Weakly nonlinear stability analysis of triple diffusive convection in a Maxwell fluid saturated porous layer

The weakly nonlinear stability of the triple diffusive convection in a Maxwell fluid saturated porous layer is investigated. In some cases, disconnected oscillatory neutral curves ave found to exist, indicating that three critical thermal Darcy-Rayleigh numbers are required to specify the linear instability criteria. However, another distinguishing feature predicted from that of Newtonian fluids is the impossibility of quasi-periodic bifurcation from the rest state. Besides, the co-dimensional two bifurcation points are located in the Darcy-Prandtl number and the stress relaxation parameter plane. It is observed that the value of the stress relaxation parameter defining the crossover between stationary and oscillatory bifurcations decreases when the Darcy-Prandtl number increases. A cubic Landau equation is derived based on the weakly nonlinear stability analysis. It is found that the bifurcating oscillatory solution is either supercritical or subcritical, depending on the choice of the physical parameters. Heat and mass transfers are estimated in terms of time and area-averaged Nusselt numbers.