Linear and nonlinear double-diffusive convection in a saturated porous layer with soret effect under local thermal non-equilibrium model

Double-diffusive convection in a fluid-saturated porous layer heated and salted from below with Soret effect is studied analytically when the fluid and solid phase are not in local thermal equilibrium, using both linear and non-linear stability analysis. The normal mode technique is used in the linear stability analysis, while a weak non-linear analysis is based on a minimal representation of truncated double-Fourier series. The generalized Darcy model including the time derivative term is employed for the momentum equation. A two-field model that represents the fluid and solid phase temperature fields separately is used for the energy equation. The effects of concentration Rayleigh number, Soret parameter, inter-phase heat transfer coefficient, the porosity modified conductivity ratio, Vadasz number, Lewis number, and the ratio of diffusivities on the stationary, oscillatory, and heat and mass transfer are shown graphically. Heat and mass transfer have been obtained in terms of the Nusselt number Nu and Sherwood number Sh, respectively. It is found that the effect of thermal and solute diffusion causes the convective instability to set in as oscillatory mode rather than stationary. Also, we found that the positive values of Soret parameter Sr destabilize the system for the stationary convection, while the negative ones stabilize it. The effect of the Soret parameter on the oscillatory curves is negligible. © 2018 by Begell House, Inc.