The Onset of Soret-Driven Ferrothermohaline Convection in An Anisotropic Darcy Porous Medium Using a Local Thermal Nonequilibrium Model: Effect of MFD Viscosity

The Onset of Soret-Driven Ferrothermohaline Convection in An Anisotropic Darcy Porous Medium Using a Local Thermal Nonequilibrium Model: Effect of MFD Viscosity

Poonam Sharma

Department of Mathematics, NSCBM Government College, Hamirpur, 177005, Himachal Pradesh, India.

ABSTRACT:

In this paper the effect of magnetic field dependent viscosity on soret-driven Ferrothermohaline convection in an anisotropic Darcy porous medium using a local thermal non-equilibrium model is investigated theoretically. Linear stability analysis is carried out for ferrofluid layer contained between two stress-free boundaries using normal mode method. The effect of various parameters such as MFD viscosity, non-buoyancy magnetization, anisotropy of permeability of porous medium, soret parameter, heat transfer coefficientis studied and results are depicted graphically.

1 INTRODUCTION:

Ferrofluids are special class of nanofluids exhibiting normal fluid properties with magnetic behaviour which enables their wide applications in science and detailed discussion is found in the book by Rosenweig (1985). Thermal convection in ferrofluids known as ferroconvection sets in due to variation of magnetization which depends onthe magnetic field, the temperature and the density of fluid. Finlayson (1970) gave modification of Rayleigh-Benard convection for ferrofluid and later on extensive study is done on ferroconvection problems. 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.

Researchers have attracted to investigate ferroconvection in porous media because of their extensive utility in environmental science and engineering. In literature most of the studies on ferro convection in porous medium considered LTE model and LTNE effects on the onset of ferro convection have been ignored inspite of their importance in many heat related problems. The book by Nield and Bejan (2013) discussed extensively the LTNE effects on free and forced convection flows in porous media. Banu and Rees (2002) studied convection in Darcy porous medium using LTNE model. 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). A nonlinear stability analysis of double-diffusive ferroconvection in porous medium using LTNE model has been studied by Sunil et al. (2010).

Anisotropy arises due to asymmetry geometry of porous matrix. Vaidyanathan et al. (2002) studied ferroconvection in an anisotropic densely packed porous medium. Shivakumara et al. (2012) have analyzed the effects of magnetic field dependent viscosity and LTNE on ferroconvection in porous medium.Hemalatha and Sivapraba (2012) analyzed effect of magnetic field dependent viscosity on ferroconvection in an anisotropic porous medium. Ravisha et al. (2017) analyzed effect of LTNE and anisotropy on thermomagnetic convection in porous medium. More recently, Murugan and Sekar (2021) investigated anisotropy and magnetic field dependent viscosity effects on soret driven ferrothermohaline convection saturating Darcy porous medium. In this work, we study effect of magnetic field dependent viscosity soret-drivenferroconvectionin an anisotropic porous medium withlocal thermal non-equilibrium. This problem to the best of our knowledge so far has not been investigated yet.

2. Mathematical Model:

Here we consider an infinite incompressible ferromagnetic fluid saturated an anisotropic porous layer of thickness ‘ ’ heated from below and salted from above in the presence of uniform vertical magnetic field (Figure 1). The viscosity of the fluid is assumed to be magnetic field dependent given by , where  is viscosity of fluid in the absence of magnetic field.