The onset of convection in a binary viscoelastic fluid saturated porous layer

Abstract

The onset of convection in a binary viscoelastic fluid-saturated porous layer is studied using a linear and a weak nonlinear stability analyses. The modified Darcy-Oldroyd model is employed as a momentum equation. The onset criterion for stationary, oscillatory, and finite amplitude 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 solute Rayleigh number, Prandtl number, diffusivity ratio, 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 heat and mass transfer. The effect of various parameters on heat and mass transfer is also brought out. The transient behaviour of the Nusselt number and Sherwood number is investigated by solving the finite amplitude equations using Runge-Kutta method. © 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.