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The onset of double diffusive convection in a binary viscoelastic fluid saturated anisotropic porous layer is studied using a linear and a weak nonlinear stability analyses. The modified Darcy law for the viscoelastic fluid of the Oldroyd type is used to model the momentum equation. The onset criterion for stationary and oscillatory convection is derived analytically. There is a competition between the processes of thermal, solute diffusions, and viscoelasticity that causes the convection to set in through oscillatory rather than stationary. The effect of anisotropy parameters, Darcy–Prandtl number, relaxation, and retardation parameters on the stability of the system is investigated. The nonlinear theory based on the truncated representation of Fourier series method is used to find the transient heat and mass transfer. The effect of various parameters on heat and mass transfer is also brought out.

Linear stability of a rotating fluid-saturated porous layer heated from below and cooled from above is studied when the fluid and solid phases are not in local thermal equilibrium. The extended Darcy model, which includes the time derivative and Coriolis terms, is employed as a momentum equation. A two-field model that represents the fluid and solid phase temperature fields separately is used for energy equation. The onset criterion for both stationary and oscillatory convection is derived analytically. It is found that a small interphase heat transfer coefficient has significant effect on the stability of the system. There is a competition between the processes of rotation and thermal diffusion that causes the convection to set in through the oscillatory mode rather than the stationary one. The rotation inhibits the onset of convection in both stationary and oscillatory mode. In addition, the effect of porosity modified conductivity ratio, Darcy-Prandtl number, and the ratio of diffusivities on the stability of the system is investigated. A weak nonlinear theory based on the truncated representation of Fourier series method is used to find the Nusselt number. The effect of thermal nonequilibrium on heat transfer is brought out. The transient behavior of the Nusselt number is also investigated by solving the finite amplitude equations using Runge-Kutta method.