Instability of parallel buoyant flow in a vertical porous layer with an internal heat source

Buoyant flow in a vertical porous layer whose open boundaries are kept at uniform and different temperatures is analysed. The presence of a uniform volumetric heat source alters the conduction profile of the temperature field for the stationary parallel flow. It is shown that this stationary flow becomes unstable when either the temperature difference between the boundaries or the intensity of the volumetric heat source are sufficiently large. The linear instability is investigated through a study of normal mode disturbances. The stability eigenvalue problem is solved numerically by employing the shooting method. The neutral stability curves are obtained and the critical parameters at onset of instability are determined.