This paper is an analytical study on natural two-dimensional convection in horizontal rectangular channels filled by isotropic and anisotropic porous media. The channel walls, assumed to be impermeable and perfectly heat conducting, are nonuniformly heated to establish a linear temperature distribution in the vertical direction. We derive the critical Rayleigh numbers for the onset of convection and examine the steady flow patterns at moderately supercritical Rayleigh numbers. The stability properties of these flow patterns are examined against two-dimensional perturbations using a weakly nonlinear theory.

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