  The emerging instability of a forced throughflow in a fluid saturated
horizontal porous duct of rectangular cross section is investigated. The duct
is heated from below by assuming the horizontal boundaries to be at different
temperatures. Both the horizontal and the vertical boundaries are impermeable
and the basic flow is parallel to such boundaries. The porous medium is
anisotropic with different permeabilities in the vertical and horizontal
directions. The effect of the anisotropy on the onset of the buoyancy driven
modal instability and absolute instability is analysed. The parametric
conditions leading to the instability of the basic flow are determined by
employing an analytical dispersion relation. The different permeabilities in
the vertical and horizontal directions come out to play opposite roles in the
onset of modal instability and in the transition to absolute instability. It is
shown that an increasing vertical permeability has a destabilising effect,
while an increasing horizontal permeability has a stabilising effect.
