The impact of feedback mechanisms on Rayleigh-Bénard penetrative convection in micro-polar fluids

This study examines the effects of feedback control and internal heat sources on the onset criterion of Rayleigh-B & eacute;nard convection (RBC) in a horizontal Boussinesq micropolar fluid layer. A linear stability analysis, employing the Chebyshev pseudospectral method, is conducted to compute the eigenvalues and assess the stability of the system under varying conditions. The analysis considers several parameters, including heat conduction, coupling, couple stress, scalar controller gain, and internal heat sources. The findings reveal that the introduction of internal heat sources destabilizes the system, while the scalar controller gain significantly delays the onset of convection, thereby enhancing system stability. Additionally, it is demonstrated that an increase in both the coupling and heat conduction parameters contributes positively to system stabilization, whereas an increase in the couple stress parameter hastens the onset of convection. Notably, the investigation indicates that the system demonstrates greater stability when the boundary is heated from above as opposed to from below. These results provide crucial insights for the control of heat transfer in micropolar fluids and suggest that optimizing the scalar controller gain, along with careful tuning of other system parameters, can significantly enhance stability. The implications of this research are substantial for the design of efficient fluid dynamical systems, particularly in scenarios requiring precise control over temperature, pressure, and flow, such as those encountered in chemical processing, power generation, and manufacturing.