Convection in porous medium using Darcy-Brinkman model with chemical reaction and higher concentration gradient effects

This study presents a comprehensive stability analysis of solutal convection in a horizontal porous layer saturated with an incompressible fluid. The governing framework combines Darcy-Brinkman momentum transport with a reaction-diffusion equation enhanced by both Laplacian and bi-Laplacian operators. Two complementary numerical algorithms, one for linear instability and the other for nonlinear energy stability, are formulated. These algorithms use the Moore-Penrose pseudoinverse, golden section search, and eigenvalue tracking techniques to determine critical solutal Rayleigh thresholds. To ensure high accuracy and computational efficiency of the Chebyshev collocation method, a residual evaluation routine is developed. A parametric analysis of the essential dimensionless groups is conducted under free-free and rigid-rigid boundary conditions. The findings indicate that higher reaction rate, stronger Brinkman drag, and enhanced hyper-diffusion each stabilize the conductive state by raising the critical Rayleigh thresholds, whereas increased solutal stratification destabilizes it by lowering the onset criteria and promoting earlier convection. The comparison of boundary scenarios indicates that rigid walls impose significantly greater stability limits than stress-free interfaces. The proposed algorithms provide a comprehensive framework for instability and stability analysis in reactive porous media flows and establish a foundation for future developments in hydrodynamic stability analysis and transient dynamics.