Numerical investigation of the effect of magnetic field on the onset of nanofluid convection

The present analysis aims at investigating the effect of a uniform vertical magnetic field on the onset of convection in an electrically conducting nanofluid layer with a new set of physical boundary condition. It is assumed that the value of the temperature can be imposed on the boundaries, but the nanoparticle fraction adjusts together with effects of Brownian and thermophoresis so that the nanoparticle flux is zero on the boundaries. Using the Galerkin method, the critical Rayleigh number on the onset of convection and the corresponding wave number are obtained in terms of various parameters numerically. The numerical computations are presented for water-based nanofluids with Al₂O₃ and Cu nanoparticles. It is found that the volumetric fraction of nanoparticle, the Lewis number, the modified diffusivity and the density ratios have a destabilizing effect, while the magnetic field has stabilizing effect on the system. The zero flux nanoparticle boundary condition has more destabilizing effect than the constant nanoparticle boundary conditions for Al₂O₃-water nanofluid, while reverse for Cu-water nanofluid.