Bidispersive Double‐Diffusive Convection in a Porous Layer: Influence of Throughflow and Gravity Variations Using a Darcy–Brinkman Model

ABSTRACT This study presents a comprehensive linear stability analysis of dual‐diffusivity convection in a bidispersive porous medium, embedding a uniform vertical throughflow and variable gravity within the framework of the Darcy–Brinkman model. Three distinct gravity variation profiles—linear, parabolic, and exponential—are systematically examined to understand their impact on convective stability. A high‐order Galerkin approximation is utilized to obtain solutions to the governing eigenvalue problem. The critical Darcy–Rayleigh number is evaluated as a function of key nondimensional parameters, including the Péclet number, gravity modulation parameter, solute Rayleigh number, permeability ratio, Lewis number, Darcy number, and the interphase momentum transfer parameter. Special attention is given to the role of throughflow direction and magnitude, with both upward and downward flows analyzed across varying gravity fields. The results indicate that exponential gravity variation markedly enhances system stability through intensified gravitational stratification, while higher permeability ratios and stronger interphase momentum transfer further stabilize the system by increasing viscous dissipation and drag coupling. A U‐shaped, nonmonotonic variation of the critical Rayleigh number with the throughflow parameter is observed, demonstrating the destabilizing role of moderate throughflows and the stabilizing influence of strong throughflows. Overall, the findings provide key insights into the complex interplay of hydrodynamic and buoyancy‐driven mechanisms in bidispersive porous systems, with implications for thermal management, geophysical flows, and engineered porous structures. The findings provide practical insights for optimizing geothermal reservoirs, chemical reactors, and environmental systems by controlling throughflow, interporosity exchange, and gravity variations to enhance stability and transport efficiency.