Nonlinear stability analysis of thermal convection in a fluid layer with slip flow and general temperature boundary condition.

The current article presents a comprehensive analysis of the influence of inconstant viscosity into thermal convection, incorporating the influence of generalized velocity (slip boundary condition) and temperature boundary conditions (physically represent imperfectly conducting boundary) within a fluid layer. Slip boundary conditions are often considered more practical than no-slip conditions (Neto et al. (2003)). Therefore, in the present work, slip boundary condition is used to discuss the effect of temperature and pressure dependent viscosity. Both linear and nonlinear stability analyses are explored, revealing a noteworthy finding: the precise alignment of the nonlinear stability boundary with the linear instability threshold. Additionally, the exchange of stability is illustrated, indicating that convection exclusively manifests in a stationary mode. The findings are derived across a spectrum of boundary scenarios, ranging from free-free to rigid-free, and rigid-rigid boundaries, encompassing both isothermal and adiabatic conditions. Notably, the slip length parameter exhibits a destabilizing effect, while convection is observed to occur more swiftly under adiabatic boundary conditions compared to isothermal conditions. The Chebyshev pseudo-spectral technique is applied to solve the eigenvalue problems obtained from linear and nonlinear stability analysis. • A system of differential equations models fluid flow between two horizontal plates • The effect of variable viscosity on the onset of convection is displayed graphically. • The principle of exchange of stability is proved. • Linear analysis determines thresholds above which solutions become unstable. • Nonlinear analysis proves the system's total perturbed energy decays exponentially. [ABSTRACT FROM AUTHOR]