Nonlinear system stabilization in an anisotropic porous medium with Oldroyd-B fluid based on an actuator and sensor array

Abstract

In this research, the authors precisely focus on the analysis of the chaotic behavior in an Oldroyd-B fluid saturated anisotropic porous medium via a feedback control technique. A four-dimensional (4D) weakly nonlinear system emerging from a Galerkin method of the constitutive and preservation equations is developed to accord with a convective stabilization with various Darcy numbers (Da) and feedback control gain value [Formula: see text]. The chaotic dynamic convection is governed by the Darcy–Rayleigh number ([Formula: see text]) and feedback control, while the Da has a significant impact on system stabilization. Their results reveal the effects of the feedback gain parameter [Formula: see text], stress relaxation parameter ([Formula: see text]), strain retardation parameter ([Formula: see text]), Darcy number (Da), mechanical ([Formula: see text]) and thermal ([Formula: see text]) anisotropy parameter on the stability and destabilization of thermal convection. Stabilization of thermal convection are important in cooling, nuclear power, and a range of technical, biological and engineering processes. In particular, feedback control gain values are discovered to be the preferred mode for the controlled onset of oscillatory convection. Finally, a graphical representation is presented to demonstrate that the feedback control approach is more effective in regulating the entire system when aperiodic external disturbances occur.