Combined Impact of Temperature-Dependent Heat Source and Gravity Fluctuation on the Onset of Darcy-Brinkman Reaction-Convection in an Anisotropic Porous Layer

This paper investigates the combined influence of temperature-dependent heat sources and gravitational fluctuations on the onset of double-diffusive reaction-convection in an anisotropic porous medium. The momentum equation is modelled using the Darcy-Brinkman approach, and linear stability analysis is conducted using normal mode analysis to formulate the eigenvalue problem. Four gravity functions linear, parabolic, cubic and exponential are analysed and the critical Rayleigh numbers for stationary and oscillatory modes are derived using a single-term Galerkin approximation. The results reveal that temperature-dependent heat sources, gravity variations, anisotropy and the Damkohler number significantly affect convection instability thresholds. Notably, exponential gravity fluctuations provide the highest system stability, delaying the onset of convection. These findings offer valuable insights into the stability behaviour of anisotropic porous systems, with applications in optimising geothermal energy systems, industrial heat management, porous media-based chemical reactors, groundwater filtration, subsurface energy storage and thermal insulation systems. Major Findings: The findings revealed that temperature-dependent heat sources and exponential gravity fluctuations delay convection onset, enhancing system stability. Linear, parabolic, and cubic gravity variations promote instability, reducing stability thresholds. Anisotropy amplifies system sensitivity to governing parameters, while the Damkohler number significantly influences instability. Exponential gravity fluctuations emerge as the most stabilizing factor.