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 varieslinearlywiththeheight. Alinearstabilityanalysisofthebasicflowiscarriedout. Thecritical 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.