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

Abstract

The double diffusive convection in a horizontal fluid saturated anisotropic porous layer, which is heated and salted from below, is studied analytically. The generalized Darcy model is employed for the momentum equation. The critical Rayleigh number, wavenumber for stationary and oscillatory modes and frequency of oscillations are obtained analytically using linear theory. The effect of anisotropy parameters, solute Rayleigh number, Lewis number and Prandtl number on the stationary, oscillatory and finite amplitude convection is shown graphically. The transient behavior of the Nusselt and Sherwood numbers is studied, by solving numerically a fifth order Lorenz type system using Runge–Kutta method. Some of the convection systems previously reported in the literature are shown to be special cases of the system presented in this study.