Stability analysis of thermosolutal second-order fluid in porous Bénard layer

Abstract Linear and nonlinear stability of the motionless state of thermosolutal second-order fluid in porous Bénard layer is investigated via Lyapunov direct method on the basis of Brinkman’s modification of the Darcy’s model. Critical Rayleigh numbers for linear and nonlinear stability are obtained for free-free, rigid-rigid and rigid-free boundaries. The stabilizing effect of solute concentration and the destabilizing effect of medium permeability and porosity on the basic motion are proved. In particular, for certain range of system parameters the sufficient and necessary condition for stability coincide. Keywords: Second-order fluid, Nonlinear stability, Porous medium, Solute concentration Mathematics Subject Classification (2000): 35Q35, 46N20, 76E06