Weakly Nonlinear Stability of Thermosolutal Convection in an Oldroyd-B Fluid-Saturated Anisotropic Porous Layer Using a Local Thermal Nonequilibrium Model

The two-temperature model of local thermal nonequilibrium (LTNE) is utilized to investigate a weakly nonlinear stability of thermosolutal convection in an Oldroyd-B fluid-saturated anisotropic porous layer. The anisotropies in permeability, thermal conductivities of the porous medium, and solutal diffusivity are accounted for by second-order tensors with their principal directions coinciding with the horizontal and vertical coordinate axes. A modified Darcy-Oldroyd model is employed to describe the flow in a porous medium bounded by impermeable plane walls with uniform and unequal temperatures as well as solute concentrations. The cubic-Landau equations are derived in the neighborhood of stationary and oscillatory onset using a modified perturbation approach and the stability of bifurcating equilibrium solutions is discussed. The advantage is taken to present some additional results on the linear instability aspects as well. It is manifested that the solutal anisotropy parameter also plays a decisive role on the instability characteristics of the system. It is found that the stationary bifurcating solution transforms from supercritical to subcritical while the oscillatory bifurcating solution transforms from supercritical to subcritical and revert to supercritical. The Nusselt and Sherwood numbers are used to examine the influence of LTNE and viscoelastic parameters on heat and mass transfer, respectively. The results of Maxwell fluid are outlined as a particular case from this study.