Numerical analysis of the onset of longitudinal convective rolls in a porous medium saturated by an electrically conducting nanofluid in the presence of an external magnetic field

The effect of a uniform external magnetic field on the onset of convection in an electrically conducting nanofluid layer is examined numerically based on non-homogeneous two-phase model (i.e., classical Buongiorno's mathematical model) which incorporates the effects of Brownian motion and thermophoresis of nanoparticles in the thermal transport mechanism of nanofluids. In this investigation, we consider that the nanofluid is Newtonian, heated from below and confined horizontally in a Darcy-Brinkman porous medium between two infinite rigid boundaries, with different nanoparticle configurations at the horizontal boundaries (i.e., top heavy and bottom heavy nanoparticle distributions). The linear stability theory has been wisely used to obtain a set of linear differential equations which are transformed to an eigenvalue problem, so that the thermal Rayleigh number R-a is the corresponding eigenvalue. The thermal Rayleigh number Ra and its corresponding wave number a are found numerically using the Chebyshev-Gauss-Lobatto collocation method for each set of fixed nanofluid parameters. The marginal instability threshold (R-ac, a(c)) characterizing the onset of stationary convection is computed accurately for wide ranges of the modified magnetic Chandrasekhar number Q, the modified specific heat increment NB, the nanoparticle Rayleigh number RN, the modified Lewis number Le, the modified diffusivity ratio N-A\ and the Darcy number D-a. Based on these control parameters and the notions of streamlines, isotherms and iso-nanoconcentrations, the stability characteristics of the system and the development of complex dynamics at the critical state are discussed in detail for both nanoparticle distributions. (C) 2017 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license.