Stability Characteristics of Non-Darcy Three-Component Marangoni Convection with Combined Dufour and Magnetic Effects in a Two-Layer Composite System

Abstract

The stability characteristics of non-Darcy three-component Marangoni convection with combined Dufour and magnetic effects in a two-layer composite system are investigated analytically using a modified Darcy–Brinkman formulation. The system consists of an upper electrically conducting fluid layer overlying a porous layer saturated with the same fluid. The upper boundary is free and deformable, with surface tension depending on temperature and the concentrations of two solute species, while the lower boundary is rigid. The basic state is quiescent, and the Boussinesq approximation is employed. The governing momentum, energy, species-transport, and magnetic-induction equations are linearized about the basic state and reduced, by normal-mode analysis, to a coupled ordinary differential eigenvalue problem. The Dufour effect is incorporated in the energy equations to represent diffusion–thermal coupling, while magnetic damping is represented through the Chandrasekhar parameters of the fluid and porous layers. Continuity of normal velocity, stress, temperature, concentration, heat flux, and mass flux is imposed at the fluid–porous interface, together with the appropriate free-surface Marangoni conditions. An exact solution procedure is used to obtain the velocity, temperature, and concentration disturbance fields, and the thermal Marangoni number is determined from the remaining coupled surface condition. The effects of wave number, Darcy number, Dufour parameter, diffusivity ratios, solutal Marangoni numbers, and magnetic parameters are examined. The results show that magnetic fields generally stabilize the system, whereas increased permeability and stronger solutal Marangoni driving can promote instability. The Dufour effect modifies the stability threshold through thermal–solutal cross-diffusion, and the two solutal components introduce additional competing transport mechanisms that are absent in double-diffusive models. The present formulation provides a unified framework for assessing the combined influence of non-Darcy resistance, triple diffusion, thermocapillarity, cross-diffusion, and magnetic damping in layered composite systems.