Soret effect on the double diffusive convection instability due to viscous dissipation in a horizontal porous channel

Abstract

The effect of the Soret parameter on the convective stability of double diffusive convection solely because of the viscous dissipation in a horizontal porous channel is studied. The lower boundary is adiabatic whereas the upper boundary is considered to be isothermal. The convective stability of the present system is governed by the solutal Rayleigh number (R) and is influenced by the viscous dissipation parameter (ξ), Lewis number (Le) and Soret parameter (Sr). For non positive values of the Soret parameter, the longitudinal rolls happen to be the most unstable ones when ξ takes small values. With positive values of the Soret parameter, the transverse rolls are seen to be the most unstable for relatively smaller values of the viscous dissipation parameter. As the viscous dissipation effect becomes stronger, the longitudinal rolls become the most unstable ones even for positive Soret parameter and the transverse rolls become more unstable for non-positive Soret parameter. It is observed that the Soret parameter has significant effect on convective instability and this is discussed. It has also been noticed that viscous dissipation shows a dual effect in presence of the Soret effect. For fixed values of the viscous dissipation parameter and Lewis number, negative values for the Soret number advances the onset of convection. Though positive values of the Soret parameter stabilizes the flow with smaller values of the Lewis number, but it destabilizes the flow when Lewis number and viscous dissipation parameter take larger values.