Buoyant flow in a vertical fluid saturated porous annulus: The Brinkman model

Laminar, steady and parallel buoyant flow in a concentric vertical annulus filled with a porous medium is studied. The Darcy–Brinkman model and the Oberbeck–Boussinesq approximation are employed. The governing equations are written in a dimensionless form and solved analytically by means of the variation of constants method. In order to investigate the onset of flow reversal, both at the inner and at the outer boundary, a dimensionless reference temperature θ0 is introduced. Moreover, this quantity is related to the usual Gr/Re parameter. The limiting cases of Darcy flow and clear fluid are investigated as well.