In this paper, linear and nonlinear stability analyses are performed to study Rayleigh-Benard convection in a porous medium saturated with nanofluid under periodic rotation. The revised boundary conditions are used. A Venezian approach is adopted to perform the linear stability analysis, while a truncated Fourier series method is adopted for nonlinear analysis. The critical Rayleigh number is corrected due to periodic rotation, making linear stability analysis. The concentration and thermal Nusselt numbers are obtained by performing a weakly nonlinear stability analysis, and their behavior is investigated by solving the time-dependent finite amplitude equations using the fourth-order Runge-Kutta method. The effect of modulated rotational speed is found to have a stabilizing effect on the system for different values of the modulation frequency.

中文翻译：

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纳米流体饱和多孔介质中周期性旋转对热不稳定性的影响

本文进行了线性和非线性稳定性分析，以研究周期性旋转下在纳米流体饱和的多孔介质中的瑞利-贝纳德对流。使用修改后的边界条件。采用Venezian方法进行线性稳定性分析，而采用截断傅立叶级数方法进行非线性分析。由于周期性旋转，对临界瑞利数进行了校正，从而进行了线性稳定性分析。通过执行弱非线性稳定性分析获得浓度和热Nusselt数，并通过使用四阶Runge-Kutta方法求解时间相关的有限振幅方程来研究其行为。对于不同的调制频率值，发现调制转速的影响对系统具有稳定作用。