FEEDBACK CONTROL OF CHAOTIC MOTION IN AN ANISOTROPIC POROUS MEDIUM UNDER MAGNETIC EFFECT

Abstract

The main purpose of this work is to provide an innovative approach for studying the chaos control of the viscoelastic fluid-saturated anisotropic porous layer under the magnetic effect and feedback control modulation. The governing flow model partial differential equations (PDEs) are transformed into ordinary differential equations (ODEs) using a powerful tool of Fourier modes and a nonlinear low-dimensional Brinkman model employed by using the truncated Galerkin method. Their results reveal the feedback gain parameter, Hartmann number, Darcy number, and the mechanical and thermal anisotropy parameters on the stabilization of thermal convection to suppress the chaos. Additionally, many real-world applications conforming to system stabilization of thermal convection are important in nuclear power energy, including turbo machinery, cooling chemical components, and electronic cooling processes. The emergence of various nonlinear flows of steady-state, periodic, and oscillatory to chaotic convection is demonstrated with the change of feedback control parameters. Also, we found that the feedback control gains parameter K value is directly proportional to the scaled Rayleigh number with the external effects on the magnetic field and anisotropic parameters. Our findings were found to be in good agreement with previous numerical results. Finally, the paper proposes the implications of using feedback control combined with magnetic effect to effectively control the chaotic system.