Rayleigh-Bénard Convection of Nanofluids with Magnetic Field and Permeability Effects

Abstract

Effect of vertical magnetic field on thermal convection of a porous nanofluid layer is considered using Darcy's law. System of nanofluid layer in which nanoparticle concentration on the top is higher than that at the bottom is considered. Normal mode technique and single term Galerkin method is employed to investigate the stability and derive the eigen value problem. Brownian motion and thermophoretic forces are introduced due to the presence of nanoparticles. The mode of instability is invariably through stationary convection. The oscillatory instability may be possible when nanoparticles concentrate near the bottom of the layer, so that two buoyancy forces act in opposite directions. The value of the critical Rayleigh number is decreased by a substantial amount due to the presence of nanoparticles. The critical Rayleigh numbers and the critical wave numbers for alumina-water nanofluid and copper-water nanofluid for different values of Chandrasekhar number and porosityare found. Alumina-water nanofluid is found to exhibit higher stability as compared to copper-water nanofluid in the presence/absence of magnetic field and/or porous medium. Effect of nanoparticle volume fraction and temperature difference on stability of the system is investigated taking permissible values of various parameters. Magnetic field, Brownian to thermal diffusivity ratio and temperature difference is found to stabilize the nanofluid layer, appreciably, whereas the effect of volume fraction of nanoparticles, density ratio and porosity is to destabilize the layer.