Double diffusive convection in a viscoelastic fluid-saturated porous layer using a thermal non-equilibrium model

The stability of a binary viscoelastic fluid-saturated porous layer which is heated from below is studied, where the fluid and solid phases are not in local thermal equilibrium. The modified Darcy-Oldroyd model is employed as a momentum equation, with the fluid and solid phase temperature fields modelled separately. It is found that the inter-phase heat transfer coefficient has a significant effect on the stability of the system. Competition between the processes of viscous relaxation and thermal diffusion cause the convection to set in through oscillatory rather than stationary instability, with the viscoelastic parameters inhibiting the onset of convection. In the case of weakly non-linear theory, both steady and unsteady cases are considered. In the unsteady case the transient behaviour of the Nusselt and Sherwood numbers is investigated. The effect of thermal non-equilibrium on heat and mass transfer is also discussed.