LAUSR

The significance of an externally applied magnetic field and an imposed negative temperature gradient on the onset of natural convection in a thin horizontal layer of alumina-water nanofluid for various sizes of spherical alumina nanoparticles (e.g., 30nm, 35nm, 40nm, 45nm) and volumetric fractions (e.g., 0.01, 0.02, 0.03, 0.04) is explored and analyzed numerically in this paper. The generalized Buongiorno's mathematical model with the simplified Maxwell's equations and the Oberbeck-Boussinesq approximation were adopted to simulate the two-phase transport phenomena, in which the Brownian motion and thermophoresis aspects are taken into account. Moreover, the rheological behavior of alumina-water nanofluid and related flow are assumed to be Newtonian, incompressible and laminar. Based on the linear stability theory, the perturbed partial differential equations (PDEs) of magnetohydrodynamic convective nanofluid flow are firstly simplified formally using the normal mode analysis technique and secondly converted to a generalized eigenvalue problem considering more realistic boundary conditions, in which the thermal Rayleigh number is the associated eigenvalue. Additionally, the resulting eigenvalue problem was solved numerically using powerful collocation methods, like Chebyshev-Gauss-Lobatto Spectral Method (CGLSM) and Generalized Differential Quadrature Method (GDQM). Furthermore, the thermo-magneto-hydrodynamic stability of the nanofluidic system and the critical size of convection cells are highlighted graphically in terms of the critical thermal Rayleigh and wave numbers, for various values of the magnetic Chandrasekhar number, the volumetric fraction and the diameter of alumina nanoparticles.