The onset of double-diffusive convection in an electrically conducting fluid-saturated porous layer is studied. The convective flow in the porous medium is induced by horizontal temperature and concentration gradients with net horizontal mass throughflow. The effect of magnetic field on the instability of convection is taken into consideration. The stability of the steady-state solution is investigated in two different approaches, namely the linear instability analysis and nonlinear stability analysis. The nonlinear stability analysis is performed by constructing the energy functional. The eigenvalue problems which are derived from the stability analyses are numerically integrated using the shooting and Runge–Kutta methods. The variation in the critical thermal Rayleigh number against each flow governing parameter is shown graphically. It is observed that Hartman number Ha2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Ha^{2}$$\end{document} delays the onset of convection to commence and helps to reduce the region of subcritical instabilities. When the solute is concentrated at lower boundary of the porous layer, the onset of convection is in the form of stationary modes, but it switches to oscillatory mode of convection when the solute is concentrated at upper boundary. Interestingly, Hartman number Ha2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Ha^{2}$$\end{document} plays an important role in delaying this transition from stationary mode to oscillatory mode of convection.

中文翻译：

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磁场对水平质量通流多孔层双扩散对流稳定性的影响

研究了导电流体饱和多孔层中双扩散对流的开始。多孔介质中的对流是由水平温度和浓度梯度与净水平质量通流引起的。考虑了磁场对对流不稳定性的影响。稳态解的稳定性通过两种不同的方法进行研究，即线性不稳定分析和非线性稳定性分析。非线性稳定性分析是通过构造能量泛函来进行的。从稳定性分析得出的特征值问题使用射击和龙格-库塔方法进行数值积分。以图形方式显示了临界热瑞利数相对于每个流动控制参数的变化。据观察，哈特曼数 Ha2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Ha^{2}$$\end{document} 延迟对流的开始并有助于减少亚临界不稳定性区域。当溶质集中在多孔层的下边界时，对流的开始以固定模式的形式出现，但当溶质集中在上边界时，它切换到振荡对流模式。有趣的是，