Convective heat transfer in Brinkman–Darcy–Kelvin–Voigt fluid with couple stress and generalized Maxwell–Cattaneo law

This article investigates thermal convection in Kelvin–Voigt fluids saturating a Brinkman–Darcy-type porous medium. We examine the linear (stationary and oscillatory), nonlinear, and unconditional nonlinear stability of this fluid under the generalized Maxwell–Cattaneo law with couple stress effects. Using the normal mode technique, we calculate the critical Rayleigh number for the linear stability under stress-free boundary conditions for both stationary and oscillatory convection. Additionally, we employ the energy method to determine the critical Rayleigh number for nonlinear and unconditional nonlinear stabilities under the same boundary conditions. All critical values were determined numerically, and various graphs were plotted to illustrate the results. Our findings reveal that a higher couple stress parameter leads to increased critical Rayleigh numbers for stationary, oscillatory, and nonlinear stability, indicating greater fluid stability and reduced susceptibility to convection. Additionally, the Kelvin–Voigt parameter significantly affects oscillatory convection, though it remains crucial within the nonlinear stability framework. These findings provide a detailed understanding of the stability behavior in this complex fluid system.