Hall Effect on Thermal Convection of a Nanofluid Layer Saturating a Porous Medium

Urvashi Gupta¹, Jyoti Ahuja²

¹Dr. S. S. Bhatnagar University Institute of Chemical Engineering and Technology, Panjab University, Chandigarh-160014, India

²Energy Research Centre, Panjab University, Chandigarh-160014, India

*Corresponding Author E-mail: dr_urvashi_gupta@yahoo.com; jyotiahuja1985@gmail.com

ABSTRACT:

The present paper investigates the stability analysis of an electrically conducting horizontal layer of nanofluid in the presence of Hall currents saturating a porous medium for bottom heavy distribution of nanoparticles. Hall currents are the effects whereby a conductor carrying an electric current perpendicular to an applied magnetic field develops a voltage gradient which is transverse to both the current and the magnetic field. The nanofluid layer incorporates the effect of Brownian motion and thermophoresis while Darcy’s law is used for the porous medium. The analysis is carried out in the framework of linear stability theory, normal mode technique and Galerkin type weighted residuals method. The present formulation of the problem leads to oscillatory mode of instability whereas for top heavy arrangement of nanoparticles the instability is invariably through stationary convection. The reason for the oscillatory mode of convection is the competition between the density gradient caused by bottom heavy nanoparticle distribution with the density variation caused by heating from the bottom. Further, it is found that the effect of magnetic field is to postpone the onset of instability while that of Hall currents and porosity is to hasten the onset of thermal convection.

KEYWORDS: Thermal convection; Nanofluid layer; Brownian motion; Darcy Law; Hall currents; Thermophoresis

1. INTRODUCTION

Nanofluids are colloidal suspensions of nanoparticles with typical dimensions of about 1-100 nm dispersed in a non conducting carrier liquids like water, kerosene, ester and hydrocarbons etc. Choi [1] was the first to suggest that such colloidal suspensions could be used as a heat transfer medium due to high thermal conductivity. Nanofluids are not naturally occurring but they are synthesized in the laboratory. The choice of base fluid particle combination depends on the application for which the nanofluid is intended. In the presence of a mere few percents of nanoparticles, a significant increase of the effective thermal conductivity has been observed by Masuda et al. [2] and Das et al. [3]. A comprehensive study of convective transport in nanofluids was made by Buongiorno [4], who proposed a new model incorporating the effects of Brownian diffusion and thermophoresis. Buongiorno’s model was applied to the problem of onset of instability in a layer of fluid heated from below by Tzou [5, 6] and Nield and Kuznetsov [7, 8]. Thermal instability of a nanofluid layer in the presence of rotation has been studied by Bhadauria and Agarwal [9], Yadav et al. [10] and Chand and Rana [11].

Investigation on the effects of magnetic field (Hall currents) for the onset of convection for regular fluid has been started several decades ago. A detailed account of the thermal instability of a Newtonian fluid, under varying assumptions of hydrodynamics and hydromagnetics has been given by Chandrasekhar [12]. Bhatia and Steiner [13], Sharma and Gupta [14] and Siddheshwar and Pranesh [15] may be considered a few among several other researchers to work on these fluids. In the past few years, nanofluids have opened a new dimension in heat transfer processes. The problem of thermal convection in a porous medium is of paramount interest because of its application in several applied fields such as geothermal reservoirs, agricultural product storage, enhanced oil recovery and the pollutant transport in underground. Thermal instability in porous medium has been studied by many authors including Horton and Rogers [16], Lapwood [17] and MacDonald [18] among others. Heris et al. [19] investigated the effect of magnetic field and nanofluid on thermal performance of two phase closed thermosyphon and Gupta et al. [20] studied the effect of magnetic field on the thermal instability of a nanofluid layer. In the present paper Hall effect on the onset of convection in a nanofluid layer saturated by a porous medium with free –free boundaries is investigated using Darcy’s law. In the present model we have employed normal mode technique and weighted residuals method to obtain the stability analysis.

7. CONCLUSIONS:

Thermal instability of a horizontal layer of nanofluid is investigated in the presence of Hall currents, employing a model that incorporates the effect of Brownian motion and thermophoresis for the case of two free boundaries. Normal mode technique and Galerkin type weighted residual method have been used to obtain an eigen value equation. The mode of instability is found to be oscillatory since. The reason for the oscillatory mode of convection in bottom heavy configuration is the competition between the density gradient caused by bottom heavy nanoparticle distribution with the density variation caused by heating from the bottom. Magnetic field stabilizes the nanofluid layer appreciably while the Hall currents and porosity destabilize the same. Further, concentration Rayleigh number has stabilizing effect for both the convections whereas Lewis number has stabilizing effect for stationary convection and destabilizing effect for oscillatory convection in the presence of Hall currents.

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Received on 02.01.2014 Accepted on 30.01.2014

Int. J. Tech. 4(1): Jan.-June. 2014; Page 214-219