Convective Instability in a Horizontal Annular Porous Duct with Conducting Walls

In the present paper, a horizontal annular duct filled by a fluid saturated porous medium is considered. The boundary wall of the duct is assumed to be impermeable and subjected to an environment temperature ther- mally stratified in the vertical direction. Darcy’s law and the Oberbeck–Boussinesq approximation are assumed. The stationary basic flow given by a zero velocity distribution and a linear vertical temperature distribution is determined analytically and its linear stability is studied numerically. The elliptic equations for the linear disurbances are written in terms of an eigenvalue problem and solved by employing a Galerkin finite element procedure, in order to determine the critical conditions for the onset of the convective instability. The neutral stability curves, and in particular the first two branches of these curves, are obtained considering an annular duct having aspect ratio 0.5 or 0.1. In both cases, a comparison with the results available in the literature for the onset condition of longitudinal rolls is performed.