  In the present paper, the effect of the Vadasz inertia term on the onset of
convective motions for a Darcy-Brinkman model is investigated. It is proved
that this term leads to the possibility for oscillatory convection to occur.
Hence, convection can occur via either oscillatory or steady motions. It is
proved analytically that the onset of steady convection is not affected by the
Vadasz term, while oscillatory convection is favoured by it. Moreover,
conditions to rule out the occurrence of oscillatory convection are determined
numerically. The influence of rotation, interaction coefficient and mechanical
and thermal anisotropies on the onset of instability is investigated, both
analytically and numerically.
