Convective instability in an inclined porous layer subject to linearly varying boundary temperatures

The stability of the parallel Hadley flow in an inclined plane porous layer where the boundaries are subject to a linearly varying temperature is studied. The inclination of the layer modifies the nature of the basic single-cell Hadley flow. In fact, the Hadley flow in an inclined layer displays a nonlinear velocity profile, with the possible existence of singularities for special inclination angles of the layer to the horizontal. The stability of the basic flow in the inclined porous layer is investigated by a linear analysis of the longitudinal rolls. The stability analysis provides the neutral stability curves for the onset of convection, and the critical values of the Rayleigh number for different inclinations of the layer. The linearized disturbance equations are solved by means of the collocation method of weighted residuals.