Effect of cross diffusion on the onset of double - diffusive convection in a porous medium

The effect of cross diffusion and the horizontal gradients of temperature and salinity on double diffusive convection in a fluid saturated densely packed porous medium is investigated using an analytical approach. The condition for the onset of convection through stationary and oscillatory modes has been reported. The effect of Soret, Dufour parameters, and horizontal gradients of temperature and salinity on the stability of the system is shown graphically. It is shown that the maximum growth rate of instability, the slope of the wave front depend on both Soret and Dufour coefficients. Some of the known results of the former problems are discussed as special cases.