Generalized differential quadrature scrutinization of an advanced MHD stability problem concerned water-based nanofluids with metal/metal oxide nanomaterials: A proper application of the revised two-phase nanofluid model with convective heating and through-flow boundary conditions

The present numerical investigation aimed to disclose the optimum characteristics of the magneto-convection phenomenon that can be happened for Newtonian nanofluids in a horizontal planar configuration under the combined influence of an imposed convective heating and a uniform vertically applied through-flow process at the permeable boundaries. In this regards, a realistic non-homogeneous MHD convective nanofluid flow model has been established properly based on the revised Buongiorno's mathematical formulation, Corcione's empirical correlations, and other known phenomenological laws for examining the therm-magneto-hydrodynamic stability of water-based nanofluids conveying tiny metal/metal oxide particles of same spherical size, like copper Cu, copper oxide CuO, aluminum Al, and alumina Al2O3, whose volume fraction was controlled passively at the permeable boundaries by exploiting the assumption of zero nanoparticles mass flux. By adopting the linear stability theory (LST) and normal mode analysis technique (NMAT), the dimensionless stationary stability equations were derived successively from the dimensionless form of the governing partial differential equations (PDEs) after several mathematical rearrangements to explore the criterion for the onset of the stationary convective mode. These linear differential equations were altered into a generalized eigenvalue problem by selecting the thermal Rayleigh number as an eigenvalue. By utilizing the generalized differential quadrature method (GDQM), the present stability problem was discretized appropriately to determine its eigenvalue spectrum for sundry values of the involved physical parameters. Among the main outcomes, it was evidenced that the suction and injection effects exhibit a dissimilar behavior on the evolution of the system, in which its thermo-magneto-hydrodynamic feature depends relatively on both the chemical constituents of the nanofluid and the electrical properties of the boundaries. Further, the magnetic Lorentz forces along with the nanomaterials loading show always a stabilizing impact. Whilst, the diameter size of nanoparticles and the thermal Biot number exert a destabilizing trend on the nanofluidic medium.