effect of variable gravity on darcy flow with impressed horizontal gradient and viscous dissipation

The effect of variable gravity on the free convection in a horizontal porous layer with viscous dissipation is investigated. the bottom boundary is taken as adiabatic and there is a non-uniform temperature distribution along the upper boundary. the effect of viscous dissipation is significant and the top boundary temperature distribution is assumed to have a constant gradient. the gravity varies linearly with the height. a linear stability analysis of the basic flow is carried out. the critical horizontal rayleigh number is calculated for oblique roll disturbances. the longitudinal rolls are found to be the most unstable ones. the viscous dissipation has a destabilizing effect. there is a drastic decrease in the value of critical horizontal rayleigh number when modified variable gravity parameter changes from -1 to 1.