Free convective onset in a bottom heated porous medium under the influence of transverse magnetic field is studied within the framework of nonlinear theory. Simple harmonic time modulation is imposed on either the bounding surface temperature or the gravitational field acting on the medium. The Darcy–Lapwood–Brinkman model of flow through porous media is employed with two basic types of physical boundary conditions. The generalized energy approach coupled with the variational principles is followed. Higher order Galerkin method is then used to determine the unconditional and sharp stability limits for arbitrary values of modulational parameters. The increase in the Hartmann number is found to inhibit instability, thereby delaying the onset of two dimensional rolls. Moreover the initiation of instability mechanism can be well adjusted through a good knowledge of the parameters involved.

在非线性理论的框架内研究了在横向磁场影响下底部加热多孔介质中的自由对流开始。简谐时间调制施加在边界表面温度或作用在介质上的引力场上。Darcy-Lapwood-Brinkman 多孔介质流动模型采用两种基本类型的物理边界条件。遵循与变分原理相结合的广义能量方法。然后使用高阶 Galerkin 方法来确定任意调制参数值的无条件和尖锐的稳定性极限。哈特曼数的增加被发现抑制了不稳定性，从而延迟了二维滚动的开始。