This study investigates the onset of thermal convection within a Casson fluid-saturated, inclined porous layer and accounting for the effect of viscous dissipation and along-slope buoyancy induced throughflow. The system consists of two parallel plates with an angle of inclination, ϕ from the horizontal and is analyzed using linear and nonlinear stability characteristics. Darcy law is used to describe the flow. The governing equations, including continuity, momentum, and energy balances, are first non-dimensionalized to introduce key parameters such as the Darcy–Rayleigh number, the Gebhart number, inclination angle, and the Casson fluid index. Linear stability analysis of disturbances is conducted by applying a normal mode technique. To complement the linear analysis, nonlinear stability is examined using the energy method, where an energy functional is constructed to determine thresholds for global nonlinear stability. The boundary eigenvalue problem in the two analyses are solved using the boundary value problem solver bvp4c routine in MATLAB. Comparisons between linear and nonlinear analyses are presented, supported by graphical representations of stability boundaries. The results reveal that longitudinal rolls are the most unstable modes and that inclination has a stabilizing effect, while the non-Newtonian nature of the Casson fluid tends to reduce the stability threshold. Increasing Gebhart number (stronger viscous dissipation) promotes instability, and along-slope buoyancy induced throughflow directionally shifts neutral curves-either amplifying or offsetting dissipation-induced destabilization depending on its direction. These findings provide insights into the complex interplay between fluid rheology, thermal dissipation, and system geometry, contributing to the understanding of thermal convection in porous media filled with non-Newtonian fluids.
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