The Onset of Double Diffusive Convection in a Binary Viscoelastic Fluid Saturated Porous Layer with Soret Effect

The onset of double diffusive convection in a binary viscoelastic fluid saturated porous layer, which is heated and salted from below in the presence of Soret effect is studied using both linear and nonlinear stability analyses. The linear theory is being related to the normal mode method. The modified Darcy law for the viscoelastic fluid of the Oldroyd type is used to model the momentum equation. The expressions for stationary, oscillatory and finite amplitude Rayleigh number are obtained as a function of the governing parameters. The effects of Soret parameter, relaxation parameter, retardation parameter, Darcy–Prandtl number, solute Rayleigh number, Lewis number, and normalized porosity on the oscillatory and finite amplitude convection is shown graphically. It is found that the effect of the positive Soret parameter, solute Rayleigh number, retardation parameter have stabilizing effect, while the negative Soret parameter, Lewis number, relaxation parameter, normalized porosity have destabilizing effect on the oscillatory and finite amplitude convection. The Darcy–Prandtl number has a dual effect on the threshold of oscillatory convection. The nonlinear theory based on truncated representation of Fourier series method is employed to find Nusselt number and Sherwood number. Further, the transient behavior of the Nusselt and Sherwood numbers is investigated by solving the nonlinear system of ordinary differential equations numerically using Runge-Kutta method.