We consider a stability analysis of a fluid in a porous layer heated from below including the effects of a superposed through-flow, porous inertia and the lateral confinement of the medium with respect to extended and localized perturbations. It is found that extended perturbations promote the appearance of down-stream moving transverse modes (T modes) provided that the Peclet number Pe remains below a critical value Pe*. We showed that the T modes are replaced by stationary longitudinal rolls (L rolls) if Pe > Pe*. On the other hand when localized perturbations are considered, a spatial stability analysis is performed to determine regions of convective and absolute instability for T modes as well as for L rolls in the filtration Rayleigh-Peclet plane. We found that while the lateral aspect ratio has a strong influence on the convective/absolute nature of secondary flows, the main effect of porous inertia is to delay the transition to the absolute instability. Quantitative comparisons between our finding and experimental results published by one of us (M.C.) are presented. As far as the solid thermal conductivity is similar to that of the fluid, it is found that the experimentally observed transition between the T modes and L rolls occurs at the border between convective and absolute instability. Moreover it has also been found that the measured and the theoretically predicted wavelengths of T modes as well as their period of oscillation are in good agreement for various combinations of Ra and Pe numbers. The agreement between theory and experiment becomes less satisfactory when the matrix is much more conductive than the fluid. Therefore the assumption of local thermal equilibrium between solid and fluid becomes debatable. (c) 2006 Elsevier Ltd. All rights reserved.