Unstable Mixed Convection Flow in a Horizontal Porous Channel with Uniform Wall Heat Flux

Buoyancy-induced instability of the horizontal flow in a plane-parallel porous channel is analysed. A model of momentum transfer is adopted where a quadratic form-drag contribution is taken into account. The basic fluid flow is parallel and stationary. Due to the uniform wall heating and the effect of the buoyancy, the velocity and the vertical temperature gradient depend on the vertical coordinate. The dynamics of small-amplitude perturbations on the basic mixed convection flow is studied numerically. Transverse, longitudinal and general oblique rolls are investigated. It is proved that the longitudinal rolls are the normal modes triggering the instability at the lowest Darcy–Rayleigh numbers. The condition of neutral stability is studied for different values of the form-drag parameter and of the Péclet number.