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An analytical study is conducted to examine the influence of thermal gradients and heat sources on the onset of two-component Rayleigh–Bènard (TCRB) convection using the Darcy model. The study takes into account the effects of local thermal non-equilibrium (LTNE), thermal profiles, and heat sources. The composite structure is horizontally constrained by adiabatic stiff boundaries, and the resulting solution to the problem is obtained using the perturbation approach. The various physical parameters have been thoroughly examined, revealing that the fluid layer exhibits dominance in the two-layer configuration. It has been observed that the parabolic profile demonstrates greater stability in comparison to the step function. Conversely, in the setup where the porous layer dominates, the step function plays a crucial role in maintaining stability. The porous layer, model (iv), exhibits greater stability in the predominant combined structure, while the linear configuration is characterized by higher instability. [ABSTRACT FROM AUTHOR]

The influence of the throughflow and gravity fluctuation on thermosolutal convection in an anisotropic porous bed with the Darcy–Brinkman effect is considered numerically. The critical Rayleigh numbers for the onset of stationary and oscillatory modes have been found via linear instability analysis. The impact of various gravitational functions in the presence of throughflow on stability is studied. The analysis has been carried out for decreasing and increasing gravity fluctuations. The convective problem has been numerically analyzed using a single-term Galerkin approach. The results show that the mechanical anisotropy parameter and Lewis number have a destabilizing effect, while the thermal anisotropy parameter, Darcy number, solutal Rayleigh number, throughflow parameter, and gravity parameter have a stabilizing effect on stationary and oscillatory convection. It is clear that the system changes in a way that makes it more stable for case (iii) gravity fluctuation and more unstable for case (iv) gravity fluctuation. [ABSTRACT FROM AUTHOR]