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

The onset of double diffusive convection in a binary viscoelastic fluid saturated anisotropic porous layer is studied using a linear and a weak nonlinear stability analyses. The modified Darcy law for the viscoelastic fluid of the Oldroyd type is used to model the momentum equation. The onset criterion for stationary and oscillatory 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 anisotropy parameters, Darcy-Prandtl number, 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 transient heat and mass transfer. The effect of various parameters on heat and mass transfer is also brought out. (C) 2009 American Institute of Physics. [DOI: 10.1063/1.3194288]