Linear and nonlinear stability analysis of generalized nanofluid convection in a porous medium with inclination effects

This paper presents a linear and nonlinear stability analysis of generalized nanofluid convection in a porous medium, considering the effects of an inclination angle β. The governing equations are derived, nondimensionalized, linearized, and discretized using finite difference methods and solved via a generalized eigenvalue solver. A generalized eigenvalue problem is formulated to determine the critical Rayleigh number Rac, and nonlinear stability is assessed using the energy method. The results show that increasing the inclination angle β significantly enhances system stability by raising the critical thresholds. Additionally, the nonlinear stability limits are consistently higher than the linear ones, indicating a more conservative stability criterion. The influence of the Lewis number Le and inclination angle β on the onset of convection is examined in detail, providing insights relevant to thermal management in energy systems and porous structures.