INVESTIGATION OF CASSON FLUID’S THERMAL AND HYDRODYNAMICAL LINEAR STABILITY IN AN ANISOTROPIC POROUS MEDIUM

This study investigates the linear stability of Casson fluid convection in an anisotropic porous medium, emphasizing the roles of thermal anisotropy, vertical throughflow, and asymmetric wall heating. The system consists of a horizontal fluid layer confined between a rigid, no-slip wall and a thermally heated wall, separated by a finite distance. The governing equations, incorporating Casson fluid rheology, porous medium anisotropy, and thermal dispersion, are reduced to a coupled set of ordinary differential equations constituting an eigenvalue problem. This eigenvalue problem is solved using spectral method, known for its spectral accuracy and computational efficiency. The analysis reveals that increasing thermal anisotropy and the anisotropy parameter of the porous medium delays the onset of convection, as indicated by higher critical Darcy-Rayleigh numbers. In contrast, the Casson fluid parameter exhibits a destabilizing influence by lowering the critical threshold. Vertical throughflow is found to have a stabilizing effect on the system, with its influence depending on the magnitude and direction of the imposed flow. The critical Rayleigh number rises by 78.26% under porous medium anisotropy and 49.63% under stronger thermal anisotropy at moderately high Darcy numbers, while remaining lower at other conditions, confirming their stabilizing influence on the system. An empirical relation has also been developed for the critical Darcy-Rayleigh number. Moreover, the anisotropy parameter ∈ is found to exhibit the highest sensitivity, showing a variation of 29.718630%, which highlights its dominant influence on the stability behavior of the system. These findings have significant implications for a range of engineering applications involving non-Newtonian fluids in anisotropic porous environments, such as enhanced oil recovery, geothermal reservoir management, and biomedical filtration systems.