Two - component / Double Diffusive Marangoni (DDM) convection with Dufour effects, in a two-layered system, has been studied analytically by using Darcy – Brinkmann Model. For fluid layer, the upper boundary is free with surface tension depending on both temperature and concentration, for porous layer the lower boundary is rigid and both the boundaries are insulating to both heat and mass. At the interface, the normal velocity, normal stress, shear stress, mass, mass flux, heat, heat flux is assumed to be continuous. The effect of different physical parameters on DDM convection is investigated in detail and results are presented graphically. The effect of Dufour parameter, which plays vital role in diffusion-thermal process, when the energy flux due to mass gradient appears, on DDM convection in a two- layer system, has been explored.

The impact of non-uniform temperature gradients on Rayleigh-Darcy convection in a composite system of couple stress fluid is discussed. The composite system is bounded by stress-free surfaces and adiabatically insulated, and the fluid-porous layers are coupled by employing appropriate interfacial boundary conditions. To determine the eigen value, the regular perturbation method is used. The effect of dimensionless parameters on Rayleigh-Darcy convection is analysed graphically, and it is demonstrated that the couple stress parameter and couple stress viscosity ratio stabilise the system, while the opposite effect is observed for the Darcy number and thermal diffusivity ratio.

The influence of linear, parabolic and inverted parabolic temperature gradients on the onset of double-diffusive Rayleigh-Darcy convection is theoretically investigated. The composite system is constrained horizontally by adiabatic and free-free thermal boundaries, and appropriate interfacial boundary conditions are used to connect fluid-porous layers. The regular perturbation approach is used to determine the critical Rayleigh number expression for different temperature gradients. Graphs are used to investigate the significance of a variety of dimensionless characteristics. The couple stress parameter, couple stress viscosity ratio, solute Rayleigh number, and solute diffusivity ratio clearly have a stabilizing effect on the system, whereas the Darcy number and thermal diffusivity ratio destabilize it.