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This paper presents an analytical and numerical study of the salt particle drift driven by thermal gradient and the nanoparticle drift due to Brownian motion in a Darcy porous layer saturated by a Maxwellian nanofluid under passive management of nanoparticle flux at the boundaries influenced by the Stefan's flow condition. Filtration law of Khuzhayorov et al. (Int J Eng Sci 38:487-504, 2000), for the Darcy-Maxwell fluid, has been used. It is shown that the steady state convection, under both linear and non-linear stability theory do not depend upon the relaxation parameter of the Maxwell fluid. Soret effect is responsible for delaying the stationary convection. It, however, enhances it in comparison to the convection in monodiffusive flow. Oscillatory convection exists, ceases and shifts to the stationary convection. In Soret effected steady convection, among heat, salt and nanoparticles, the transport of nanoparticles is most active while among monodiffusive, double diffusive and Soret governed convection, the heat transfer is most active in Soret induced convection. Streamlines, isotherms and isohalines are shown for steady as well as unsteady convection. Results are compared with some of the existing results.

Soret-Dufour phenomenon in a Darcy-Maxwell Brownian nanofluid is performed using a macroscopic filtration model, suggested by Alishayev (Hydromechanics 3:166-174, 1974). For nanoparticle flux at the boundaries passive management, influenced by the management of concentration flux assumed in Stefan's flow, is considered. Normal mode technique is used to analyse the stationary and oscillatory convections under the linear stability theory. The effects of different phenomenon are quantified by dimensionless parameters. It is found that the Soret parameter has dual behaviour for stationary convection and destabilizing behaviour for oscillatory convection, whereas the Dufour parameter has a stabilizing effect for both stationary and oscillatory convections. Nonlinear stability analysis provides the behaviour of flux of heat, salt and nanoparticles in the flow field through Nu , Nu C and Nu . Steady and unsteady convections are discussed. A graphical representation of streamlines, isotherms, isohalines and flow lines of nanoparticles concentrations is presented.Keywords Darcy-Maxwell nanofluid · Soret-Dufour-driven convection · Linear and nonlinear instability · Passive management of nanoparticle at the boundaries

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