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

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 the rmophoresis 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.