Soret effect on double diffusive convection in a Darcy porous medium saturated with a couple stress fluid

Abstract

Double diffusive convection in a couple stress fluid saturated porous layer with Soret effect is studied using linear and weak non-linear stability analyses. The linear analysis is based on the classical normal mode technique, while the non-linear analysis is based on truncated representation of Fourier series. The modified Darcy equation that includes the time derivative term 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 effect of the couple stress parameter, Lewis number, solute Rayleigh number, Vadasz number, Soret parameter and normalized porosity on the stationary, oscillatory and finite amplitude convection are shown graphically. It is found that the effect of couple stress is quite large and the positive Soret parameter has destabilizing effect, while the negative Soret parameter has stabilizing effect on the stationary, oscillatory and finite amplitude convection. The Lewis number has stabilizing effect in the case of stationary and finite amplitude modes, with destabilizing effect in the case of oscillatory modes. The heat and mass transfer decreases with an increase in the values of couple stress parameter while both increase with increase in the value of the solute Rayleigh number. The Lewis number has contrasting effect on heat mass transfer. The transient behavior of the Nusselt and Sherwood numbers is studied by solving numerically a fifth order Lorenz type system using Runge-Kutta method.