Viscous dissipation and instability in a heterogeneous porous layer with horizontal throughflow

The horizontal throughflow in a heterogeneous porous channelis analysed by means of Darcy's law and the Oberbeck-Boussinesq approximation. A horizontal porous layer, bounded by impermeable boundaries and infinitely wide is considered. The lower boundary is assumed to be thermally insulated, while the upper boundary is assumed to be isothermal. The basic velocity and temperature distributions are influenced by the effect of the viscous dissipation, as well as by the boundary conditions. A transverse heterogeneity for the permeability and for the thermal conductivity is taken into account. The main task of this work is to investigate the role of this heterogeneity in changing the threshold for the onset of instability. A linear stability analysis by means of the normal modes method is performed. The onset of instability against longitudinal rolls is studied. The eigenvalue problem is solved numerically.