The impact of variable gravity field on the onset of Casson fluid convective motion in a porous layer

The present investigation is aimed to study the joint influence of variable gravity and Casson parameter on the onset of convection in the presence of porous media. The numerical method is explored using linear stability analysis. Four types of variable gravity field is considered namely linear, parabolic, cubic, and exponential. Using the normal mode technique eigenvalue problem for three different boundary conditions free-free, rigid-free, and rigid-rigid is solved numerically in MATLAB R2024a. The effect of Casson parameter and Darcy number are analyzed for different types of boundary conditions. The critical Rayleigh number (Rac) and wave number (ac) are calculated and shown in the tables for different boundary conditions. The results show that the increasing value of Casson parameter and Darcy number enhanced the onset of convection hence they stabilized the system. The size of convection cells decreases with an increase in variable gravity parameter, on the other hand, due to Darcy number the size of the convection cell increases. It has been also found that for exponential variation system is more stable and for cublic variable gravity it is less stable.