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This study investigates the influence of rotation and couple stresses on the convective stability of the Navier–Stokes–Voigt fluid under various boundary conditions, employing both nonlinear (via the energy method) and linear (using the normal mode analysis method) approaches. The eigenvalue problem is derived for both analyses and solved using the Galerkin method to obtain the Rayleigh number. It has been observed that the critical Rayleigh number is identical for both analyses, confirming global stability and the absence of subcritical instabilities. Notably, we find that increasing the couple stress parameter significantly narrows the spectrum of wave numbers for oscillatory modes. Conversely, higher Taylor numbers and Kelvin–Voigt parameters expand the wave number spectrum for oscillatory convection. While couple stresses and rotational effects provide stabilizing influences, the Kelvin–Voigt parameter acts as a destabilizing factor for oscillatory convection. These findings offer valuable insights with potential applications in improving fluid stability and thermal management across a wide array of industries, including industrial cooling systems, aerospace engineering, biomedical devices, energy systems, and environmental engineering.