Instability of Combined Forced and Free Flow in an Inclined Porous Channel

The aim of this paper is to analyze the onset of convective instability in a plane porous channel inclined to the horizontal. A net upslope or downslope flow is considered, so that mixed convection takes place as caused by the uniform and symmetric heat fluxes prescribed on the impermeable bounding walls. The thermoconvective instability of the basic flow is studied versus small-amplitude wavelike perturbations. The hybrid analytical-numerical technique adopted in this paper, in order to track and illustrate the parametric changes of neutral stability curves, is Galerkin's method of weighted residuals. Numerical values at significant points on the neutral stability curves are obtained by employing an accurate Runge-Kutta solver combined with the shooting method.