Instability of the buoyant parallel flow in a heterogeneous medium with an impressed horizontal heat flux

The present study is aimed to investigate the onset of convection in a fluid saturated porous medium. More precisely. an infinitely wide horizontal porous layer with vertical heterogeneity is considered. The lower plane boundary is assumed to be impermeable and thermally insulated (adiabatic). The temperature distribution on the upper plane boundary is assumed to be prescribed and linearly varying in the horizontal direction. It is shown that these boundary conditions are compatible with a buoyancy-induced parallel-flow solution such that the temperature gradient is inclined with respect to the vertical direction. The basic parallel flow is perturbed by small-amplitude roll disturbances, so that a linear analysis of the neutral stability is carried out. The local balance equations for the disturbances are solved numerically. The critical conditions for the onset of convection are determined.