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.

中文翻译：

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具有金属/金属氧化物纳米材料的水基纳米流体的高级 MHD 稳定性问题的广义微分正交审查：具有对流加热和通流边界条件的修正两相纳米流体模型的适当应用

本数值研究旨在揭示在强对流加热和在渗透边界处均匀垂直施加的通流过程的综合影响下，牛顿纳米流体在水平平面配置中可能发生的磁对流现象的最佳特性. 在这方面，基于修正的 Buongiorno 数学公式、Corcione 经验相关性和其他已知的现象学定律，正确建立了一个现实的非均匀 MHD 对流纳米流体流动模型，用于检查水基纳米流体输送的热磁流体动力学稳定性。相同球形尺寸的微小金属/金属氧化物颗粒，如铜Cu、氧化铜CuO、铝Al和氧化铝Al ₂ O ₃，通过利用零纳米粒子质量通量的假设，其体积分数在可渗透边界处被被动控制。采用线性稳定性理论（LST）和正态模态分析技术（NMAT），从无量纲形式的偏微分方程（PDE），经过多次数学重排，依次推导出无量纲稳态稳定性方程，探索起始判据。的静止对流模式。通过选择热瑞利数作为特征值，这些线性微分方程变成了广义特征值问题。通过利用广义微分求积法（GDQM），当前的稳定性问题被适当地离散化，以确定其特征值谱，用于所涉及的物理参数的各种值。在主要结果中，有证据表明抽吸和注入效应对系统演化表现出不同的行为，其中其热磁流体动力学特征相对取决于纳米流体的化学成分和电学性质。边界。此外，磁性洛伦兹力以及纳米材料负载始终显示出稳定的影响。同时，纳米颗粒的直径尺寸和热比奥数对纳米流体介质产生不稳定的趋势。其中其热磁流体动力学特征相对取决于纳米流体的化学成分和边界的电学性质。此外，磁性洛伦兹力以及纳米材料负载始终显示出稳定的影响。同时，纳米颗粒的直径尺寸和热比奥数对纳米流体介质产生不稳定的趋势。其中其热磁流体动力学特征相对取决于纳米流体的化学成分和边界的电学性质。此外，磁性洛伦兹力以及纳米材料负载始终显示出稳定的影响。同时，纳米颗粒的直径尺寸和热比奥数对纳米流体介质产生不稳定的趋势。