On the linear stability analysis of a Maxwell fluid with double-diffusive convection

The problem of double-diffusive convection and cross-diffusion in a Maxwell fluid in a horizontal layer in porous media is re-examined using the modified Darcy–Brinkman model. The effect of Dufour and Soret parameters on the critical Darcy–Rayleigh numbers is investigated. Analytical expressions of the critical Darcy–Rayleigh numbers for the onset of stationary and oscillatory convection are derived. Numerical simulations show that the presence of Dufour and Soret parameters has a significant effect on the critical Darcy–Rayleigh number for over-stability. In the limiting case some previously published results are recovered.