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 neighbourhood 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 the present study.

The effects of horizontal pressure gradient and Soret coefficient on the onset of double-diffusive convection in a fluid-saturated porous layer under the influence of local thermal nonequilibrium (LTNE) temperatures are analyzed. Darcy's law with local acceleration term, which involves the two-field temperature model describing the fluid and solid phases separately and the approximation of Oberbeck-Boussinesq, is used. The dynamics of small-amplitude perturbations on the basic mixed convection flow is studied numerically. Using the Galerkin method along with the QZ-algorithm, the eighth order eigenvalue differential equation obtained by employing linear stability analysis is solved. The solution provides the neutral stability curves and determines the threshold of linear instability, and the critical values of thermal Darcy-Rayleigh number, wave number, and the frequency at the onset of instability are determined for various values of control parameters. It is found that, rather than the stationary motion, the instability is found to be via oscillatory motion. Besides, the contribution to each parameter on stability characteristics is explored in detail, and some relevant findings have been described that have not been reported hitherto in the literature.