Thermosolutal convective instability and viscous dissipation effect in a fluid-saturated porous medium

The combined effects of the double-diffusion and of the viscous dissipation on the convective instability in a fluid-saturated porous medium with a basic horizontal throughflow are investigated. A horizontal porous layer with an impermeable adiabatic lower wall and an impermeable isothermal upper wall is considered. The parallel boundary walls are assumed to have uniform, but unequal, concentrations of the solute. A linear stability analysis is carried out both numerically and by a first-order perturbation method. General disturbances having the form of oblique rolls are considered, reducing either to longitudinal rolls or to transverse rolls in the special cases of roll axes parallel or orthogonal to the basic flow direction, respectively. It is shown that the combined effects of viscous dissipation and mass diffusion may lead to the instability of the basic horizontal flow. Either the longitudinal rolls or the transverse rolls may be the preferred modes of instability depending on the value of the viscous dissipation parameter Ξ. The longitudinal rolls are the most unstable when Ξ < 61.86657.