The effect of a nonuniform basic temperature gradient on the convective instability of a fluid-saturated porous layer with general velocity and thermal conditions

The effects of a nonuniform basic temperature gradient and bounding permeable walls on Rayleigh-Benard convection in a sparsely packed porous medium are investigated using the single term Galerkin method. The nature of the boundaries dictates general boundary conditions on velocity and temperature. The classical results of free-free, rigid-free and rigid-rigid boundaries with isothermal or adiabatic boundaries are recovered as limiting cases of the present study. The multi-layer porous media problem has practical implications in situations where fluids are used as a working medium and porous media are used as dampers.