Modified Darcy-Brinkmann Two-Component Marangoni Convection: Stability in the Presence of Dufour and Magnetic Effects within a Two-Layer Composite System with Free-Free Boundaries

An analytical investigation is carried out to examine the onset of modified Darcy–Brinkmann two-component Marangoni convection in the presence of Dufour and magnetic effects within a two-layer fluid–porous composite system subjected to free-free boundary conditions. The system consists of a fluid layer overlying a sparsely packed porous layer saturated with the same fluid. The surface tension is assumed to depend on both temperature and concentration variations, while Dufour cross-diffusion and magnetohydrodynamic effects are incorporated into the governing model. Using linear stability theory, an exact analytical expression for the critical thermal Marangoni number is derived. The influences of the Darcy number, magnetic parameter, Dufour parameter, diffusivity ratios, viscosity ratio, and solutal Marangoni number on the onset of convection are examined in detail. The results reveal that magnetic effects, diffusivity ratios, and wave number stabilize the system, whereas Darcy number and solutal Marangoni effects promote instability. Furthermore, the Dufour effect significantly modifies the instability threshold through diffusion–thermal coupling. The present study provides new insight into thermocapillary transport phenomena in composite fluid–porous systems relevant to crystal growth, material processing, geothermal engineering, and energy technologies.

Modified Darcy–Brinkman model, Magneto hydrodynamics, Two-layer composite system, Dufour effect, Double Diffusive Convection, Marangoni Convection.

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