Triple diffusive convection with Soret–Dufour effects in a Maxwell nanofluid saturated in a Darcy porous medium

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\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{Nu}}$$\end{document}, NuC\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{Nu}}_{C}$$\end{document} and Nuϕ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{Nu}}_{\phi }$$\end{document}. Steady and unsteady convections are discussed. A graphical representation of streamlines, isotherms, isohalines and flow lines of nanoparticles concentrations is presented.