In this numerical examination, the thermal stability of an electrically conducting nanofluid is deliberated comprehensively by considering the presence of an externally applied magnetic field along with an imposed vertical throughflow. Additionally, this thin nanofluidic layer is supposed to have a Newtonian rheological behavior, heated from below, and confined horizontally between two permeable rigid plates of infinite extension. Herein, the governing conservation equations are strengthened realistically by the revised version of the Buongiorno's mathematical model, in which the vertical component of the mass flux of solid nanoparticles is presumed to vanish entirely at the horizontal permeable boundaries. After specifying the basic state of the present nanofluid problem, the linear stability theory and normal mode analysis technique are applied properly to obtain the principal stability equations. Finally, the eigenvalue problem derived analytically is tackled thereafter numerically via the Chebyshev-Gauss-Lobatto Spectral Method (CGLSM), in which the thermal Rayleigh number is chosen as an eigenvalue. As a main result, it was demonstrated that the throughflow effect exhibits a dual behavior on the complex dynamics of the system. However, the excreted magnetic field has always a stabilizing impact on the nanofluidic medium.

在此数值检查中，通过考虑外部施加的磁场以及强加的垂直通流来全面研究导电纳米流体的热稳定性。另外，该薄的纳米流体层应该具有牛顿流变行为，从下方加热，并水平地限制在两个无限延伸的可渗透刚性板之间。在此，Buongiorno数学模型的修订版对控制的守恒方程进行了现实的增强，其中假定固体纳米粒子质量通量的垂直分量在水平渗透边界处完全消失。在指定当前纳米流体问题的基本状态之后，适当应用线性稳定性理论和正态分析技术来获得主稳定性方程。最后，解析得出的特征值问题随后通过Chebyshev-Gauss-Lobatto谱方法（CGLSM）进行数值求解，其中选择热瑞利数作为特征值。作为主要结果，证明了通流效应对系统的复杂动力学表现出双重行为。但是，排出的磁场始终对纳米流体介质具有稳定的影响。结果表明，通流效应对系统的复杂动力学表现出双重行为。但是，排出的磁场始终对纳米流体介质具有稳定的影响。结果表明，通流效应对系统的复杂动力学表现出双重行为。但是，排出的磁场始终对纳米流体介质具有稳定的影响。