Convection in a magnetic nanofluid saturating a porous medium under the influence of a variable gravity field

This paper presents a numerical investigation of the onset of instability in a thin magnetic nanofluid (or ferrofluid) layer saturating a porous medium, subject to a gravity field which varies with distance across the layer. A model that accounts for the effect of Brownian diffusion, thermophoresis, magnetophoresis and Darcy's law is considered. We employed the Chebyshev pseudospectral method and QZ algorithm to obtain the numerical solutions. The impact of important parameters, which affect the instability of the system has been analyzed at the onset of convection for water-based and ester-based magnetic nanofluids. The results indicate that increase in the width of magnetic nanofluid layer (d), Langevin parameter (αL), gravity coefficient (δ), permeability parameter (K); and decrease in the Lewis number (Le), concentration Rayleigh number (Rn), modified diffusivity ratio (NA), nonlinearity of fluid magnetization (M3) is to delay the onset of convection.