magnetic field dependent viscosity and LTNE on ferroconvection in porous medium.

Anisotropy is observed in numerous systems in nature and industry. Vaidyanathan et al. (2002a) studied ferroconvection in an anisotropic densely packed porous medium. Vaidyanathan et al. (2002b, 2002c) investigated the effect of magnetic field dependent viscosity on Ferroconvection in sparsely distributed porous medium with and without rotation. Sunil et al. (2011) performed nonlinear stability analysis of ferroconvection in rotating porous medium using LTNE model. Hemalatha (2014) carried out study of magnetic field dependent viscosity on soret driven ferrothermohaline convection in rotating porous medium. Recently, Sekar and Murugan (2019) performed analytical study of corolis force and MFD viscosity on soret driven ferrothermohaline convection in a darcy anisotropic porous medium. In this paper we study effect of MFD viscosity and Coriolis force on linear instability in soret-driven ferroconvection saturating anisotropic porous medium with LTNE model. This problem to the best of our knowledge has not been investigated so far.

2 Governing Equations

We consider an infinite incompressible ferrofluid saturated an anisotropic porous layer of thickness ‘ ’ rotating with uniform constant angular velocity  , heated from below and salted from above in the presence of uniform vertical magnetic field (Figure 1). The boundaries of the layer are taken to be free and soret effect is considered. Also, the solid and fluid phases of porous medium are not in local thermodynamic equilibrium.